CN117784564A

CN117784564A - Waveguide with four graded coatings

Info

Publication number: CN117784564A
Application number: CN202311110889.4A
Authority: CN
Inventors: Y·夏; T·施密顿
Original assignee: Envisics Ltd
Current assignee: Envisics Ltd
Priority date: 2022-09-27
Filing date: 2023-08-30
Publication date: 2024-03-29

Abstract

A waveguide comprising a pair of complementary surfaces arranged to provide a waveguide therebetween. A first surface of the pair of complementary surfaces includes a plurality of first layers and a plurality of second layers. Each first layer includes a first dielectric. Each second layer includes a second dielectric. Each of the first and second layers has a first end and a second end. The percent change in the thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values. The total number of the first layer and the second layer is greater than the total number of the discrete allowable values. The refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

Description

Waveguide with four graded coatings

Technical Field

The present disclosure relates to pupil expansion or hologram replication. More particularly, the present disclosure relates to waveguides, display systems including at least one waveguide according to the present disclosure, hologram replication methods using the at least one waveguide, and methods of waveguiding holographic wavefronts. More particularly, the present invention relates to a method of improving the uniformity of copies of holograms output by waveguides and optical components (e.g., optical layers, dielectric layers, or dielectric stacks).

Background

Light scattered from the object contains amplitude and phase information. This amplitude and phase information can be captured by well known interference techniques, for example, on a photosheet to form a holographic record or "hologram" comprising interference fringes. The hologram may be reconstructed by irradiation with suitable light to form a two-or three-dimensional holographic reconstructed or replay image representing the original object.

Computer-generated holography can numerically simulate the interference process. Computer-generated holograms may be calculated by techniques based on mathematical transformations such as fresnel or fourier transforms. These types of holograms may be referred to as fresnel/fourier transform holograms or simply fresnel/fourier holograms. A fourier hologram may be considered as a fourier domain/planar representation of an object or a frequency domain/planar representation of an object. Computer-generated holograms may also be computed, for example, by coherent ray tracing or point cloud techniques.

The computer-generated hologram may be encoded on a spatial light modulator arranged to modulate the amplitude and/or phase of the incident light. For example, electrically addressable liquid crystals, optically addressable liquid crystals, or micromirrors may be used to effect light modulation.

Spatial light modulators typically comprise a plurality of individually addressable pixels, which may also be referred to as cells or elements. The light modulation scheme may be binary, multi-level or continuous. Alternatively, the device may be continuous (i.e. not include pixels), so the light modulation may be continuous across the device. The spatial light modulator may be reflective, meaning that the light is modulated to reflect the output. The spatial light modulator may likewise be transmissive, which means that the light is modulated to transmit output.

Holographic projectors may be provided using the systems described herein. Such projectors have found application in head-up displays "HUDs".

Disclosure of Invention

Aspects of the disclosure are defined in the appended independent claims.

The present disclosure relates generally to image projection. It relates to a method of image projection and an image projector comprising a display device. The present disclosure also relates to a projection system comprising an image projector and a viewing system, wherein the image projector projects or relays light from a display device to the viewing system. The present disclosure is equally applicable to both monocular and binocular viewing systems. The viewing system may include one or more eyes of a viewer. The viewing system comprises an optical element (e.g. the lens of a human eye) having optical power and a viewing plane (e.g. the retina of a human eye). The projector may be referred to as a "light engine". The display device and the image formed (or perceived) using the display device are spatially separated from each other. The viewer forms or perceives an image on the display plane. In some embodiments, the image is a virtual image, and the display plane may be referred to as a virtual image plane. In other embodiments, the image is a real image formed by holographic reconstruction and the image is projected or relayed to the viewing plane. An image is formed by illuminating a diffraction pattern (e.g., a hologram) displayed on a display device.

The display device includes pixels. The pixels of the display device diffract light. The magnitude of the maximum diffraction angle depends on the size of the pixel (and other factors such as the wavelength of the light) according to well known optical principles.

In an embodiment, the display device is a spatial light modulator, such as a liquid crystal on silicon ("LCOS") Spatial Light Modulator (SLM). Light propagates from the LCOS over a range of diffraction angles (e.g., from zero to a maximum diffraction angle) to an observation entity/system such as a camera or eye. In some embodiments, magnification techniques can be used to increase the range of available diffraction angles beyond the conventional maximum diffraction angle of LCOS.

In some examples, the image (formed by the displayed hologram) propagates to the eye. For example, spatially modulated light of an intermediate holographic reconstruction/image formed on a free space or screen or other light receiving surface between the display device and the observer may propagate to the observer.

In some other examples, (light of) the hologram itself propagates to the eye. For example, spatially modulated light of a hologram (which has not yet been fully converted into holographic reconstruction, i.e. an image) -may be informally referred to as being "encoded" with/by the hologram-propagates directly to the eyes of the observer. The observer may perceive a real or virtual image. In these embodiments, no intermediate holographic reconstruction/image is formed between the display device and the viewer. Sometimes, in these embodiments, the lens of the eye performs a hologram to image conversion or transformation. The projection system or light engine may be configured to effectively direct the viewer at the display device.

According to well known optical principles, the angular range of light propagating from a display device that an eye or other viewing entity/system can observe varies with the distance between the display device and the viewing entity. For example, at a viewing distance of 1 meter, only a small range of angles from the LCOS may propagate through the pupil of the eye to form an image on the retina at a given eye location. The angular range of light rays propagating from the display device determines the portion of the image that is "visible" to the observer, which light rays can successfully propagate through the pupil of the eye to form an image on the retina at a given eye location. In other words, not all parts of the image are visible from any point on the viewing plane (e.g., any one eye position within a viewing window such as an eye box).

In some embodiments, the image perceived by the viewer is a virtual image that appears upstream of the display device, that is, the viewer perceives the image farther from them than the display device. Thus, conceptually, it can be said that a viewer is viewing a virtual image through a "display device sized window", which may be very small, e.g., 1 cm in diameter, and relatively large, e.g., 1 meter. And the user will observe the window of the display device size through the pupil of their eye, the pupil may also be very small. Thus, at any given time, the field of view becomes smaller and the particular angular range that can be seen is strongly dependent on the eye position.

The pupil expander solves how to increase the angular range of light rays propagating from the display device, and the light rays can successfully propagate through the pupil of the eye to form an image. Display devices are typically (relatively) small and the projection distance is (relatively) large. In some embodiments, the projection distance is at least one order of magnitude, e.g., at least two orders of magnitude, greater than the diameter or width (i.e., the size of the pixel array) of the entrance pupil and/or aperture of the display device. Embodiments of the present disclosure relate to a configuration in which a hologram of an image is propagated to the human eye instead of the image itself. In other words, the light received by the observer is modulated according to the hologram of the image. However, other embodiments of the present disclosure may relate to configurations in which an image is propagated to the human eye instead of a hologram-for example by so-called indirect viewing, in which light of a holographic reconstructed or "replay image" formed on a screen (or even in free space) is propagated to the human eye.

The use of a pupil expander laterally increases the viewing area (i.e., the user's eye-box) to enable some movement of the eye while still enabling the user to see the image. As will be appreciated by those skilled in the art, in an imaging system, a viewing area (a user's eye box) is the area where an observer's eye is able to perceive an image. The present disclosure relates to non-infinite virtual image distances, i.e. near field virtual images, but is equally applicable to virtual images formed at infinity or even real images formed downstream of a display device/hologram.

Traditionally, two-dimensional pupil expanders include one or more one-dimensional optical waveguides, each formed using a pair of opposing reflective surfaces, wherein the output light from the surfaces forms a viewing window or eye box-e.g., an eye box or eye box for viewing by a viewer. Light received from a display device (e.g. spatially modulated light from an LCOS) is replicated by the or each waveguide so as to increase the field of view (or viewing area) in at least one dimension. In particular, the waveguide enlarges the viewing window by creating additional rays or "copies" by dividing the amplitude of the incident wavefront.

The display device may have an active or pixel display area having a first dimension of less than 10 cm, for example less than 5 cm or less than 2 cm. The propagation distance between the display device and the viewing system may be greater than 1m, for example greater than 1.5m or greater than 2m. The optical propagation distance within the waveguide may be up to 2m, for example up to 1.5m or up to 1m. The method is capable of receiving images and determining a corresponding hologram of sufficient quality in less than 20ms, such as less than 15ms or less than 10 ms.

In some embodiments described in accordance with the present disclosure by examples of diffractive or holographic light fields only, the hologram is configured to route light into a plurality of channels, each channel corresponding to a different portion (i.e., sub-region) of the image. The hologram may be presented, such as displayed, on a display device, such as a spatial light modulator. When displayed on a suitable display device, the hologram may spatially modulate light that may be converted into an image by the viewing system. The channels formed by the diffractive structures are referred to herein as "hologram channels" merely to reflect that they are light channels encoded by holograms having image information. The light of each channel can be said to be in the holographic domain, not in the image or spatial domain. In some embodiments, the hologram is a fourier or fourier transform hologram, so the hologram domain is the fourier or frequency domain. The hologram may likewise be a fresnel or fresnel transformed hologram. Holograms are described herein as routing light into a plurality of hologram channels, merely to reflect that an image that can be reconstructed from a hologram has a finite size, and can be arbitrarily divided into a plurality of image sub-regions, where each hologram channel will correspond to each image sub-region. Importantly, the hologram of this example is characterized by how it distributes image content when illuminated. In particular, holograms divide image content angularly. That is, each point on the image is associated with a unique ray angle in the spatially modulated light formed by the hologram upon illumination-at least a unique pair of angles, since the hologram is two-dimensional. For the avoidance of doubt, such holographic behaviour is not conventional. When illuminated, the spatially modulated light formed by this particular type of hologram may be divided into a plurality of hologram channels, with each hologram channel being defined by a range of ray angles (in two dimensions). From the foregoing, it will be appreciated that any hologram channel (i.e., sub-range of ray angles) that may be considered in spatially modulating light will be associated with a corresponding portion or sub-region of an image. That is, all information required to reconstruct that portion or sub-region of the image is contained within the angular subrange of the spatially modulated light formed by the hologram of the image. When spatially modulated light is viewed as a whole, there is not necessarily any evidence of a plurality of discrete light channels. However, in some arrangements, a plurality of spatially separated hologram channels are formed by deliberately leaving the region of the target image from which the hologram was calculated blank or empty (i.e. there is no image content).

Nonetheless, holograms can still be identified. For example, if only a continuous portion or sub-region of the spatially modulated light formed by the hologram is reconstructed, only a sub-region of the image should be visible. If different successive portions or sub-regions of spatially modulated light are reconstructed, different sub-regions of the image should be visible. Another identifying feature of this type of hologram is that the shape of the cross-section of any hologram channel corresponds substantially to (i.e. is substantially the same as) the shape of the entrance pupil, although the sizes may be different-at least at the correct plane of the calculation hologram. Each light/hologram channel propagates from the hologram at a different angle or range of angles. While these are example ways of characterizing or identifying this type of hologram, other ways may be used. In summary, holograms disclosed herein are characterized and identified by how the image content is distributed within the hologram encoded light. Furthermore, for the avoidance of any doubt, references herein to holograms configured to direct light or angularly divide an image into a plurality of hologram channels are by way of example only, and the present disclosure is equally applicable to any type of holographic light field or even any type of pupil expansion of a diffracted or diffracted light field.

In general terms, a system is disclosed herein that provides pupil expansion for an input light field, wherein the input light field is a diffracted or holographic light field comprising a divergent light beam. As described above, by creating one or more copies of the input ray (or ray bundle), pupil expansion (which may also be referred to as "image replication" or "pupil replication") enables the size of the area in which the observer can see the image (or may receive the light of the hologram, the observer's eyes forming the image) to be increased. Pupil expansion may be provided in one or more dimensions. For example, a two-dimensional pupil expansion may be provided, wherein each dimension is substantially orthogonal to the respective other dimension. In embodiments where the wavefront is a holographic wavefront, the process may be described as hologram replication.

The system may be provided in a compact and streamlined physical form. This makes the system suitable for a wide range of practical applications, including those where space is limited and asset value is high. For example, it may be implemented in a head-up display (HUD), such as a vehicle or automobile HUD.

The spatial light modulator may be arranged to display a hologram. Diffracted or divergent light may include light encoded with/by a hologram, rather than light reconstructed by an image or hologram. Thus, in such embodiments, the pupil expander may be said to replicate the hologram or form at least one copy of the hologram to convey that the light delivered to the observer is spatially modulated according to the hologram of the image rather than the image itself. That is, the diffracted light field propagates to the observer.

In some embodiments, two one-dimensional waveguide pupil expanders are provided, each arranged to effectively increase the size of the exit pupil of the system by forming multiple copies or copies of the exit pupil (or light of the exit pupil) of the spatial light modulator. The exit pupil may be understood as the physical area of the system output light. It can also be said that each waveguide pupil expander is arranged to expand the size of the exit pupil of the system. It can also be said that each waveguide pupil expander is arranged to expand/increase the size of the eye box in which an observer's eye can be located, so as to see/receive light output by the system.

In this disclosure, the term "replica" is used merely to reflect that spatially modulated light is split such that the composite light field is directed along a plurality of different light paths. The term "replica" is used to refer to each occurrence or instance of a composite light field after a replication event, such as partial reflection-transmission of a pupil expander. Each copy propagates along a different optical path. Some embodiments of the present disclosure relate to the propagation of light encoded with holograms instead of images-i.e. light spatially modulated with holograms of images instead of the images themselves. Those skilled in the art of holography will appreciate that the composite light field associated with the propagation of light encoded with a hologram will vary with propagation distance. The term "replica" as used herein is independent of propagation distance, so the two optical branches or paths associated with a replication event are still referred to as "replicas" of each other, even though the branches have different lengths, such that the composite optical field evolves differently along each path. That is, even though, according to the present disclosure, two composite light fields are related to different propagation distances, they are still considered "duplicates" -assuming they originate from the same duplication event or a series of duplication events.

As described above, the optical waveguide serving as a pupil expander can guide an optical field between a pair of parallel surfaces. This can be achieved by internal reflection between the parallel surfaces. A first surface of the pair of surfaces may be partially transmissive-reflective. A second surface of the pair of surfaces may be reflective. Thus, the optical field will be split at each internal reflection at the first surface such that multiple copies of the optical field are transmitted through the region of the first surface forming the waveguide output port. Thus, the viewing window (and the eye box) is enlarged by the waveguide.

The intensity and spectrum of each successive replica emitted by the waveguide is preferably substantially constant between the replicas. For example, the integral of the light intensity of each replica may be substantially constant, the average of the light intensity of each replica may be substantially constant, and/or the distribution of the light intensity of each replica may be substantially constant. Copies having a substantially constant intensity and spectrum are referred to herein as spatially uniform, and waveguides that emit such copies are referred to herein as providing spatially uniform emission. Spatially uniform replicas advantageously reduce or minimize variability in brightness of an image (or different regions thereof) perceived by an observer moving around an (extended) viewing window. Furthermore, the overall quality of the hologram received by the observer (and/or the final image perceived by the observer) may be improved, especially if the hologram comprises a plurality of different wavelengths of light.

The intensity of the light being waveguided between the first and second surfaces of the waveguide will decrease after each division of the light field at the first surface. Conventional waveguides may generally include a first surface having a constant transmissivity. This results in a decrease in the intensity of each successive replica. In other words, such conventional waveguides do not provide spatially uniform emission.

A graded coating may be applied to the waveguide to provide a first surface having varying transmissivity. In particular, the coating may be arranged such that the transmittance of the first surface increases in the waveguide direction. The graded coating may be arranged such that an increase in the transmissivity of the first surface in the waveguide direction accounts for (e.g. at least partly compensates for) a decrease in the intensity of the light guided by the light. However, current graded coatings often result in high absorption losses of the waveguide light. Furthermore, these coatings generally allow very limited control of the spectral properties, especially disadvantageous when the light to be waveguided comprises a plurality of wavelengths. While some improved graded coatings are available, these coatings are expensive, time consuming and complex to manufacture, and often cannot be reliably manufactured. For example, such a coating may include multiple layers (typically 20 or more layers) of dielectric material, each layer having a unique percentage change in thickness from a first end to a second end of the layer. Such a complex layered structure may be necessary to provide a substantially spatially uniform emission for the entire visible spectrum, but is slow to manufacture and difficult to manufacture reliably (e.g., a classifier that may need to be moved is present in the coating chamber).

The present disclosure solves the technical problem of providing spatially uniform emission from a waveguide pupil expander such that the intensity and spectrum of each replica are substantially similar. The present disclosure proposes an improved waveguide pupil expander that provides substantially uniform emission at least at certain wavelengths, such as red, green and blue wavelengths. The first surface of the waveguide comprises a plurality of alternating layers of first and second dielectrics having different refractive indices. Instead of each layer having a unique percent thickness variation, in the present disclosure each layer of dielectric has a percent thickness variation of one of a discrete number of values, the discrete number of values being less than the total number of layers. In some embodiments, the number of discrete or allowed values does not exceed four. In some embodiments, the number of layers is at least twice the number of discrete values.

The multilayer structure obtained by the conventional design technique is very complex and unsuitable for industrial scale-up. This complexity is due in part to the need to achieve uniformity across three different wavelengths. The inventors reconsidered the design process and focused on restricting it in a way that simplifies the desired manufacturing method and relaxing it in other ways that do not affect the image forming (e.g. holographic) process. In particular, the inventors have focused on how to simplify the required coating machine. The inventors have found that sufficient optical performance for three-colour hologram replication can still be achieved if the number of different gradients used in the stack is limited (e.g. reduced to less than five or even less than four or three) and a degree of freedom is introduced for intermediate wavelengths (e.g. wavelengths between the three hologram wavelengths). Manufacturing costs are significantly reduced because the number of different grading tools is reduced.

The inventors have found that a faster and more reliable manufacturing process can be used to produce the laminate of the present invention, with each layer having a unique percentage change in thickness, compared to the conventional processes required to produce the laminate. The inventors have realized that by limiting the design of the waveguide coating to consider only a specific region of the visible spectrum, such alternating stacks according to the present invention can be arranged to provide desired optical properties, such as spatially uniform emission and low absorption losses at those wavelengths (but not necessarily at other wavelengths). As such, the waveguides of the present disclosure may be particularly well suited for applications where light of a particular wavelength is being waveguided rather than being full spectrum. For example, in many applications, spatially uniform emission of red, green, and/or blue light from the waveguide may be desired, but no other wavelengths (e.g., in the yellow region of the spectrum) are desired. Such applications include heads-up displays. The waveguides of the present disclosure may be suitable for such applications. As will be appreciated by those skilled in the art, red, green, and blue light may be used to generate a full color image.

According to a first aspect, a waveguide is provided. The waveguide comprises a pair of parallel/complementary surfaces arranged to provide a waveguide therebetween. A first surface of the pair of parallel/complementary surfaces comprises a plurality of layers. The plurality of layers may be said to comprise a plurality of first dielectric layers and a plurality of second dielectric layers. The plurality of layers may include a plurality of first layers. Each of the plurality of first layers may include a first dielectric. The plurality of layers may include a plurality of second layers. Each of the plurality of second layers may include a second dielectric. The multiple layers of the first and second dielectrics may form part of a dielectric stack. The plurality of layers of the first and second dielectrics may be arranged in an alternating configuration. As used herein, "[ first or second ] dielectric layer" may mean that the respective layer comprises the respective dielectric. In some embodiments, the respective layers may be composed of respective materials. In some embodiments, the respective layers may include one or more additional materials (in addition to the respective dielectric materials). Thus, in such embodiments, the respective layers may not be comprised of the [ first or second ] respective dielectrics.

Each (first and second) layer (of the first and second dielectrics) has a first end and a second end. The first end may be the (optical) input end and the second end may be the (optical) output end of the final replica or the end of the output port/window. The percent change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete (e.g., allowed) values. The total number of layers is greater than the total number of discrete values. As used herein, "total number of layers" refers to the total number of layers. This may include the total number of first layers/multilayers comprising the first dielectric and the total number of second layers/multilayers comprising the second dielectric. In some embodiments, the total number of layers is equal to the sum of the number of first layers and the number of second layers, or the sum of the number of layers of the first dielectric and the number of layers of the second dielectric. The refractive index difference between the first dielectric and the second dielectric is greater than 0.4, alternatively greater than 0.5. The refractive index difference may refer to a maximum refractive index difference between the first dielectric and the second dielectric.

Unless otherwise indicated, "percent thickness change" of a layer as referred to herein refers to the percent change in the layer thickness from a first end of the layer to a second end of the layer. The percent change in layer thickness may be: 100x (t) _f –t _i )/t _i Wherein t is _i Is the thickness of the corresponding layer at the first end, t _f Is the thickness of the corresponding layer at the second end. In some embodiments, the thickness of a layer may refer to the physical thickness of the corresponding layer. In some embodiments, thickness may refer to the optical thickness or optical path length of a layer. Thus, thickness may refer to the physical path length through the layer at a given location multiplied by the refractive index of the layer at the given location. If the refractive index of the layers is constant from the first end to the second end, the optical thickness/path length may correspond to the physical thickness of the corresponding layer from the first end to the second end. Thus, in this context, reference to thickness may refer to an optical path length, and a percent change in thickness may refer to a percent change in optical path length.

In general, each of the plurality of layers may be parallel to the other layers. The first end of each layer may be aligned with the first ends of the other layers and the second end of each layer may be aligned with the other layers. In other words, each layer may have a length and/or width substantially similar to the other layers, but may differ in thickness or depth. The multiple layers of the first and second dielectrics may be referred to as a stack, or simply a dielectric stack.

As used herein, an "alternating arrangement" of first and second dielectric layers means that each layer of a first dielectric is separated from the next closest layer of the first dielectric by the second dielectric layer, and vice versa.

As used herein, a plurality of discrete values means a plurality of values that are different from one another. In other words, none of the plurality of discrete values is identical to any other discrete value. The magnitude and/or polarity of each discrete value may be different. The discrete value may be referred to as an "allowed" value or a "predetermined" value. The rate of change of thickness of each layer may be selected during manufacture or determined therefrom. For example, if multiple layers of the first surface of the waveguide are fabricated using shadow masks, the rate of change of thickness of each layer may be related to the shape of the shadow mask such that each discrete value is related to the corresponding shadow mask. Those skilled in the art will appreciate that the discrete values "allowed" or "predetermined" may take any suitable value that provides the desired optical properties in the case of the particular multilayer structure of the first and second dielectrics, and that the suitable value may be calculated or determined, for example, using simulation. Each discrete value may be positive or negative. Positive values indicate an increase in thickness from the first end to the second end, and negative values indicate a decrease in thickness from the first end to the second end.

The percent change in thickness of each layer is equal to one of a plurality of discrete values. Because the number of layers is greater than the number of discrete values, at least two layers have the same percentage of thickness variation from the respective first end to the respective second end. In some embodiments, more than two, optionally four or more, optionally 6 or more, optionally 8 or more, optionally 10 or more of the plurality of layers may have the same percentage thickness variation from the respective first end to the respective second end (and thus the layers may be associated with the same discrete value). In some embodiments, the layers having the same percentage of thickness variation as each other are layers of the same dielectric (i.e., all layers having a particular percentage of thickness variation value are layers of the first dielectric or layers of the second dielectric).

Each layer of the first or second dielectric may increase or decrease in (optical) thickness in the waveguide direction. The first direction may be defined from a first end to a second end of each of the plurality of layers. The pair of parallel surfaces may be arranged to provide a waveguide in a first direction. In other words, light guided by the pair of surfaces may interact with the first end before interacting with the second end. Further, each layer of the first or second dielectric may increase or decrease in thickness in the first direction.

The percentage change in (optical) thickness of the layer from the first end to the second end may be positive as the (optical) thickness of the layer increases from the respective first end to the respective second end. The discrete values associated with such layers may be positive. The percentage change in (optical) thickness of the layer from the first end to the second end may be negative as the (optical) thickness of the layer decreases from the respective first end to the respective second end. The discrete values associated with such layers may be negative.

The minimum (optical) thickness and the discrete value of the percentage of thickness change for each of the plurality of (first and second) layers of (first and second) dielectric may be selected to provide a waveguide having desired optical characteristics, in particular having desired transmission behavior, to produce spatially uniform emission. These parameters may depend on, among other things, the material properties (in particular refractive index) of the first and second dielectrics, the angle of incidence of the light entering the waveguide, the wavelength of the incident light, and the distance between a pair of parallel surfaces of the waveguide. As will be appreciated by those skilled in the art, there will be a plurality (typically a relatively large number) of multi-layer arrangements to provide waveguides having the desired optical characteristics. However, a common advantage of all these arrangements is that the layered structure of the first surface provides the desired optical properties and can be manufactured quickly, cheaply and reliably.

One example of a fast, inexpensive and reliable method of fabricating (first and second) layers (of first and second dielectrics) may include forming the layers by depositing respective dielectric materials on the waveguide substrate. Shadow masks may be used to control the flow of dielectric material over the substrate. Preferably, a shadow mask having a trapezoid shape may be used. The percent change in thickness of each layer may be determined by the shape of the mask, and the total thickness of each layer may be determined by the length of time that the dielectric material is allowed to flow. When the shadow mask is trapezoidal, the percent change in thickness of each layer may correspond to the percent change in the shorter side to the longer side of the trapezoidal shape of the shadow mask. A different shadow mask may be associated with each discrete value. For example, if there are first through fourth percent change values, four different shadow masks may be used to make the coating. The waveguide substrate can advantageously be simply moved between different material sources with different shadow masks.

The plurality of discrete values may comprise or consist of two or more discrete (allowed) values, optionally three or more discrete (allowed) values, optionally four or more (allowed) values. The plurality of discrete values may consist of two to six discrete values, alternatively two to four discrete values, alternatively four discrete values. The number of discrete values may preferably be significantly lower than the total number of layers. For example, in some embodiments, the total number of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers.

The plurality of discrete values may include a first value, a second value, and a third value. Each (first) layer (of the first dielectric) may have a percent thickness variation equal to the first value or the second value. In other words, there may be only two options for the percentage change in thickness of each (first) layer of the first dielectric.

At least one (second) layer of the (second) dielectric may have a percent thickness variation equal to a third value. When each layer of the first dielectric has a first discrete value or a second discrete value, this may mean that at least one layer of the second dielectric has a different percentage change in thickness relative to all layers of the first dielectric.

The plurality of discrete values may include a fourth value in addition to the first through third values. Each layer of the second dielectric may have a percent thickness variation equal to the third value or the fourth value. In other words, there may be only two options for the percentage change in the thickness of each layer of the second dielectric. When each layer of the first dielectric has a first discrete value or a second discrete value, this may mean that each layer of the second dielectric has a different percent thickness relative to all layers of the first dielectric.

Preferably, the rate of change of the thickness (e.g., optical and/or physical thickness) of each layer of the first and second dielectrics may be constant. Each layer may have a linear profile when the rate of change of the physical thickness of each layer is constant. It may be simpler to manufacture a dielectric layer having a linear profile. Furthermore, it will be appreciated by those skilled in the art that it may be simpler to calculate/determine discrete allowable values for stacks having a linear profile.

The waveguide may be arranged to guide an optical field input at a second surface of the pair of parallel surfaces of the waveguide. The light field may be generated by the display device. The waveguide may be arranged to receive a light field from the display device. The light field may comprise diffracted light. The light field may be encoded with a hologram.

The waveguide may be referred to as a waveguide pupil expander. In some embodiments, the pair of parallel/complementary surfaces are elongated or elongate surfaces that are relatively long along a first dimension and relatively short along a second dimension, e.g., relatively short along each of two other dimensions, each dimension being substantially orthogonal to each of the respective other dimensions.

In some embodiments, the first surface of the waveguide may be partially reflective-transmissive. In some embodiments, a second surface of the pair of parallel surfaces of the waveguide may be substantially fully reflective. In this way, light that is guided between the first and second surfaces of the waveguide may be reflected by each of the first and second surfaces. At each reflection on the first surface, the light field may be divided such that a portion of the light field is transmitted out of the waveguide at each reflection point, creating a copy of the input light field at each reflection point. The remaining light may be reflected by the first surface. In this way, the waveguide may act as a pupil expander.

In some embodiments, the first surface may provide a plurality, n, of light emitting regions for light that is waveguided between the first surface and the second surface. The plurality of light emitting regions may be distributed along the length of the first surface in the waveguide direction. A replica of the input wavefront can be generated at each transmitting zone. The first end of each of the first and second dielectric layers may be at or adjacent to the first light emitting region. The second end of each of the first and second dielectric layers may be at or adjacent to the nth light emitting region.

The internal angle of incidence of each emission region may be in the range of 0 to 70 degrees, preferably in the range of 10 to 50 degrees.

In some embodiments, the transmissivity of the first surface increases in the waveguide direction. More specifically, in some embodiments, the transmissivity of the first surface at the first and second visible wavelengths may increase in the waveguide direction. In an embodiment, the first and second visible wavelengths are different. In particular, the difference between the first and second visible wavelengths may be at least 50 nanometers, alternatively at least 70nm. The transmittance of the first surface at the first and second visible wavelengths may increase with distance from the first light emission region to the nth light emission region to maintain the intensities of the plurality of light emissions substantially constant at the first and second wavelengths. This may advantageously provide spatially uniform emission (at the first and second wavelengths) of light from the waveguide. In some embodiments, the transmissivity of the first surface at the third wavelength may increase in the waveguide direction (in addition to the increase in transmissivity for the first and second wavelengths). The transmittance of the first surface at the third visible wavelength may increase with the distance from the first light emitting region to the nth light emitting region to maintain the intensities of the plurality of light emitting regions substantially constant at the first, second and third wavelengths. As described above, this may advantageously provide spatially uniform emission (at the first, second and third wavelengths) of light from the waveguide. In an embodiment, the first, second and third visible wavelengths are different. In particular, the difference between the first or second visible wavelength and the third visible wavelength may be at least 50 nanometers, alternatively at least 70nm.

At other wavelengths (i.e., not the first, second, and optional third visible wavelengths), the transmissivity of the first surface may or may not increase in the waveguide direction. As previously mentioned, the waveguides of the present disclosure may be particularly advantageous where the waveguides are of discrete wavelengths of light rather than light where the waveguides have a continuous spectrum. The inventors have appreciated that parameters such as thickness and percent thickness variation values of the layers of the first and second dielectrics may be selected to provide the desired transmittance variation behavior at only the first, second and third wavelengths, and that the layers may not be required to provide the same transmittance behavior at other wavelengths. The inventors have found that by limiting the problem of providing varying transmittance behaviour to only certain wavelengths, a coating comprising multiple layers with the same thickness variation rate can provide the desired transmittance behaviour, which as mentioned above can be manufactured cheaply, rapidly and reliably, while still providing acceptable transmittance characteristics.

The first wavelength mentioned above may preferably be red visible light, for example in the range 630-670 nm. The second wavelength may preferably be green visible light, for example in the range of 500-540 nm. The third wavelength may preferably be blue visible light, for example in the range of 430-470 nm. In other words, the first wavelength may correspond to red visible light. The second wavelength may correspond to green visible light. The third wavelength may correspond to blue visible light.

Preferably, the transmittance T (n) of the first surface at each emission point may satisfy the following equation: t (n) = (T (n-1))/(1-T (n-1) ]× [1-L ]), where L is the optical loss factor of the waveguide material.

The first dielectric may be a first oxide, fluoride, sulfide or nitrate of a first transition metal or semiconductor. The second dielectric may be a second oxide, fluoride, sulfide or nitrate of a second transition metal or semiconductor. In some embodiments, the first dielectric comprises silicon, titanium, tantalum, niobium, or hafnium. In some embodiments, the second dielectric comprises another of silicon, titanium, tantalum, niobium, or hafnium.

The thickness of each layer may be in the range of 2 to 300 nm. The thickness of each layer cannot be outside this range at any point between the first and second ends. In some embodiments, each layer may have a thickness in the range of 20 to 300 nm.

The minimum thickness of each layer may be between 2 and 300nm, alternatively between 20 and 300 nm. The maximum thickness of each layer may be between 2 and 300nm, alternatively between 20 and 300 nm. The minimum thickness of each layer is less than the maximum thickness of the corresponding layer. The minimum or maximum thickness of each layer may be at the first end of the layer. The other of the minimum or maximum thickness of the respective layer may be at the second end of the layer.

At least one of the plurality of discrete values of the percent change in thickness may be positive. At least one of the plurality of discrete values of the percent change in thickness may be negative.

A positive percentage change in thickness may indicate an increase in thickness of the respective layer from the first end to the second end. In other words, a positive percentage change in thickness may indicate that the thickness of the respective layer increases in the waveguide direction. A negative percentage change in thickness may indicate a decrease in thickness of the respective layer from the first end to the second end. In other words, a negative percentage change in thickness may indicate that the thickness of the respective layer decreases in the waveguide direction.

Each of the plurality of discrete values of the percent change in thickness may be in the range of-150% to +150%.

The number of layers of the plurality of layers may be at least 10 layers, alternatively at least 15 layers, alternatively at least 20 layers. The number of layers of the plurality of layers may be in the range of 10 to 30, optionally 15-25.

In a second aspect, a holographic system is provided. The holographic system comprises a display device. The display device is arranged to display a hologram of the image and to output spatially modulated light in accordance with the hologram. The holographic system further comprises at least a first waveguide according to the first aspect. In other words, the holographic system comprises a waveguide comprising a pair of parallel/complementary surfaces arranged to provide the waveguide therebetween, wherein a first surface of the pair of parallel surfaces comprises a plurality of layers. The plurality of layers may include a plurality of first dielectric layers and a plurality of second dielectric layers. The plurality of layers may include a plurality of first layers, each first layer including (or being comprised of) a first dielectric. The plurality of layers may include a plurality of second layers, each second layer including (or being comprised of) a second dielectric. The multiple layers may be arranged in a stack. The plurality of layers may be arranged in an alternating configuration. The percent change in the thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values; wherein the total number of first and second dielectric layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4, alternatively 0.5. The first waveguide is arranged to receive light encoded with a hologram output by the display device at a second surface of the pair of parallel surfaces.

The plurality of discrete values may comprise or consist of two or more discrete (allowed) values, optionally three or more discrete values, optionally four or more values. The plurality of discrete values may consist of two to six discrete values, alternatively two to four discrete values, alternatively four discrete values. The number of discrete values may preferably be significantly lower than the total number of layers. For example, in some embodiments, the total number of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers.

The plurality of discrete (allowed) values may include a first value, a second value, and a third value. Each layer of the first dielectric may have a percent thickness variation equal to the first value or the second value. In other words, there may be only two options for the percentage change in the thickness of each layer of the first dielectric.

At least one layer of the second dielectric may have a percent thickness variation equal to a third value. When each layer of the first dielectric has a first discrete value or a second discrete value, this may mean that at least one layer of the second dielectric has a different percentage change in thickness relative to all layers of the first dielectric.

In some aspects, the display device is part of a display system of a holographic system. The display device may be a pixelated display device, such as a Spatial Light Modulator (SLM) or a liquid crystal on silicon (LCoS) SLM, arranged to provide or form diffracted or divergent light. In these aspects, the aperture of a Spatial Light Modulator (SLM) is the limiting aperture of the system. That is, the aperture of the spatial light modulator, and more specifically, the size of the area defining the array of light modulating pixels contained within the SLM, determines the size (e.g., spatial extent) of the beam of light that can leave the system. In accordance with the present disclosure, it is stated that by using at least one waveguide pupil expander, the exit pupil of the system is expanded to reflect that the exit pupil of the system (which is limited by a small display device having pixel dimensions for light diffraction) becomes larger in spatial extent.

In some embodiments, the light field is spatially modulated according to the hologram. In other words, in these aspects, the light field comprises a "holographic light field". The hologram may be displayed on a pixelated display device. The hologram may be a Computer Generated Hologram (CGH). It may be a fourier hologram or a fresnel hologram or a point cloud hologram or any other suitable type of hologram. Alternatively, holograms may be calculated so as to form channels of holographic light, each channel corresponding to a different portion of an image that the observer wants to observe (or perceive if it is a virtual image). The pixelated display device may be configured to display a plurality of different holograms consecutively or sequentially. Each of the aspects and embodiments disclosed herein may be applied to the display of multiple holograms.

The holographic system may comprise a second waveguide. Like the first waveguide, the second waveguide may comprise a pair of parallel surfaces arranged to provide a waveguide therebetween. A first surface of a pair of parallel surfaces of the second waveguide may be partially reflective-transmissive. The second surface of the pair of parallel surfaces of the second waveguide may be reflective. At least a portion of the first surface may refer to or define the output of the second waveguide. At least a portion of the second surface may refer to or define an input of the second waveguide. The second waveguide may be referred to as a second pupil expander. The second waveguide may be orthogonal to the first waveguide.

The first surface of the pair of parallel surfaces of the second waveguide may provide a plurality, n, of light emitting regions for light of the waveguide between the first surface and the second surface. The internal angle of incidence of each emitter region may be in the range 0 to 75 degrees, alternatively 10 to 50 degrees.

The first surface of the first waveguide, in particular the output port, may be coupled to the input port of the second waveguide. The second waveguide may be arranged to guide the optical field (including some, preferably most, preferably all copies of the optical field output by the first waveguide) from its input port to the respective output port by internal reflection between a pair of parallel surfaces of the second waveguide pupil expander.

The first waveguide may be arranged to provide pupil expansion or replication in a first direction and the second waveguide pupil expander may be arranged to provide pupil expansion or replication in a second, different direction. The second direction may be substantially orthogonal to the first direction. The second waveguide may be arranged to maintain the pupil expansion provided by the first waveguide in a first direction and expand (or replicate) some, preferably most, preferably all copies it receives from the first waveguide in a different second direction. The second waveguide may be arranged to receive the optical field directly or indirectly from the first waveguide. One or more other elements may be provided along the propagation path of the optical field between the first and second waveguide pupil expanders.

The first waveguide may be substantially elongate and the second waveguide may be substantially planar. The elongated shape of the first waveguide may be defined by a length along the first dimension. The planar or rectangular shape of the second waveguide may be defined by a length along a first dimension and a width or breadth along a second dimension substantially orthogonal to the first dimension. The size or length of the first waveguide along its first dimension corresponds to the length or width of the second waveguide pupil expander along its first or second dimension, respectively. The second surface of the pair of parallel surfaces of the second waveguide including its input port may be shaped, sized and/or positioned to correspond to the area defined by the output port on the first surface of the first pair of parallel surfaces on the first waveguide pupil expander such that the second waveguide is arranged to receive each replica output by the first waveguide.

The first and second waveguides may together provide a pupil expansion in a first direction and in a second direction perpendicular to the first direction, optionally with a plane containing the first and second directions substantially parallel to a plane of the second waveguide pupil expander. In other words, the first and second dimensions, respectively defining the length and width of the second waveguide pupil expander, may be parallel to the first and second directions, respectively (or to the second and first directions, respectively), wherein the waveguide pupil expander provides pupil expansion. The combination of the first waveguide pupil expander and the second waveguide pupil expander may be generally referred to as a "pupil expander".

It can be said that the expansion/duplication provided by the first and second waveguide expanders has the effect of expanding the exit pupil of the display system in each of the two directions. The region defined by the extended exit pupil may in turn define an extended eyebox region from which an observer may receive light of the input diffracted or divergent light field. The eyebox region may be said to lie in or define a viewing plane.

The two directions of exit pupil expansion may be coplanar or parallel with the first and second directions in which the first and second waveguide pupil expanders provide replication/expansion. Alternatively, in an arrangement comprising other elements such as an optical combiner, for example a windscreen of a vehicle, the exit pupil may be considered to be the exit pupil from the other elements, for example the exit pupil from the windscreen. In this arrangement, the exit pupil may be non-coplanar and non-parallel with the first and second directions in which the first and second waveguide pupil expanders provide replication/expansion. For example, the exit pupil may be substantially perpendicular to the first and second directions, with the first and second waveguide pupil expanders providing replication/expansion.

The viewing plane and/or the eyebox areas may be non-coplanar or non-parallel with the first and second directions in which the first and second waveguide pupil expanders provide replication/expansion. For example, the viewing plane may be substantially perpendicular to the first and second directions, wherein the first and second waveguide pupil expanders provide replication/expansion.

The second waveguide may have one or more features of the waveguide described in relation to the first aspect. For example, the first surface of the second waveguide may include multiple layers of the first dielectric and multiple layers of the second dielectric. The plurality of layers of the first dielectric and the second dielectric may be arranged in an alternating configuration. The percent change in thickness of each layer of the first dielectric from the first end to the second end may have a first value or a second value.

Each layer of the first and second dielectrics may have a first end and a second end, wherein a percentage change in the thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values; wherein the total number of first and second dielectric layers is greater than the total number of discrete allowed values. Preferably, the percentage change in the thickness of each layer of the second dielectric from the first end to the second end may have a third value or a fourth value. The rate of change of thickness of each layer of the first and second dielectrics may be constant. The refractive index difference between the first dielectric and the second dielectric may be greater than 0.4, alternatively 0.5.

Features of the waveguide applied to the first aspect of the second waveguide may provide the same advantages as described for the first aspect. In particular, as described above, the second waveguide having the first surface comprising the layered structure may provide spatially uniform emission of the optical field and may be manufactured in a relatively inexpensive, fast and reliable manner.

As described above, the first surface of the second waveguide may provide a plurality, i.e. n, of light emitting regions for light of the waveguide between the first surface and the second surface. The transmittance of the first surface at the first, second and third visible wavelengths may increase with distance from the first light emission region to the nth light emission region in order to maintain the intensities of the plurality of light emissions substantially constant at the first, second and third wavelengths. The first wavelength may be in the range of 630-670nm, the second wavelength may be in the range of 500-540nm, and the third wavelength may be in the range of 430-470 nm. The transmissivity T (n) of the first surface of the second waveguide at each emission point may satisfy the following equation: t (n) = (T (n-1))/(1-T (n-1) ]× [1-L ]), where L is the optical loss factor of the waveguide material. The first dielectric of the second waveguide may be a first oxide, fluoride, sulfide or nitrate of a first transition metal or semiconductor. The second dielectric of the second waveguide may be a second oxide, fluoride, sulfide or nitrate of a second transition metal or semiconductor. Each of the first to fourth values of the percent change in thickness of the layer of the first surface of the second waveguide may be in the range of-150% to +150%. The number of layers of the plurality of layers may be in the range of 10 to 30, optionally 15-25. The first value of the percentage change may be different from the third value of the percentage change. The second value of the percentage change may be different from the fourth value of the percentage change.

The first waveguide may be substantially elongate. The first and second surfaces may be elongate surfaces. The second waveguide may be planar. The first and second surfaces are major surfaces of a planar second waveguide.

In a third aspect, a method of waveguiding an optical field is provided. The method includes introducing light into a first waveguide including a pair of parallel surfaces. The method further includes directing light by internal reflection between a pair of parallel surfaces.

The first waveguide may be a waveguide according to the first aspect. In particular, a first surface of the pair of parallel surfaces comprises a plurality of layers of first dielectrics and a plurality of layers of second dielectrics arranged in an alternating configuration. Each layer of the first and second dielectrics has a first end and a second end. The percent change in the thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values. The total number of first and second dielectric layers is greater than the total number of discrete allowed values. The refractive index difference between the first dielectric and the second dielectric is greater than 0.4, alternatively 0.5.

The first surface provides a plurality, n, of light emitting regions for light that is waveguided between the first surface and the second surface, optionally wherein the internal angle of incidence of each emitting region is in the range of 10 to 50 degrees.

The plurality of discrete values may comprise or consist of two or more discrete values, optionally three or more discrete values, optionally four or more values. The plurality of discrete values may consist of two to six discrete values, alternatively two to four discrete values, alternatively four discrete values. The number of discrete values may preferably be significantly lower than the total number of layers. For example, in some embodiments, the total number of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers. In some embodiments, the number of allowed values is less than 50% or less than 25% of the number of layers.

The plurality of discrete values may include a first value, a second value, and a third value. Each layer of the first dielectric may have a percent thickness variation equal to the first value or the second value. In other words, there may be only two options for the percentage change in the thickness of each layer of the first dielectric.

The step of directing light into the waveguide may include directing light having a first visible wavelength, a second visible wavelength, and a third visible wavelength. The first wavelength may be in the range of 630-670nm, the second wavelength may be in the range of 500-540nm, and the third wavelength may be in the range of 430-470 nm. The transmittance of the first surface at the first, second, and third visible wavelengths increases with distance from the first light emission region to the nth light emission region to maintain the intensities of the plurality of light emissions substantially constant at the first, second, and third wavelengths.

The method may further include directing light into a second waveguide comprising a pair of parallel surfaces and directing light by internal reflection between the pair of parallel surfaces. The step of introducing light into the second waveguide may be performed after the step of introducing light into the first waveguide. The light directed into the second waveguide may be light that has been emitted from the first output.

According to a fourth aspect, there is provided a method of manufacturing or providing a waveguide. The method includes providing a waveguide substrate including a pair of parallel surfaces arranged to provide a waveguide therebetween; and applying the plurality of layers of first dielectric and the plurality of layers of second dielectric to the waveguide substrate such that the first and second dielectric layers are in an alternating configuration.

The waveguide may be a waveguide according to the first aspect. In particular, each layer of the first and second dielectrics may have a first end and a second end, wherein a percentage change in the thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowed values. The total number of first and second dielectric layers may be greater than the total number of discrete allowed values. The refractive index difference between the first dielectric and the second dielectric may be greater than 0.4, alternatively 0.5.

The step of applying multiple layers of the first dielectric and the second dielectric may include depositing a first layer of the first or second dielectric onto a surface of the waveguide substrate; a second layer of the first or second dielectric is then deposited over the first layer.

The step of depositing each layer of the first or second dielectric may comprise controlling the flow of the respective dielectric material towards the waveguide substrate using a shadow mask.

The step of depositing each layer of the first or second dielectric may comprise controlling the flow of the first dielectric material with a different shadow mask for each discrete allowed value. The step of depositing each layer of the first dielectric includes controlling the flow of the first dielectric using either the first or second shadow mask. The method may include depositing at least one layer of a second dielectric using a third shadow mask. The method may include depositing each layer of the second dielectric using a third or fourth shadow mask. At least one, optionally each, of the first through fourth shadow masks includes a trapezoidal opening, optionally an isosceles trapezoidal opening.

In another aspect, a waveguide is provided comprising a pair of parallel surfaces arranged to provide a waveguide therebetween, wherein a first surface of the pair of parallel surfaces comprises a plurality of layers of a first dielectric and a plurality of layers of a second dielectric arranged in an alternating configuration, wherein each layer of the first and second dielectrics has a first end and a second end, wherein a percentage change in thickness of each layer of the first dielectric from the first end to the second end of the layer has a first value or a second value; wherein the percent change in thickness of the at least one layer of the second dielectric from the first end to the second end has a third value; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4, alternatively 0.5.

In another aspect, a waveguide is provided comprising a pair of parallel surfaces arranged to provide a waveguide therebetween, wherein a first surface of the pair of parallel surfaces comprises a plurality of layers of a first dielectric and a plurality of layers of a second dielectric arranged in an alternating configuration, wherein each layer of the first and second dielectrics has a first end and a second end, wherein a percentage change in thickness of each layer of the first dielectric from the first end to the second end of the layer has a first value or a second value; wherein the percent change in thickness of each layer of the second dielectric from the first end to the second end of the layer has a third value or a fourth value; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4, alternatively 0.5.

In another aspect, a method of designing a waveguide is provided, the waveguide comprising a pair of parallel surfaces, a first surface of the pair comprising a plurality of layers of a first dielectric, and comprising a plurality of layers of a first dielectric and a plurality of layers of a second dielectric arranged in an alternating configuration, wherein each layer of the first and second dielectrics has a first end and a second end. The method includes determining, calculating, or computing a plurality of discrete values of percent change in thickness of each of a plurality of layers from the first end to the second end. The determined, calculated or computed value may provide a waveguide comprising a first surface having a predetermined (or target) transmissivity.

The target transmittance may correspond to a transmittance of the first surface increasing from the first end to the second end. The target transmittance is preferably a transmittance that provides spatially uniform emission from the waveguide, as has been described with respect to the previous aspects.

The waveguide may be a waveguide according to the first aspect. In particular, the plurality of discrete values may comprise or consist of two or more discrete (allowed) values, optionally three or more discrete (allowed) values, optionally four or more (allowed) values. The plurality of discrete values may consist of two to six discrete values, alternatively two to four discrete values, alternatively four discrete values. The number of discrete values may preferably be significantly lower than the total number of layers. For example, in some embodiments, the total number of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers.

At least one layer of the second dielectric may have a percent thickness variation equal to a third value. When each layer of the first dielectric has a first discrete value or a second discrete value, this may mean that at least one layer of the second dielectric has a different percentage change in thickness relative to all layers of the first dielectric. Preferably, each layer of the second dielectric may have a percent thickness variation equal to the third value or the fourth value.

The target transmittance may comprise a transmittance value for the first wavelength range. The target transmittance may comprise a transmittance value for the second wavelength range. The target transmittance may comprise a transmittance value for the third wavelength range. The target transmittance may include only transmittance values for the wavelength of interest (or predetermined wavelength). Thus, the computational model only needs to consider the performance of the waveguide at the wavelength of interest, while the performance of the waveguide at other wavelengths can be ignored. The wavelength of interest or predetermined wavelength may comprise or consist of a first wavelength range, a second wavelength range and/or a third wavelength range. The first wavelength range may be between 630 and 670 nm. The second wavelength range may be between 500 and 540 nm. The third wavelength may be between 430 and 470 nm. Preferably, the first, second and/or third wavelength ranges consist of a single wavelength. Those skilled in the art will appreciate that this type of light may be output by a laser.

Determining, calculating, or computing the plurality of discrete values may include using a computational model or modeling the transmissivity of the first waveguide from the first end to the second end.

The computational model may simulate the optical performance of a waveguide with specific material properties. In particular, the computational model may simulate the transmissivity of a first surface of a waveguide having particular material properties when light rays are incident on the waveguide at particular predetermined angles of incidence. The transmittance may depend on the refractive indices of the first and second dielectric materials and the number, absolute thickness, and percent thickness change of the first and second dielectric layers. The skilled person will be familiar with such a computational model for the design of an optical element.

The waveguide may include a predetermined number of layers (e.g., more than 12 layers, more than 16 layers, more than 20 layers) of the first and second dielectric materials. The material of the first dielectric may be predetermined. The material of the second dielectric may be predetermined. The method may comprise inputting the number of layers and the material properties of the first and second dielectrics, in particular the respective refractive indices of the first and second dielectrics, into a computational model. The method may further include inputting the wavelength of interest into a computational model.

The method may include determining a plurality of discrete values of the percent change in thickness of each layer of the waveguide using a computational model.

The method may include outputting a discrete value of the percent change in layer thickness determined using the computational model.

The step of determining, calculating, or computing a plurality of discrete values using a computational model may include randomly generating a first set of discrete values of percent variation in layer thickness.

The method may include assigning one of the first discrete values to each dielectric layer of the first waveguide. This may include assigning a first value and/or a second value to each first dielectric layer. This may include assigning a third and/or fourth value to each second dielectric layer.

The method may further include randomly generating a first set of values for the absolute thickness of the plurality of layers and assigning the values to the first and second dielectric layers of the first waveguide.

The method may include determining a first transmittance output of the first waveguide.

The method may include comparing the first transmittance output to a target transmittance. This may include comparing the transmittance value of the first waveguide from the first end to the second end with a corresponding target value of the target transmittance. If the difference between the target transmittance and the first transmittance output is less than a predetermined value, the method may include outputting a first set of discrete values. Otherwise, the method may include modifying the first set of discrete values to form a second set of discrete values based on the comparison. The method may be repeated n iterations until the difference between the target transmittance and the first transmittance output is less than a predetermined value.

The term "hologram" is used to refer to a record containing amplitude information or phase information about an object, or some combination thereof. The term "holographic reconstruction" is used to refer to the optical reconstruction of an object formed by illuminating a hologram. The system disclosed herein is described as a "holographic projector" because the holographic reconstruction is a real image and is spatially separated from the hologram. The term "replay field" is used to refer to a 2D region within which a holographic reconstruction is formed and which is fully focused. If the hologram is displayed on a spatial light modulator comprising pixels, the replay field will repeat in the form of a plurality of diffraction orders, each diffraction order being a copy of the zero order replay field. The zero order playback field generally corresponds to the preferred or main playback field because it is the brightest playback field. The term "playback field" shall be taken to mean a zero-order playback field unless explicitly stated otherwise. The term "replay plane" is used to refer to a plane in space that contains all replay fields. The terms "image", "replay image" and "image region" refer to the region of the replay field illuminated by the holographically reconstructed light. In some embodiments, an "image" may include discrete points, which may be referred to as "image points," or simply as "image pixels" for convenience.

The terms "encoding", "writing" and "addressing" are used to describe the process of providing a plurality of pixels of the SLM with a corresponding plurality of control values that respectively determine the modulation level of each pixel. The pixels of the SLM are said to be configured to "display" the light modulation profile in response to receiving a plurality of control values. Thus, the SLM can be said to "display" a hologram, and the hologram can be considered as an array of light modulating values or levels.

It has been found that a holographic reconstruction of acceptable quality can be formed from a "hologram" that contains only phase information related to the fourier transform of the original object. Such holographic recordings may be referred to as phase-only holograms. The embodiments relate to phase-only holograms, but the disclosure is equally applicable to amplitude-only holograms.

The present disclosure is equally applicable to the formation of holographic reconstructions using amplitude and phase information related to the fourier transform of the original object. In some embodiments, this is achieved by complex modulation using a so-called full complex hologram containing amplitude and phase information about the original object. Since the value (gray level) assigned to each pixel of a hologram has an amplitude and phase component, such a hologram may be referred to as a full complex hologram. The value (gray level) assigned to each pixel can be represented as a complex number having amplitude and phase components. In some embodiments, a full complex computer generated hologram is calculated.

Reference may be made to the phase value, phase component, phase information or simply the phase of a pixel of a computer generated hologram or spatial light modulator, as shorthand for "phase delay". That is, any of the phase values described are actually numbers (e.g., in the range of 0 to 2π) representing the amount of phase delay provided by that pixel. For example, a pixel described as having a pi/2 phase value of a spatial light modulator will delay the phase of the received light by pi/2 radians. In some embodiments, each pixel of the spatial light modulator may operate in one of a plurality of possible modulation values (e.g., phase delay values). The term "gray scale" may be used to refer to a number of available modulation levels. For example, the term "gray level" may be used for convenience to refer to only a plurality of available phase levels in the phase modulator, even though different phase levels do not provide different shades of gray. For convenience, the term "gray scale" may also be used to refer to a plurality of available complex modulation levels in a complex modulator.

Thus, the hologram comprises a gray scale array, i.e. an array of light modulating values, such as an array of phase delay values or complex modulating values. A hologram is also considered a diffraction pattern because it is a pattern that causes diffraction when displayed on a spatial light modulator and illuminated with light having a wavelength that is relative to (typically smaller than) the pixel pitch of the spatial light modulator. Reference is made herein to combining holograms with other diffraction patterns, such as those used as lenses or gratings. For example, a diffraction pattern acting as a grating may be combined with a hologram to translate the replay field in the replay plane, or a diffraction pattern acting as a lens may be combined with a hologram to focus the holographic reconstruction on the replay plane in the near field.

Although different embodiments and groups of embodiments, respectively, may be disclosed in the following detailed description, any feature of any embodiment or group of embodiments may be combined with any other feature or combination of features of any embodiment or group of embodiments. That is, all possible combinations and permutations of features disclosed in the present disclosure are contemplated.

The following statements are also disclosed:

item 1. A waveguide comprising a pair of parallel surfaces arranged to provide a waveguide therebetween, wherein a first surface of the pair of parallel surfaces comprises a plurality of first dielectric layers and a plurality of second dielectric layers arranged in an alternating configuration, wherein each of the first and second dielectric layers has a first end and a second end, wherein a percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowed values; wherein the total number of first and second dielectric layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

Item 2. The waveguide of item 1, wherein the plurality of discrete allowed values consists of two to six discrete values, optionally two to four discrete values, optionally four discrete values.

The waveguide of item 3, wherein the plurality of discrete allowed values comprises a first value, a second value, and a third value, and wherein each layer of the first dielectric has a percent thickness variation equal to the first value or the second value, and wherein at least one layer of the second dielectric has a percent thickness variation equal to the third value.

The waveguide of any of the preceding items, wherein the plurality of discrete allowed values comprises first through fourth values, and wherein the percent change in thickness of each layer of the second dielectric is equal to the third value or the fourth value.

The waveguide of any of the preceding items, wherein the rate of change of thickness of each layer of the first and second dielectrics is constant.

The waveguide of any of the preceding items, wherein the first surface is partially reflective-transmissive and/or the second surface of the pair of parallel surfaces is substantially fully reflective, and wherein the first surface provides a plurality of n light emitting regions for light of the waveguide between the first surface and the second surface, optionally wherein the internal angle of incidence of each emitting region is in the range of 0 to 70 degrees, optionally 10 to 50 degrees.

Item 7. The waveguide of item 6, wherein the transmittance of the first surface at the first, second, and third visible wavelengths increases with distance from the first light emitting region to the nth light emitting region to maintain the intensities of the plurality of light emissions substantially constant at the first, second, and third wavelengths.

The waveguide of item 7, wherein the first wavelength is in the range of 630-670nm, the second wavelength is in the range of 500-540nm, and the third wavelength is in the range of 430-470 nm.

Item 9. The waveguide of item 7 or 8, wherein the transmittance T (n) of the first surface at each emission point satisfies the following equation: t (n) = (T (n-1))/(1-T (n-1) ]× [1-L ]), where L is the optical loss factor of the waveguide material.

The waveguide of any preceding item, wherein the first dielectric is a first oxide, fluoride, sulfide or nitrate of a first transition metal or semiconductor and the second dielectric is a second oxide, fluoride, sulfide or nitrate of a second transition metal or semiconductor.

The waveguide of any preceding item, wherein the thickness of each layer is in the range of 2 to 300nm, optionally between 20 and 200 nm.

The waveguide of any preceding item, wherein at least one of the first through fourth values of the ratio is positive and at least one of the first through fourth values of the percent thickness variation is negative.

Item 13. The waveguide of any preceding item, wherein each of the first to fourth values of percent thickness variation is in the range of-150% to +150%.

Item 14. A holographic system, comprising:

a display device arranged to display a hologram of an image and to output spatially modulated light in accordance with the hologram;

a first waveguide arranged to receive light encoded with a hologram output by the display device at a second surface of the pair of parallel surfaces;

wherein a first surface of the pair of parallel surfaces comprises a plurality of layers of first dielectrics and a plurality of layers of second dielectrics arranged in an alternating configuration, wherein each layer of the first and second dielectrics has a first end and a second end, wherein a percent change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values; wherein the total number of first and second dielectric layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

Item 15. The holographic system of item 14, further comprising a second waveguide comprising a pair of parallel surfaces arranged to provide a waveguide therebetween.

Item 16. The holographic system of item 15, wherein the first surface of the first waveguide is arranged to provide a plurality, n, of light emitting regions for light of the waveguide between the first surface and the second surface, and the second surface of the second waveguide is arranged to receive light from the n light emitting regions of the first waveguide.

The holographic system of item 15 or 16, wherein the second waveguide is a waveguide according to any of the preceding claims.

The holographic system of any of claims 14 to 16, wherein the first waveguide is substantially elongate, and wherein the first and second surfaces are elongate surfaces.

The holographic system of any of items 14 to 18, wherein the second waveguide is planar, and wherein the first and second surfaces are major surfaces of a planar second waveguide.

Item 20. A method of waveguiding an optical field, the method comprising:

directing light into a first waveguide comprising a pair of parallel surfaces; and

directing light by internal reflection between the pair of parallel surfaces;

The waveguide method of any of the preceding items, wherein the first surface provides a plurality, n, of light emitting regions for light that is guided between the first surface and the second surface, optionally wherein the internal angle of incidence of each emitting region is in the range of 10 to 50 degrees.

Item 22. A method of providing a waveguide, the method comprising:

providing a waveguide substrate comprising a pair of parallel surfaces arranged to provide a waveguide therebetween;

applying a plurality of layers of a first dielectric and a plurality of layers of a second dielectric to the waveguide substrate such that the first and second dielectric layers are in an alternating configuration;

The method of item 22, wherein the step of applying multiple layers of the first dielectric and the second dielectric comprises depositing a first layer of the first or second dielectric to a surface of the waveguide substrate; a second layer of the first or second dielectric is then deposited over the first layer.

The method of item 24, wherein the step of depositing each layer of the first or second dielectric comprises controlling a flow of the respective dielectric material toward the waveguide substrate using a shadow mask.

The method of item 24, wherein the step of depositing each layer of the first or second dielectric comprises controlling the flow of the first dielectric material with a first shadow mask or a second shadow mask, and controlling the flow of the second dielectric material with a third or fourth shadow mask, wherein at least one, optionally each, of the first through fourth shadow masks comprises a trapezoidal opening, optionally an isosceles trapezoidal opening.

Drawings

Specific embodiments are described by way of example only with reference to the following drawings:

FIG. 1 is a schematic diagram showing a reflective SLM producing a holographic reconstruction on a screen;

FIG. 2A shows a first iteration of an example Gerchberg-Saxton type algorithm;

FIG. 2B illustrates a second and subsequent iteration of an example Gerchberg-Saxton type algorithm;

FIG. 2C illustrates an alternative second and subsequent iteration of the example Gerchberg-Saxton type algorithm;

FIG. 3 is a schematic diagram of a reflective LCOS SLM;

FIG. 4A shows an image comprising a plurality of image areas (bottom) and a corresponding hologram comprising a plurality of hologram elements (top);

FIG. 4B shows a hologram featuring routing or directing holographically encoded light into a plurality of discrete hologram channels;

FIG. 5 shows a system arranged to deliver the optical content of each hologram channel of FIG. 4B to the eye through different optical paths;

FIG. 6 shows a perspective view of a pair of stacked image replicators arranged to expand a light beam in two dimensions;

FIG. 7 shows a schematic cross-sectional view of a first waveguide according to the present invention;

FIG. 8 shows a close-up cross-sectional schematic view of a portion of the first waveguide of FIG. 7;

FIG. 9 shows a graph of the ideal increased transmissivity of a waveguide in the waveguide direction;

FIGS. 10A-C show graphs relating to a first example of a waveguide according to the present invention comprising 12 alternating SiO2 and TiO2 layers, wherein FIGS. 10A and 10B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 10C shows a comparison of the transmittance of a first surface of the first example waveguide with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

FIG. 11 shows a graph of the transmittance of the waveguide of the first example at other wavelengths compared to the ideal transmittance;

12A-C show graphs relating to a second example of a waveguide according to the invention comprising 12 alternating SiO2 and TiO2 layers, wherein FIGS. 12A and 12B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 12C shows a comparison of the transmittance of the first surface of the second example waveguide with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

13A-C show graphs relating to a third example of a waveguide according to the invention comprising 16 alternating SiO2 and TiO2 layers, wherein FIGS. 13A and 13B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 13C shows a comparison of the transmittance of the first surface of the waveguide of the third example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

fig. 14A-C show graphs related to a fourth example of a waveguide according to the invention comprising 20 alternating SiO2 and TiO2 layers, wherein fig. 14A and 14B show the thicknesses of the SiO2 and TiO2 layers, respectively, and fig. 14C shows a comparison of the transmittance of the first surface of the waveguide of the fourth example with the ideal transmittance of the red, green and blue wavelengths for which the waveguide is designed;

15A-C show graphs relating to a fifth example of a waveguide according to the invention comprising 20 alternating SiO2 and TiO2 layers, wherein FIGS. 15A and 15B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 15C shows a comparison of the transmittance of the first surface of the waveguide of the fifth example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

FIGS. 16A-C show graphs relating to a sixth example of a waveguide according to the present invention comprising 24 alternating SiO2 and TiO2 layers, wherein FIGS. 16A and 16B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 16C shows a comparison of the transmittance of the first surface of the waveguide of the sixth example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

17A-C show graphs relating to a seventh example of a waveguide according to the present invention comprising 24 alternating layers of SiO2 and TaO5, wherein FIGS. 17A and 17B show the thicknesses of the SiO2 and TaO5 layers, respectively, and FIG. 17C shows a comparison of the transmittance of the first surface of the waveguide of the seventh example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

18A-C show graphs relating to an eighth example of a waveguide according to the present invention comprising 24 alternating SiO2 and TaO5 layers, wherein FIGS. 18A and 18B show the thicknesses of the SiO2 and TaO5 layers, respectively, and FIG. 18C shows a comparison of the transmittance of the first surface of the eighth example waveguide with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

fig. 19A-C show graphs relating to a ninth example of a waveguide according to the invention comprising 30 alternating layers of SiO2 and HfO2, wherein fig. 19A and 19B show the thicknesses of the SiO2 and HfO2 layers, respectively, and fig. 19C shows a comparison of the transmittance of the first surface of the waveguide of the ninth example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

FIG. 20 shows a schematic cross-sectional view of a portion of an apparatus for fabricating a waveguide according to the present invention, wherein a waveguide substrate passes under a source of dielectric material;

Fig. 21 is a schematic view of the shadow mask of the apparatus of fig. 20 including four apertures, the cross-section lying in a plane orthogonal to the cross-sectional plane of fig. 20;

FIGS. 22A-D show schematic cross-sectional views of four different waveguide substrates, each having a layer of dielectric material formed on a first surface using the shadow mask of FIG. 21, wherein each layer is formed using a different aperture of the shadow mask;

23A-C show graphs relating to a tenth example of a waveguide according to the present invention comprising 24 alternating layers of SiO2 and SiN4, wherein FIGS. 23A and 23B show the thicknesses of the SiO2 and SiN4 layers, respectively, and FIG. 23C shows a comparison of the transmittance of the first surface of the waveguide of the tenth example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed;

24A-C show graphs relating to an eleventh example of a waveguide according to the present invention comprising 24 alternating SiO2 and TiO2 layers, wherein FIGS. 24A and 24B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 24C shows a comparison of the transmittance of the first surface of the waveguide of the eleventh example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide is designed; and

fig. 25A-C show graphs relating to a twelfth example of a waveguide comprising 30 alternating layers of SiO2 and Nb2O5 according to the present invention, wherein fig. 25A and 25B show the thicknesses of the SiO2 and Nb2O5 layers, respectively, and fig. 25C shows a comparison of the transmittance of the first surface of the waveguide of the twelfth example with the ideal transmittance of the red, green and blue wavelengths of the waveguide design.

The same reference numbers will be used throughout the drawings to refer to the same or like parts.

Detailed Description

The invention is not limited to the embodiments described below, but extends to the full scope of the appended claims. That is, the present invention may be embodied in different forms and should not be construed as limited to the described embodiments set forth herein for purposes of illustration.

Unless otherwise indicated, singular terms may include the plural.

Structures described as being formed on/under another structure should be interpreted as including the case where the structures are in contact with each other, and further, the case where a third structure is provided therebetween.

In describing temporal relationships, such as when the temporal sequence of events is described as "after," "subsequent," "next," "previous," etc., the present disclosure should be considered to include continuous and discontinuous events unless otherwise indicated. For example, unless terms such as "just," "immediately adjacent," or "directly" are used, the description should be taken to include the discontinuous case.

Although the terms "first," "second," etc. may be used herein to describe various elements, these elements are not limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of the appended claims.

Features of different embodiments may be partially or wholly coupled to or combined with one another and interoperate differently from one another. Some embodiments may be performed independently of each other or may be performed together in interdependent relationship.

Optical arrangement

FIG. 1 illustrates an embodiment in which a computer-generated hologram is encoded on a single spatial light modulator. The computer generated hologram is the fourier transform of the object for reconstruction. Thus, it can be said that the hologram is a fourier domain or frequency domain or spectral domain representation of the object. In this embodiment, the spatial light modulator is a reflective liquid crystal on silicon "LCOS" device. The hologram is encoded on a spatial light modulator and a holographic reconstruction is formed at the replay field, e.g. a light receiving surface such as a screen or a diffuser.

Light source 110, such as a laser or laser diode, is arranged to illuminate SLM140 via collimating lens 111. The collimating lens causes a substantially planar wavefront of light to be incident on the SLM. In fig. 1, the direction of the wavefront is off-normal (e.g., two or three degrees from a plane that is truly orthogonal to the transparent layer). However, in other embodiments, the substantially planar wavefront is provided at normal incidence and the beam splitter is arranged to split the input and output optical paths. In the embodiment shown in fig. 1, the arrangement is such that light from the light source reflects from the mirrored back surface of the SLM and interacts with the light modulating layer to form an outgoing wavefront 112. The outgoing wavefront 112 is applied to optics comprising a fourier transform lens 120, the focal point of the fourier transform lens 120 being located at a screen 125. More specifically, fourier transform lens 120 receives the modulated light beam from SLM140 and performs a frequency-space transform to produce a holographic reconstruction at screen 125.

Notably, in this type of hologram, each pixel of the hologram contributes to the overall reconstruction. There is no one-to-one correlation between a particular point (or image pixel) on the replay field and a particular light modulation element (or hologram pixel). In other words, the modulated light leaving the light modulation layer is distributed over the entire replay field.

In these embodiments, the position of the holographic reconstruction in space is determined by the diopter (focus) of the fourier transform lens. In the embodiment shown in fig. 1, the fourier transform lens is a physical lens. That is, the fourier transform lens is an optical fourier transform lens, and performs fourier transform optically. Any lens can act as a fourier transform lens, but the performance of the lens will limit the accuracy of the fourier transform it performs. The skilled person understands how to use a lens to perform an optical fourier transform.

Hologram calculation

In some embodiments, the computer generated hologram is a fourier transform hologram, or simply a fourier hologram or a fourier-based hologram, in which the image is reconstructed in the far field by utilizing the fourier transform characteristics of a positive lens. The fourier hologram is calculated by fourier transforming the desired light field in the replay plane back to the lens plane. The fourier transform may be used to calculate a computer generated fourier hologram.

The fourier transform hologram may be calculated using an algorithm such as the Gerchberg-Saxton algorithm. Furthermore, the Gerchberg-Saxton algorithm may be used to calculate holograms in the Fourier domain (i.e., fourier transformed holograms) from only the amplitude information in the spatial domain (e.g., photographs). Phase information about the object is effectively "retrieved" from the amplitude-only information in the spatial domain. In some embodiments, a computer-generated hologram is computed from the amplitude-only information using the Gerchberg-Saxton algorithm, or a variant thereof.

The Gerchberg-Saxton algorithm considers the intensity profile I of the beam when known to be in planes A and B, respectively _A (x, y) and I _B (x, y) and I _A (x, y) and I _B (x, y) is related by a single fourier transform. For a given intensity cross section, the phase distribution approximation ψ in planes A and B is determined respectively _A (x, y) and ψ _B (x, y). The Gerchberg-Saxton algorithm finds the solution to this problem by following an iterative process. More specifically, the Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeating transmission of the representation I between the spatial domain and the Fourier (spectral or frequency) domain _A (x, y) and I _B (x, y) data sets (amplitude and phase). A corresponding computer-generated hologram in the spectral domain is obtained by at least one iteration of the algorithm. The algorithm is convergent and arranged to produce a hologram representing the input image. The hologram may be an amplitude-only hologram, a phase-only hologram, or a full complex hologram.

In some embodiments, only the phase hologram is calculated using an algorithm based on the Gerchberg-Saxton algorithm, such as the algorithm described in uk patent 2498170 or 2501112, the entire contents of which are incorporated herein by reference. However, embodiments disclosed herein describe computing phase-only holograms by way of example only. In these embodiments, the Gerchberg-Saxton algorithm retrieves phase information ψ [ u, v ] of the Fourier transform of a dataset, which yields known amplitude information T [ x, y ], where the amplitude information T [ x, y ] represents a target image (e.g., a photograph). Since amplitude and phase are combined in nature in the fourier transform, the transformed amplitude and phase contain useful information about the accuracy of the computed data set. Thus, the algorithm may be used iteratively with feedback of amplitude and phase information. However, in these embodiments, only the phase information ψ [ u, v ] is used as a hologram to form a holographic representation of the target image at the image plane. A hologram is a dataset (e.g. a 2D array) of phase values.

In other embodiments, an algorithm based on the Gerchberg-Saxton algorithm is used to calculate the full complex hologram. A full complex hologram is a hologram having an amplitude component and a phase component. A hologram is a data set (e.g., a 2D array) comprising an array of complex data values, wherein each complex data value comprises an amplitude component and a phase component.

In some embodiments, the algorithm processes complex data and the fourier transform is a complex fourier transform. Complex data may be considered to include (i) a real component and an imaginary component, or (ii) an amplitude component and a phase component. In some embodiments, the two components of complex data are processed differently at various stages of the algorithm.

Fig. 2A illustrates a first iteration of an algorithm for computing a phase-only hologram, according to some embodiments. The input to the algorithm is an input image 210 comprising a 2D array of pixels or data values, wherein each pixel or data value is an amplitude or amplitude value. That is, each pixel or data value of the input image 210 has no phase component. Thus, the input image 210 may be considered as amplitude only or intensity only distribution. An example of such an input image 210 is a photograph or a frame of video comprising a time series of frames. The first iteration of the algorithm begins with a data formation step 202A that includes assigning a random phase value to each pixel of the input image using a random phase distribution (or random phase seed) 230 to form a starting complex data set, wherein each data element of the data set includes an amplitude and a phase. It can be said that the initial complex data set represents the input image in the spatial domain.

The first processing block 250 receives the initial complex data set and performs a complex fourier transform to form a fourier transformed complex data set. The second processing block 253 receives the fourier transformed complex data set and outputs a hologram 280A. In some embodiments, hologram 280A is a phase-only hologram. In these embodiments, the second processing block 253 quantizes each phase value and sets each amplitude value to 1 to form the hologram 280A. Each phase value is quantized according to a phase level that can be represented on a pixel of the spatial light modulator that will be used to "display" only the phase hologram. For example, if each pixel of the spatial light modulator provides 256 different phase levels, each phase value of the hologram is quantized to one of the 256 possible phase levels. Hologram 280A is a phase-only fourier hologram representing an input image. In other embodiments, hologram 280A is a full complex hologram that includes an array of complex data values (each including an amplitude component and a phase component) derived from a received fourier transformed complex data set. In some embodiments, the second processing block 253 constrains each complex data value to one of a plurality of allowable complex modulation levels to form the hologram 280A. The constraining step may include setting each complex data value to a nearest allowable complex modulation level in the complex plane. Hologram 280A may be said to represent an input image in the spectral or fourier or frequency domain. In some embodiments, the algorithm stops at this point.

However, in other embodiments, the algorithm continues as indicated by the dashed arrow in FIG. 2A. In other words, the steps following the dashed arrows in fig. 2A are optional (i.e., not essential to all embodiments).

The third processing block 256 receives the modified complex data set from the second processing block 253 and performs an inverse fourier transform to form an inverse fourier transformed complex data set. The complex data set of the inverse fourier transform can be said to represent the input image in the spatial domain.

The fourth processing block 259 receives the complex data set of the inverse fourier transform and extracts the distribution of amplitude values 211A and the distribution of phase values 213A. Optionally, the fourth processing block 259 evaluates the distribution of amplitude values 211A. In particular, the fourth processing block 259 may compare the distribution of amplitude values 211A of the complex data set of the inverse fourier transform with the input image 510, the input image 510 itself of course being the distribution of amplitude values. If the difference between the distribution of amplitude values 211A and the input image 210 is sufficiently small, the fourth processing block 259 may determine that the hologram 280A is acceptable. That is, if the difference between the distribution of amplitude values 211A and the input image 210 is sufficiently small, the fourth processing block 259 may determine that the hologram 280A is a sufficiently accurate representation of the input image 210. In some embodiments, the distribution of the phase values 213A of the complex data set of the inverse fourier transform is ignored for comparison purposes. It will be appreciated that any number of different methods may be employed to compare the distribution of amplitude values 211A to the input image 210, and that the present disclosure is not limited to any particular method. In some embodiments, the mean square error is calculated and if the mean square error is less than a threshold, then hologram 280A is considered acceptable. If the fourth processing block 259 determines that the hologram 280A is not acceptable, further iterations of the algorithm may be performed. However, this comparison step is not required, and in other embodiments, the number of iterations of the algorithm performed is predetermined or preset or user-defined.

Fig. 2B shows a second iteration of the algorithm and any further iterations of the algorithm. The distribution of phase values 213A of the previous iteration is fed back by the processing block of the algorithm. The distribution of amplitude values 211A is rejected, facilitating the distribution of amplitude values of the input image 210. In a first iteration, the data forming step 202A forms a first complex data set by combining a distribution of amplitude values of the input image 210 with a random phase distribution 230. However, in the second and subsequent iterations, the data forming step 202B includes forming a complex data set by combining (i) the distribution of phase values 213A from the previous iteration of the algorithm with (ii) the distribution of amplitude values of the input image 210.

The complex data set formed by the data forming step 202B of fig. 2B is then processed in the same manner as described with reference to fig. 2A to form a second iterative hologram 280B. Therefore, a description of the process is not repeated here. When the second iteration hologram 280B has been calculated, the algorithm may stop. However, any number of further iterations of the algorithm may be performed. It will be appreciated that the third processing block 256 is only required when the fourth processing block 259 is required or when further iterations are required. The output hologram 280B generally becomes better with each iteration. In practice, however, a point is typically reached where no measurable improvement is observed, or the positive benefits of performing further iterations are offset by the negative effects of the additional processing time. Thus, the algorithm is described as iterative and convergent.

Fig. 2C shows an alternative embodiment of the second and subsequent iterations. The distribution of phase values 213A of the previous iteration is fed back by the processing block of the algorithm. The distribution of amplitude values 211A is rejected, facilitating an alternative distribution of amplitude values. In this alternative embodiment, the alternative distribution of amplitude values is derived from the distribution of amplitude values 211 of the previous iteration. Specifically, the processing block 258 subtracts the distribution of amplitude values of the input image 210 from the distribution of amplitude values 211 of the previous iteration, scales the difference by a gain factor α, and subtracts the scaled difference from the input image 210. This is expressed mathematically by the following equation, where the subscript text and number represent the number of iterations:

R _n+1 [x,y]＝F'{exp(iψ _n [u,v])}

ψ _n [u,v]＝∠F{η·exp(i∠R _n [x,y])}

η＝T[x,y]-α(|R _n [x,y]|-T[x,y])

wherein:

f' is the inverse fourier transform;

f is the forward fourier transform;

r < x, y > is the complex data set output by the third processing block 256;

t [ x, y ] is the input or target image;

angle is the phase component;

ψ is phase-only hologram 280B;

η is the new distribution of amplitude values 211B; and

alpha is the gain factor.

The gain factor α may be fixed or variable. In some embodiments, the gain factor α is determined based on the size and rate of the input target image data. In some embodiments, the gain factor α depends on the number of iterations. In some embodiments, the gain factor α is only a function of the number of iterations.

In all other respects, the embodiment of fig. 2C is identical to the embodiments of fig. 2A and 2B. It can be said that only the phase hologram ψ (u, v) comprises the phase distribution in the frequency or fourier domain.

In some embodiments, the fourier transform is performed using a spatial light modulator. In particular, the hologram data is combined with second data providing optical power. That is, the data written to the spatial light modulation includes hologram data representing an object and lens data representing a lens. When displayed on a spatial light modulator and illuminated with light, the lens data mimics a physical lens-i.e., it focuses the light in the same manner as the corresponding physical optical element. Thus, the lens data provides optical power or focusing power. In these embodiments, the physical fourier transform lens 120 of fig. 1 may be omitted. It is known how to calculate data representing the lens. The data representing the lens may be referred to as a software lens. For example, a phase-only lens may be formed by calculating the phase retardation caused by each point of the lens due to its refractive index and spatially varying optical path length. For example, the optical path length at the center of the convex lens is greater than the optical path length at the edge of the lens. Only the amplitude lens may be formed by a fresnel zone plate. In the field of computer-generated holography, it is also known how to combine data representing a lens with a hologram so that the fourier transformation of the hologram can be performed without the need for a physical fourier lens. In some embodiments, the lensed data is combined with the hologram by simple addition, such as simple vector addition. In some embodiments, a physical lens is used in conjunction with a software lens to perform the fourier transform. Alternatively, in other embodiments, the fourier transform lens is omitted entirely, so that holographic reconstruction occurs in the far field. In a further embodiment, the hologram may be combined in the same way with raster data, i.e. data arranged to perform a raster function such as image steering. Also, it is known in the art how to calculate such data. For example, a phase-only grating may be formed by modeling the phase delay caused by each point on the surface of the blazed grating. The amplitude-only grating may simply be superimposed with the amplitude-only hologram to provide angular steering of the holographic reconstruction. The second data providing lensing and/or steering may be referred to as a light processing function or light processing pattern to distinguish from hologram data, which may be referred to as an image forming function or image forming pattern.

In some embodiments, the fourier transform is performed by a combination of a physical fourier transform lens and a software lens. That is, some of the optical power that contributes to the fourier transform is provided by the software lens, while the remaining optical power that contributes to the fourier transform is provided by one or more physical optics.

In some embodiments, a real-time engine is provided that is arranged to receive image data and calculate holograms in real-time using an algorithm. In some embodiments, the image data is video comprising a sequence of image frames. In other embodiments, the hologram is pre-computed, stored in computer memory and recalled as needed for display on the SLM. That is, in some embodiments, a repository of predetermined holograms is provided.

Embodiments relate, by way of example only, to fourier holography and the Gerchberg-Saxton type algorithm. The present disclosure is equally applicable to fresnel holography and fresnel holograms that can be calculated by similar methods. The present disclosure is also applicable to holograms calculated by other techniques such as point cloud based methods.

Light modulation

A spatial light modulator may be used to display a diffraction pattern comprising a computer-generated hologram. If the hologram is a phase-only hologram, a spatial light modulator modulating the phase is required. If the hologram is a full complex hologram, a spatial light modulator that modulates phase and amplitude may be used, or a first spatial light modulator that modulates phase and a second spatial light modulator that modulates amplitude may be used.

In some embodiments, the light modulating elements (i.e., pixels) of the spatial light modulator are cells containing liquid crystals. That is, in some embodiments, the spatial light modulator is a liquid crystal device in which the optically active component is liquid crystal. Each liquid crystal cell is configured to selectively provide a plurality of light modulation levels. That is, each liquid crystal cell is configured to operate at a light modulation level selected from a plurality of possible light modulation levels at any time. Each liquid crystal cell is dynamically reconfigurable to a different light modulation level than the plurality of light modulation levels. In some embodiments, the spatial light modulator is a reflective Liquid Crystal On Silicon (LCOS) spatial light modulator, although the present disclosure is not limited to this type of spatial light modulator.

LCOS devices provide dense arrays of light modulating elements or pixels within a small aperture (e.g., a few centimeters wide). The pixels are typically about 10 microns or less, which results in a diffraction angle of a few degrees, meaning that the optical system can be compact. The small aperture of a fully illuminated LCOS SLM is much easier than the large aperture of other liquid crystal devices. LCOS devices are typically reflective, meaning that the circuitry driving the LCOS SLM pixels can be buried under a reflective surface. This results in a higher aperture ratio. In other words, the pixels are densely packed, meaning that there is little dead space between the pixels. This is advantageous because it reduces optical noise in the playback field. LCOS SLMs use a silicon backplane, which has the advantage that the pixels are optically flat. This is particularly important for phase modulation devices.

A suitable LCOS SLM is described below, by way of example only, with reference to fig. 3. LCOS devices are formed using a monocrystalline silicon substrate 302. It has a 2D array of square planar aluminum electrodes 301, spaced apart by gaps 301a, arranged on the upper surface of the substrate. Each electrode 301 may be addressed by a circuit 302a buried in the substrate 302. Each electrode forms a respective plane mirror. An alignment layer 303 is disposed on the electrode array, and a liquid crystal layer 304 is disposed on the alignment layer 303. The second orientation layer 305 is arranged on a planar transparent layer 306, for example made of glass. A single transparent electrode 307 made of, for example, ITO is disposed between the transparent layer 306 and the second alignment layer 305.

Each square electrode 301 together with the coverage area of the transparent electrode 307 and the intermediate liquid crystal material define a controllable phase modulating element 308, commonly referred to as a pixel. The effective pixel area or fill factor is the percentage of the total pixel that is optically active, taking into account the space between pixels 301 a. By controlling the voltage applied to each electrode 301 relative to the transparent electrode 307, the characteristics of the liquid crystal material of the respective phase modulating element can be varied to provide a variable retardation to light incident thereon. The effect is to provide only phase modulation to the wavefront, i.e. no amplitude effects occur.

The described LCOS SLM outputs spatially modulated light in a reflective manner. Reflective LCOS SLMs have the advantage that the signal lines, grating lines and transistors are located under the mirror, which results in a high fill factor (typically greater than 90%) and high resolution. Another advantage of using a reflective LCOS spatial light modulator is that the thickness of the liquid crystal layer may be half that required when using a transmissive device. This greatly increases the switching speed of the liquid crystal (a key advantage of projecting moving video images). However, the teachings of the present disclosure can equally be implemented using transmissive LCOS SLMs.

Optical channel

The optical system disclosed herein is applicable to pupil expansion with any diffracted light field. In some embodiments, the diffracted light field is a holographic light field-i.e., a composite light field spatially modulated according to the hologram of the image rather than the image itself. In some embodiments, the hologram is a special type of hologram that angularly divides/directs image content. This type of hologram is further described herein as merely an example of a diffracted light field compatible with the present disclosure. Other types of holograms may be used in conjunction with the display systems and light engines disclosed herein.

A display system and method including a waveguide pupil expander is described below. As will be familiar to readers of skill in the art, a waveguide may be considered a "pupil expander" in that it may be used to augment the area that light emitted by a relatively small light emitter (e.g., a relatively small SLM or other pixelated display device used in the apparatus described herein) may be observed by a human observer or other viewing system located some distance (e.g., a relatively large distance) from the light emitter. The waveguide achieves this by increasing the number of transmission points that output light to the observer. As a result, light may be seen from a plurality of different observer positions, for example, an observer may be able to move their head, thereby moving their line of sight, while still being able to see light from the light emitters. Thus, it can be said that by using the waveguide pupil expander, the "eye box" or "eye movement box" of the observer is enlarged. This has many useful applications such as, but not limited to, heads-up displays, such as, but not limited to, automotive heads-up displays.

The display systems described herein may be configured to direct light, e.g., a diffracted light field, through a waveguide pupil expander to provide pupil expansion in at least one dimension, e.g., in two dimensions. The diffracted light field may include light output by a Spatial Light Modulator (SLM), such as an LCOS SLM. For example, the diffracted light field may include light encoded by a hologram displayed by the SLM. For example, the diffracted light field may include holographically reconstructed image light, corresponding to a hologram displayed by SL M. The hologram may include a Computer Generated Hologram (CGH), such as, but not limited to, a point cloud hologram, a fresnel hologram, or a fourier hologram. Holograms may be referred to as "diffractive structures" or "modulation patterns". The SLM or other display device may be arranged to display a diffraction pattern (or modulation pattern) comprising a hologram and one or more other elements, such as a software lens or diffraction grating, in a manner familiar to the skilled reader.

The hologram may be calculated to provide guidance of the diffracted light field. This is described in detail in GB2101666.2, GB2101667.0 and GB2112213.0, all of which are incorporated herein by reference. In general, holograms can be calculated to correspond to images to be holographically reconstructed. The image to which the hologram corresponds may be referred to as an "input image" or "target image". The hologram may be calculated such that when it is displayed on the SLM and properly illuminated, it forms a light field (output by the SLM) comprising a spatially modulated light cone. In some embodiments, the light cone comprises a plurality of continuous light channels of spatially modulated light, which correspond to respective continuous areas of the image. However, the present disclosure is not limited to this type of hologram.

Although we refer to herein as a "hologram" or "Computer Generated Hologram (CGH)", it should be understood that the SLM may be configured to display a plurality of different holograms either continuously or dynamically according to sequence. The systems and methods described herein are applicable to dynamic display of a plurality of different holograms.

Fig. 4A to 5 show examples of one type of hologram that may be displayed on a display device, such as an SLM, which may be used in combination with the pupil expander disclosed herein. However, this example should not be considered as limiting the present disclosure.

Fig. 4A shows an image 452 for projection, comprising eight image areas/components V1 to V8. For example only, fig. 4A shows eight image components, and image 452 may be divided into any number of components. Fig. 4A also shows a coded light pattern 454 (i.e., a hologram) that may reconstruct the image 452-e.g., when transformed by a lens of a suitable viewing system. The coded light pattern 454 includes first through eighth sub-holograms or components H1 through H8 corresponding to the first through eighth image components/regions V1 through V8. Fig. 4A further shows how the hologram breaks down the image content by angle. Thus, the hologram is characterized by its guiding of light. This is shown in fig. 4B. Specifically, the hologram in this example directs light into a plurality of discrete areas. In the example shown, the discrete areas are discs, but other shapes are also contemplated. The size and shape of the optimum disk after propagation through the waveguide may be related to the size and shape of the aperture of the optical system (e.g., the entrance pupil of the viewing system).

Fig. 5 shows a viewing system 500 comprising a display device displaying holograms calculated as shown in fig. 4A and 4B.

The viewing system 500 includes a display device that includes an LCOS 502 in this arrangement. LCOS 502 is arranged to display a modulation pattern (or "diffraction pattern") comprising a hologram and project light that has been holographically encoded to eye 505, eye 505 comprising a pupil acting as aperture 504, lens 509, and a retina acting as a viewing plane (not shown). There is a light source (not shown) arranged to illuminate the LCOS 502. The lens 509 of the eye 505 performs the hologram-to-image conversion. The light source may be of any suitable type. For example, it may comprise a laser source.

The viewing system 500 further includes a waveguide 508 between the LCOS 502 and the eye 505. The presence of the waveguide 508 enables all angular content from the LCOS 502 to be received by the eye, even at the relatively large projection distances shown. This is because the waveguide 508 acts as a pupil expander in a well known manner and is therefore only briefly described here.

Briefly, the waveguide 508 shown in FIG. 5 includes a substantially elongated structure. In this example, waveguide 508 comprises an optical plate of refractive material, although other types of waveguides are well known and may be used. The waveguide 508 is positioned to intersect the cone of light (i.e., the diffracted light field) projected from the LCOS 502, for example, at an oblique angle. In this example, the size, position, and location of the waveguide 508 is configured to ensure that light from each of the eight light beams within the light cone enters the waveguide 508. Light from the cone of light enters the waveguide 508 via a first planar surface of the waveguide 508 (located closest to the LCOS 502) and is at least partially guided along the length of the waveguide 508 before being emitted via a second planar surface of the waveguide 508 (located closest to the eye) that is substantially opposite the first surface. It will be readily appreciated that the second planar surface is partially reflective, partially transmissive. In other words, as each ray propagates from the first planar surface within waveguide 508 and impinges on the second planar surface, some light will be transmitted out of waveguide 508 and some will be reflected back by the second planar surface to the first planar surface. The first planar surface is reflective such that all light striking it from within waveguide 508 will be reflected back to the second planar surface. Thus, some light may simply be refracted between the two planar surfaces of waveguide 508 before being transmitted, while other light may be reflected, and thus may undergo one or more reflections (or "bounces") between the planar surfaces of waveguide 508 before being transmitted.

Fig. 5 shows a total of nine "bounce" points B0 through B8 along the length of waveguide 408. Although as shown in fig. 4A, light associated with all points of the image (V1-V8) is transmitted out of the waveguide at each "bounce" from the second planar surface of the waveguide 508, only light from one angular portion of the image (e.g., light of one of V1 to V8) has a trajectory that enables it to reach the eye 505 from each respective "bounce" point B0 to B8. Furthermore, light from different angular portions (V1 to V8) of the image reaches the eye 505 from each respective "bounce" point. Thus, in the example of fig. 5, each angular channel of encoded light reaches the eye only once from waveguide 508.

The above-described methods and apparatus may be implemented in a variety of different applications and viewing systems. For example, they may be implemented in head-up displays (HUDs) or in head or Helmet Mounted Devices (HMDs) such as Augmented Reality (AR) HMDs.

Although virtual images have been generally discussed herein, which require the eye to convert the received modulated light to form a perceived image, the methods and apparatus described herein may be applied to real images.

Two-dimensional pupil expansion

Although the arrangement shown in fig. 5 includes a single waveguide that provides pupil expansion in one dimension, pupil expansion may be provided in more than one dimension, for example in two dimensions. Furthermore, while the example in fig. 5 uses holograms that have been calculated to create light channels, each light channel corresponding to a different portion of an image, the present disclosure and the systems described below are not limited to this hologram type.

Fig. 6 shows a perspective view of a system 600 comprising two replicators 604, 606 arranged for expanding a light beam 602 in two dimensions.

In the system 600 of fig. 6, the first replicator 604 includes a first pair of surfaces stacked parallel to each other, arranged to provide replication or pupil expansion in a manner similar to the waveguide 508 of fig. 5. The first pair of surfaces are similar in size and shape to each other (and in some cases identical) and are substantially elongated in one direction. The collimated beam 602 is directed to an input on a first replicator 604. The light of beam 602 is replicated in a first direction along the length of first replicator 604 due to the process of internal reflection between the two surfaces, as well as the partial transmission of light from each of a plurality of output points on one of the surfaces (the upper surface, as shown in fig. 6), as is familiar to the skilled reader. Thus, a first plurality of duplicate beams 608 are emitted from the first replicator 604 towards the second replicator 606.

The second replicator 606 comprises a second pair of surfaces stacked parallel to each other, arranged to receive each collimated beam of the first plurality of beams 608, and further arranged to provide replication or pupil expansion by expanding each of these beams in a second direction substantially orthogonal to the first direction. The first pair of surfaces are similar in size and shape to each other (and in some cases identical) and are substantially rectangular. The second replicator is implemented with a rectangular shape such that it has a length along a first direction to receive the first plurality of light beams 608 and a length along a second orthogonal direction to provide replication in the second direction. The light of each beam within the first plurality of beams 608 is replicated in the second direction due to the internal reflection process between the two surfaces and the partial transmission of light from each of the plurality of output points on one of the surfaces (the upper surface as shown in fig. 6). Thus, a second plurality of light beams 610 is emitted from the second replicator 606, wherein the second plurality of light beams 610 includes replicas of the input light beam 602 along each of the first direction and the second direction. Thus, the second plurality of light beams 610 may be considered to comprise a two-dimensional grid or array of duplicate light beams.

Thus, it can be said that the first and second replicators 604, 605 of FIG. 6 combine to provide a two-dimensional replicator (or "two-dimensional pupil expander").

Improved waveguide

As described with respect to fig. 5, light in the waveguide 508 is reflected between the partially reflective, partially transmissive, and reflective surfaces of the waveguide. The light may undergo one or more reflections or bounces between the two reflective/reflective-transmissive planar surfaces, and at each point of bounces on the partially transmissive surface, the light is split such that a portion of the light is emitted out of the waveguide and the remaining (typically larger) portion of the light is reflected to continue to propagate between the two surfaces of the waveguide. This effectively results in the partially transmissive surface of the waveguide providing n light emitting regions for light of the waveguide between the first surface and the second surface. After each bounce point/launch region, the intensity of the light propagating in the waveguide will decrease. In other words, the intensity of light propagating in the waveguide decreases in the direction of the waveguide.

Desirably, the intensity of light emitted from the waveguide at each of the n light emitting regions is substantially the same. This may be achieved by providing an improved waveguide in which a layered coating is provided on a partially transmissive surface of the waveguide such that the transmissivity of the partially transmissive surface decreases in the direction of the waveguide. This illustrates the decrease in intensity of light propagating in the waveguide direction.

Fig. 7 is a schematic cross-sectional view of a waveguide 708 according to the present disclosure. The waveguide 708 includes a first surface 702 and a second surface 704. The optical field 706 (represented by a ray in fig. 7) is shown propagating through the waveguide 708. The second surface 704 comprises an input port arranged to receive a light field. The first surface 702 is partially transmissive, partially reflective, and includes a coating 703. The term "coating" is used herein for convenience only and those skilled in the art will appreciate that components described as "coating" may be formed by any method, including but not limited to coating processes. The second surface 704 is substantially totally reflective (except at the input end). Fig. 7 shows the path of the optical field through the waveguide, bouncing between the first and second surfaces. At each reflection at the first surface, the light field is split such that a portion of the light field is emitted through the first surface, while the remaining portion is reflected and continues to propagate between the first and second surfaces by reflection. Thus, an emission region is effectively formed at each reflection point. Fig. 7 shows 6 emitter regions, however those skilled in the art will appreciate that there may of course be a greater or lesser number of reflective and emitter regions. Fig. 7 is merely illustrative.

The coating 703 includes multiple layers of first dielectrics and multiple layers of second dielectrics that are alternately arranged. This is shown in fig. 8. The layer of the coating is denoted herein by a number and the layer in contact with the first surface 702 is the first layer (layer 901). Layer 902 is on top of layer 901 and layer 903 is on top of layer 902. The layer furthest from the first surface 702 on top of layer 903 is a fourth layer 904. In this example, layers 901 and 903 are formed of silicon dioxide (SiO 2) and layers 902 and 904 are formed of titanium dioxide (TiO 2) such that the layers are in an alternating configuration with subsequent SiO2 layers (first dielectric) separated by TiO2 layers (second dielectric).

Each of the layers 901 to 904 has a varying thickness in the waveguide direction (left to right in fig. 9), and in this embodiment, has a linear profile as an example. In other words, the rate of change of the thickness of each layer is constant. The profile of each layer can be characterized by a percentage change in thickness. Each layer has a first end 906 and a second end 908. The percent change in thickness is defined as the change in thickness from the first end 906 to the second end 908 divided by the thickness of the first end 906 multiplied by 100. For the case of the first layer 901, the percent change in thickness is 100× (final thickness 912-initial thickness 910)/initial thickness 910.

Layer 903 has the same percentage change in thickness as layer 901. In addition, the percentage change values of layers 901 and 903 are both positive (i.e., the thickness of the layers increases from first end 906 to second end 908). Layers 902 and 904 have different percentage variations from each other and from layers 901 and 903. In addition, the percent change of layers 902 and 904 is both negative (i.e., the thickness of the layers decreases from first end 906 to second end 908).

The inventors have found that by selecting a suitable number of alternating layers of the first and second dielectric, which layers have a suitable thickness and percentage change in thickness from the first end to the second end, a first surface of the waveguide with increased transmissivity in the direction of the waveguide can be provided. In this way, the intensity of the light field emitted at each emission region (i.e. the intensity of each replica emitted at each emission region) is substantially constant. This may advantageously achieve a substantially spatially uniform light emission from the waveguide.

Fig. 9 shows an ideal exponential increase in the transmissivity of the first surface 702, which shows the transmissivity in the Y-axis and the position along the first surface 702 in the X-axis. The numbers on the X-axis represent the n-emission regions. Specifically, the transmittance was according to the followingThe equation increases: Where L is the optical loss factor of the waveguide material.

The example shown in fig. 8 is merely representative. Fig. 8 is not drawn to scale. Typically, the coating according to the invention comprises more than four layers. The following discloses 9 examples of layered coatings according to the invention, which provide a satisfactory increase in the transmittance of the first surface. Each of these examples is determined by simulation. The skilled artisan will appreciate that the present disclosure is not limited to the examples disclosed herein. For example, the coating may include a different number of layers (more or less) than the coatings disclosed herein. Furthermore, layers of different dielectric materials may be used.

First example

Fig. 10a to 10c relate to a first real example of a coating according to the invention. The coating of this first example comprised 12 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 12 such that light emitted from the waveguide passes through each of the layers 1 to 12 in turn. The odd layers (layers L1, L3, L5, L7, L9, and L11) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10 and L12) are TiO2 layers.

Fig. 10a and 10b show how the thickness of each layer varies with distance along the first surface of the waveguide (i.e. from the first end to the second end of each layer). The Y-axis represents thickness and the X-axis represents position in the waveguide direction. The numbers 1 to 10 on the X-axis represent the emission areas of the first surface. Fig. 10a shows the SiO2 layer (i.e. the odd layer in this example). Fig. 10b shows a TiO2 layer (i.e. an even layer in the example).

As shown in fig. 10a, there are two subsets of SiO2 layers. The first subset of layers has a first value of percent thickness variation. These layers are represented by continuous (i.e., uninterrupted) lines in fig. 10 a. The second subset of layers has a second value different from the percent thickness variation of the first value. These layers are indicated in fig. 10a by dashed (i.e. broken) lines. The first and second values in this example are both negative. In this example, the first value of the percent change is-50% +/-10%. The second value of the percent change is-60% +/-10%. For the avoidance of doubt, the first value is different from the second value. The minimum thickness of the thinnest layer is 50nm +/-15nm.

As shown in fig. 10b, there are two subsets of TiO2 layers. The first subset of layers has a third value of percent thickness variation. These layers are represented by continuous lines in fig. 10 b. The second subset of layers has a fourth value of percent thickness variation different from the first value. These layers are indicated by dashed lines in fig. 10 b. The first and second values in this example are both positive. In this example, the third value of the percent change is 20% +/-10%. The fourth value of the percent change is 60% +/-10%. The minimum thickness of the thinnest layer is 50nm +/-15nm.

Those skilled in the art will appreciate that while the percent thickness variation of the two layers may be the same, the maximum and minimum thicknesses of the layers may be different. For example, a first layer having a minimum thickness of 2nm and a maximum thickness of 4nm has a percentage increase of 100%. The second layer, having a minimum thickness of 5nm and a maximum thickness of 10nm, also has a 100% percent increase, although the absolute thickness of the two layers is different.

The coating waveguide according to the invention generally behaves differently at different wavelengths. As the skilled person will appreciate, a combination of blue, green and red may be used to provide a full color image (i.e. light having three different wavelengths). For example, in many holographic systems, blue, green, and red light sources are used to produce full color images. If the waveguide of the present disclosure is adapted for use in such a system, the transmittance of the coated first surface should substantially follow the ideal transmittance shown in fig. 9 at each desired wavelength.

Fig. 10c is a graph showing the transmittance of the first surface of the waveguide of the first example. The Y-axis represents transmittance. The X-axis represents the nth emitter region along the first surface of the waveguide. The solid (uninterrupted) line 1002 of fig. 10c represents the ideal transmission behavior (also shown in fig. 9). Three dashed (intermittent) lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 10c are associated with blue laser 1004, green laser 1006 and red laser 1008, respectively. Fig. 10c shows how the coating of the first example provides good transmission properties at each of the three wavelengths.

The inventors have realized that when the problem of providing varying transmissivity behavior is limited to only three specific wavelengths, an alternating stack of first and second dielectric layers can provide a desired transmissivity increase in the waveguide direction even when the number of discrete values of the thickness percentage variation is smaller (preferably significantly smaller) than the total number of layers. This is advantageous because it may be simpler, cheaper and more reliable to manufacture than a coating comprising a unique percentage change in the thickness of each layer. This will be explained with reference to the following first example.

The first example includes a 12-layer dielectric. However, from the first end to the second end of the layer, the percent change in thickness of each layer has one of four discrete allowable values. In particular, the percentage change in thickness of each layer of the first dielectric is equal to the first value or the second value, and the percentage change in thickness of each layer of the second dielectric is equal to the third value or the fourth value. Thus, the total number of layers of the first and second dielectrics (i.e., 12) is greater than the total number of discrete allowed values (i.e., 4). As shown in fig. 10c, the transmittance of the blue, green and red wavelengths for which the coating is designed is acceptable. However, as shown in fig. 11, the transmittance of the coated waveguide does not perform well at other wavelengths.

Fig. 11 is a diagram. The Y-axis of fig. 11 represents transmittance. The X-axis represents the nth emitter region along the first surface of the waveguide. The solid line 1102 represents the ideal transmittance of the first surface. The solid line 1102 appears different from that shown in fig. 9, but because the ratio of the Y-axis in fig. 11 is different from that in fig. 9. The three dashed lines show the simulated transmittance of the waveguide of the first example without the waveguide configured for three different wavelengths of electromagnetic radiation (1104, 1106, 1108). The three dashed lines indicate that the transmittance of the coated waveguide does not correspond to the desired behavior at the respective wavelengths. The 1104 wavelength deviates very significantly from the ideal behavior.

Thus, a waveguide with the first example coating may not be acceptable for transmittance at wavelengths other than the particular wavelength for which the waveguide coating is designed. But this is not important for applications where the wavelengths are not transmitted through the waveguide (i.e., not used for imaging).

Second example

Fig. 12a to 12c relate to a second real example of a coating according to the invention. The coating of this second example also contained 12 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 12 such that light emitted from the waveguide passes through each of the layers 1 to 12 in turn. The odd layers (layers L1, L3, L5, L7, L9, and L11) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10 and L12) are TiO2 layers.

Fig. 12a and 12b show how the thickness of each layer varies with distance along the first surface of the waveguide (i.e. from the first end to the second end of each layer). The Y-axis represents thickness and the X-axis represents position in the waveguide direction. The numbers 1 to 10 on the X-axis represent the emission areas of the first surface. Fig. 12a shows the SiO2 layer (i.e. the odd layer). Fig. 12b shows a TiO2 layer (i.e. even layer).

As shown in fig. 12a, there are two subsets of SiO2 layers. The first subset of layers has a first value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 12 a. The second subset of layers has a second value different from the percent thickness variation of the first value. These layers are represented by dashed (broken) lines in fig. 12 a. In this example, the first value of the percentage change is +80++/-10%. The second value of the percent change is-60% +/-10%. The minimum thickness of the thinnest layer is 40nm +/-15nm.

As shown in fig. 12b, there are two subsets of TiO2 layers. The first subset of layers has a third value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 12 b. The second subset of layers has a fourth value of the thickness percentage that is different from the third value. These layers are represented by dashed (broken) lines in fig. 12 b. The third value of the percent change is +45++/-10%. The fourth value of the percent change is-20% +/-10%. The minimum thickness of the thinnest layer is 40nm +/-10%.

Fig. 12c is a graph showing the transmittance of a first surface of a waveguide including a layered coating of a second example. The Y-axis represents transmittance. The X-axis represents the nth emitter region along the first surface of the waveguide. The solid (uninterrupted) line 1202 of fig. 12c represents the ideal transmission behavior (also shown in fig. 9). Three dashed (intermittent) lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 12c are associated with blue laser 1204, green laser 1206 and red laser 1208, respectively. Fig. 12c shows how the waveguide of the second example provides acceptable transmission performance at each of the three wavelengths.

Third example

Fig. 13a to 13c relate to a third real example of a coating according to the invention. The coating of this third example comprises 16 alternating layers of SiO2 and TiO 2. The layers are numbered 1 to 16 such that light emitted from the waveguide passes through each of the layers 1 to 16 in turn. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, and L15) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10, L12, L14 and L16) are TiO2 layers.

Fig. 13a and 13b show how the thickness of each layer varies with distance along the first surface of the waveguide (i.e. from the first end to the second end of each layer). The Y-axis represents thickness and the X-axis represents position in the waveguide direction. The numbers 1 to 10 on the X-axis represent the emission areas of the first surface. Fig. 13a shows the SiO2 layer (i.e. the odd layer). Fig. 13b shows a TiO2 layer (i.e. even layer).

As shown in fig. 13a, there are two subsets of SiO2 layers. The first subset of layers has a first value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 13 a. The second subset of layers has a second value different from the percent thickness variation of the first value. These layers are indicated by dashed (broken) lines in fig. 13 a. The first value of the percent change is-5% +/-2%. The second value of the percent change is-70% +/-10%. The minimum thickness of the thinnest layer is 20nm +/-15nm.

As shown in fig. 13b, there are two subsets of TiO2 layers. The first subset of layers has a third value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 13 b. The second subset of layers has a fourth value of the thickness percentage that is different from the third value. These layers are indicated by dashed (broken) lines in fig. 13 b. The third value of the percent change is +60++/-10%. The fourth value of the percent change is +5++/-2%. The minimum thickness of the thinnest layer is 35nm +/-15nm.

Fig. 13c is a graph showing the transmittance of a first surface of a waveguide including a layered coating of a third example. The Y-axis represents transmittance. The X-axis represents the nth emitter region along the first surface of the waveguide. The solid line 1302 of fig. 13c represents the ideal transmission behavior (also shown in fig. 9). Three dashed (intermittent) lines show the simulated transmittance of the waveguide at three different electromagnetic wave wavelengths. The three wavelengths shown in fig. 13c relate to blue laser 1304, green laser 1306 and red laser 1308, respectively. Fig. 13c shows how the waveguide of the third example provides acceptable transmission performance at each of the three wavelengths.

Fourth example

Fig. 14a to 14c relate to a fourth real example of a coating according to the invention. The coating of this fourth example comprises 20 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 20 such that light emitted from the waveguide passes through each of the layers 1 to 20 in turn. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, and L19) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, and L20) are TiO2 layers.

Fig. 14a and 14b show how the thickness of each layer varies with distance along the first surface of the waveguide (i.e. from the first end to the second end of each layer). The Y-axis represents thickness and the X-axis represents position in the waveguide direction. The numbers 1 to 10 on the X-axis represent the emission areas of the first surface. Fig. 14a shows the SiO2 layer (i.e. the odd layer). Fig. 14b shows a TiO2 layer (i.e., even layer).

As shown in fig. 14a, there are two subsets of SiO2 layers. The first subset of layers has a first value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 14 a. The second subset of layers has a second value different from the percent thickness variation of the first value. These layers are represented by dashed (broken) lines in fig. 14 a. The first value of the percent change is-15% +/-10%. The second value of the percent change is-60% +/-10%. The minimum thickness of the thinnest layer is 5nm +/-2nm.

As shown in fig. 14b, there are two subsets of TiO2 layers. The first subset of layers has a third value of percent thickness variation. These layers are represented by continuous (uninterrupted) lines in fig. 14 b. The second subset of layers has a fourth value of the thickness percentage that is different from the third value. These layers are represented by dashed (broken) lines in fig. 14 b. The third value of the percent change is +30++/-10%. The fourth value of the percent change is +10++/-5%. The minimum thickness of the thinnest layer is 20nm +/-15nm.

Fig. 14c is a graph showing the transmittance of a fourth surface of a waveguide including the layered coating of the first example. The Y-axis represents transmittance. The X-axis represents the nth emitter region along the first surface of the waveguide. The solid line 1402 of fig. 14c represents the ideal transmission behavior (also shown in fig. 9). The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 14c relate to blue laser 1404, green laser 1406 and red laser 1408, respectively. Fig. 14c shows how the waveguide of the fourth example provides acceptable transmission performance at each of the three wavelengths.

Fifth example

Fig. 15a to 15c relate to a fifth real example of a coating according to the invention. The coating of this fifth example comprised 20 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 20 such that light emitted from the waveguide passes through each of the layers 1 to 20 in turn. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, and L19) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, and L20) are TiO2 layers. Fig. 15a shows the SiO2 layer (i.e. the odd layer). Fig. 15b shows a TiO2 layer (i.e., even layer).

The first subset of layers of fig. 15a has a first value of percent thickness change represented by continuous (uninterrupted) lines. A second subset of the layers has a second value of percent thickness variation represented by a dashed (discontinuous) line. The first value of the percent change is-10% +/-5%. The second value of the percent change is-90% +/-5%. The minimum thickness of the thinnest layer is 5nm +/-2nm.

The first subset of layers of fig. 15b has a third value of percent thickness change, represented by a continuous (uninterrupted) line. The second subset of layers has a fourth value of the thickness percentage represented by a dashed (discontinuous) line. The third value of the percent change is +25++/-10%. The fourth value of the percent change is-0.5% +/-0.05%. The minimum thickness of the thinnest layer is 40nm +/-15nm.

Fig. 15c shows how the waveguide of the fifth example provides acceptable transmission performance at each of the three wavelengths. The solid line 1502 of fig. 15c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 15c relate to blue laser light 1504, green laser light 1506 and red laser light 1508, respectively.

Sixth example

Fig. 16a to 16c relate to a sixth real example of a coating according to the invention. The sixth example coating comprises 24 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, and L23) are SiO2 layers. The even numbered layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22 and L24) are TiO2 layers. Fig. 16a shows the SiO2 layer (i.e. the odd layer). Fig. 16b shows a TiO2 layer (i.e., even layer).

The first subset of layers of fig. 16a has a first value of percent thickness change represented by continuous (uninterrupted) lines. A second subset of the layers has a second value of percent thickness variation represented by a dashed (discontinuous) line. The first value of the percent change is +20++/-10%. The second value of the percent change is-55% +/-10%. The minimum thickness of the thinnest layer is 15nm +/-10nm.

The first subset of layers of fig. 16b has a third value of percent thickness change, represented by a continuous (uninterrupted) line. The second subset of layers has a fourth value of the thickness percentage represented by a dashed (discontinuous) line. The third value of the percent change is +20++/-10%. The fourth value of the percent change is +15++/-10%. The minimum thickness of the thinnest layer is 10nm +/-5nm.

Fig. 16c shows how the waveguide of the sixth example provides acceptable transmission performance at each of the three wavelengths. The solid line 1602 of fig. 16c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 15c relate to blue laser 1604, green laser 1606 and red laser 1608, respectively.

Seventh example

Fig. 17a to 17c relate to a seventh real example of a coating according to the invention of the present disclosure. The seventh example coating includes 24 alternating layers of SiO2 and TaO 5. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, and L23) are SiO2 layers. The even numbered layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22 and L24) are TaO5 layers. Fig. 17a shows the SiO2 layer (i.e. the odd layer). Fig. 17b shows the TaO5 layer (i.e. even layer).

The first subset of layers of fig. 17a has a first value of percent thickness change represented by continuous (uninterrupted) lines. A second subset of the layers has a second value of percent thickness variation represented by a dashed (discontinuous) line. The first value of the percentage change is +110.0% +/-10%. The second value of the percent change is-20% +/-10%. The minimum thickness of the thinnest layer is 60nm +/-15nm.

The first subset of layers of fig. 17b has a third value of percent thickness change, represented by a continuous (uninterrupted) line. The second subset of layers has a fourth value of the thickness percentage represented by a dashed (discontinuous) line. The third value of the percent change is +20++/-10%. The fourth value of the percent change is-70% +/-10%. The minimum thickness of the thinnest layer is 20nm +/-15nm.

Fig. 17c shows how the waveguide of the sixth embodiment provides acceptable transmission performance at each of the three wavelengths. The solid line 1702 of fig. 17c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 15c relate to blue laser 1604, green laser 1606 and red laser 1608, respectively.

Eighth example

Fig. 18a to 18c relate to an eighth real example of a coating according to the invention. The eighth example coating comprised 24 alternating layers of SiO2 and TaO 5. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, and L23) are SiO2 layers. The even numbered layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22 and L24) are TaO5 layers. Fig. 18a shows the SiO2 layer (i.e. the odd layer). Fig. 18b shows the TaO5 layer (i.e. even layer).

The first subset of layers of fig. 18a has a first value of percent thickness change represented by continuous lines. The second subset of layers has a second value of percent thickness variation represented by the dashed line. The first value of the percent change is-10% +/-5%. The second value of the percent change is-75% +/-10%. The minimum thickness of the thinnest layer is 20nm +/-15nm.

The first subset of layers of fig. 18b has a third value of percent thickness change, represented by a continuous line. The second subset of layers has a fourth value of percent thickness indicated by the dashed line. The third value of the percent change is +65++/-10%. The fourth value of the percent change is-5% +/-2%. The minimum thickness of the thinnest layer is 55nm +/-15nm.

Fig. 18c shows how the waveguide of the eighth example provides acceptable transmission performance at each of the three wavelengths. The solid line 1802 of fig. 18c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 18c relate to blue laser 1804, green laser 1806 and red laser 1808, respectively.

Ninth example

Fig. 19a to 19c relate to a ninth real example of a coating according to the invention. The coating of this ninth example included 30 alternating layers of SiO2 and HfO 2. The layers are numbered from 1 to 30 such that light emitted from the waveguide passes through each of the layers 1 to 30 in turn. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, L23, L25, L27, and L29) are SiO2 layers. The even numbered layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22, L24, L26, L28, and L30) are HfO2 layers. Fig. 19a shows the SiO2 layer (i.e. the odd layer). Fig. 18b shows the HfO2 layer (i.e., even layer).

The first subset of layers of fig. 19a has a first value of percent thickness change represented by continuous lines. The second subset of layers has a second value of percent thickness variation represented by the dashed line. The first value of the percent change is-100% +/-10%. The second value of the percent change is-2% +/-0.5%. The minimum thickness of the thinnest layer is 0.1nm +/-0.01nm.

The first subset of layers of fig. 19b has a third value of percent thickness variation represented by continuous lines. The second subset of layers has a fourth value of percent thickness indicated by the dashed line. The third value of the percent change is +15++/-5%. The fourth value of the percent change is-0.5% +/-0.25%. The minimum thickness of the thinnest layer is 10nm +/-5nm.

Fig. 19c shows how the waveguide of the ninth example provides acceptable transmission performance at each of the three wavelengths. The solid line 1902 of fig. 19c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 19c relate to blue laser 1904, green laser 1906 and red laser 1908, respectively.

Method of manufacture

An advantage of the layered coating of the present disclosure is that it can be manufactured in an inexpensive, fast and reliable manner. Here, an example of such a method is disclosed. However, those skilled in the art will appreciate that other methods are possible.

The method comprises the following steps: providing a waveguide substrate comprising a pair of parallel surfaces arranged to provide a waveguide therebetween; and applying the plurality of first dielectric layers and the plurality of second dielectric layers to the waveguide substrate such that the first and second dielectric layers are in an alternating configuration.

The apparatus for performing the method comprises two sources of a first dielectric material (e.g. SiO 2) and two sources of a second dielectric material (e.g. TiO 2), a shadow mask comprising first to fourth trapezoidal apertures, and means for moving the waveguide substrate relative to the shadow mask. Each aperture of the shadow mask is associated with a source of dielectric material. During the fabrication of each layer, dielectric material from one of the sources is configured to flow through one of the apertures of the shadow mask. The waveguide substrate is moved relative to the shadow mask (and vice versa) such that the shadow mask is positioned between the light source and the waveguide substrate. The waveguide substrate passes under the aperture and a layer of dielectric material is formed on a surface of the waveguide substrate. This is shown in fig. 19.

Fig. 20 is a schematic cross-sectional view of a portion of an apparatus for manufacturing waveguides according to the present invention, the cross-section being in the X-Y plane. The portion of the apparatus shown in fig. 20 includes a first source of SiO2 and a shadow mask 2004, the shadow mask 2004 including a first aperture 2006. Waveguide substrate 2008 (in the form of a glass or plexiglass block or plate) is also shown. The SiO2 material 2010 is configured to flow out of the first source 2002 and through the first aperture 2006 of the shadow mask 2004. The flow of material is in the negative Y direction. The shape of the first aperture 2006 determines the shape of the SiO2 flow downstream of the shadow mask 2004. Fig. 20 is not drawn to scale.

The means (not shown) for moving the waveguide substrate 2008 is arranged to move the waveguide substrate 2008 in a first plane perpendicular to the Y-direction such that the waveguide substrate 2008 passes under the first aperture 2006. In some embodiments, the motion is entirely in the X direction. However, in other embodiments, the waveguide substrate 2008 may be rotated in a first plane such that the motion is in the X-direction and the Z-direction.

In fig. 20, the waveguide substrate 2008 has not yet passed under the first aperture 2006, and therefore there is no dielectric coating on the waveguide substrate 2008. As the waveguide substrate passes under the first aperture 2006 (in the X-direction), a dielectric coating is deposited on the substrate. Typically, to make a complete layer, the waveguide substrate 2008 will need to pass under the first aperture 2006 multiple times until the desired thickness is obtained.

Once the first layer 2010 is formed, the waveguide substrate 2008 will move under one of the sources of the second dielectric material such that a second layer (of the second dielectric material) is formed on top of the first layer 2010 of the first dielectric material.

Fig. 21 is a schematic view of a shadow mask 2004 taken in the X-Z plane (i.e., orthogonal to the view plane of fig. 20). The shadow mask includes four apertures, a first aperture 2006 (as described above), a second aperture 2102, a third aperture 2104, and a fourth aperture 2106. The first and third apertures 2006, 2104 are each connected to a source of a first dielectric material. The second and fourth apertures 2102 and 2106 are each connected to a source of a second dielectric material. Each aperture has a trapezoidal shape with a short base and a long base.

To fabricate subsequent alternating layers of first and second dielectric materials, the waveguide substrate 2008 is sequentially moved under different apertures. The order of the layers may be controlled according to the order of the apertures under which the waveguide substrate 2008 moves. The waveguide substrate 2008 is rotated/moved relative to the shadow mask 2004 so as to pass under different apertures such that the waveguide substrate 2008 passes under the apertures in the X-direction and such that the short and long sides of the apertures are spaced apart in the Z-direction. In this way, the thickness of each deposited layer varies in the Z direction. The percent change in thickness of the layer from the first end to the second end (in the Z direction) will depend on the percent change in width of the short and long sides of the corresponding aperture. This will be explained with reference to fig. 21.

Fig. 22a to 22d are schematic cross-sectional views of four different first layers formed on a waveguide substrate 2008, respectively. Fig. 22a shows a layer 2202 formed when a waveguide substrate 2008 passes under a first aperture 2006. Fig. 22b shows layer 2204 formed when waveguide substrate 2008 passes under second aperture 2102. Fig. 22c shows layer 2206 formed when waveguide substrate 2008 passes under second aperture 2104. Fig. 22d shows layer 2208 formed when waveguide substrate 12008 passes under second aperture 2106. As the skilled artisan will appreciate, the thickness profile of each of the layers 2202-2208 corresponds to the shape of the respective aperture.

In particular, layers 2202 and 2206 have a positive gradient from left to right because the widths of apertures 2006 and 2104 increase in the Z direction of the waveguide substrate as the shadow mask and waveguide substrate are rotated relative to one another. The percent change in thickness of layer 2206 is greater than the percent change in thickness of layer 2202 because the percent change in width of the short side of aperture 2104 relative to the long side is greater than aperture 2006. Layers 2204 and 2208 have a negative gradient from left to right because the widths of apertures 2102 and 2106 decrease in the Z direction as the shadow mask and waveguide substrate are rotated relative to each other. The percent change in thickness of layer 2204 is greater than the percent change in thickness of layer 2208 because the percent change in width of the short side of aperture 2102 relative to the long side is greater than aperture 2106.

As will be appreciated, the arrangement of shadow masks 2004 having four differently shaped apertures with two apertures connected to a first dielectric material source and two apertures connected to a second dielectric material source provides a means for fabricating multiple layers of first dielectrics and multiple layers of second dielectrics arranged in an alternating configuration. Each layer of the first dielectric will have a percent thickness variation equal to either the first value or the second value, where all layers having the first value are associated with, for example, the first aperture 2006 and all layers having the second value are associated with, for example, the second aperture 2102. Each layer of the second dielectric will have a thickness percentage variation equal to the first value or the second value, wherein all layers having a third value are associated with, for example, the third aperture 2104 and all layers having a second value are associated with, for example, the fourth aperture 2106. In other words, a method for manufacturing a layered coating according to the invention is provided.

An advantage of this fabrication method is that the waveguide substrate can be quickly and simply moved/rotated as needed to pass under the aperture of the shadow mask 2004 to create multiple alternating layers of first and second dielectric materials as needed. The number of unique shadow masks having different shapes determines the number of discrete values of the thickness percentage variation of the layer that can be obtained, and thus the thickness percentage variation of any particular layer can be controlled simply by selecting the aperture sequence. The absolute thickness of any layer can be controlled by controlling the speed at which the waveguide substrate passes under a particular shadow mask 2004 or by controlling the material flow rate.

It should be understood that the fabrication methods disclosed herein are not limited to four apertures and two sources of dielectric material. For example, increasing or decreasing the number of differently shaped shadow masks will simply have the effect of increasing or decreasing the discrete number of allowed percentage changes in the thickness values of the available layers.

Tenth example

Fig. 23a to 23c relate to a tenth real example of a coating according to the invention. The tenth example coating comprises 24 alternating layers of SiO2 and Si3N 4. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, and L23) are SiO2 layers. The even layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22 and L24) are Si3N4 layers. Fig. 23a shows the SiO2 layer (i.e. the odd layer). Fig. 23b shows the Si3N4 layer (i.e. even layer).

The first subset of layers of fig. 23a has a first value of percent thickness variation represented by continuous lines. The second subset of layers has a second value of percent thickness variation represented by the dashed line. The first value of the percent change is-60% +/-10%. The second value of the percent change is-25% +/-5%.

The first subset of layers of fig. 23b has a third value of percent thickness variation represented by continuous lines. The second subset of layers has a fourth value of percent thickness indicated by the dashed line. The third value of the percent change is +60++/-10%. The fourth value of the percent change is 15% +/-2%.

Fig. 23c shows how the waveguide of the tenth example provides acceptable transmission performance at each of the three wavelengths. The solid line 2302 of fig. 23c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 23c relate to blue 2304, green 2306 and red 2308 lasers, respectively.

Eleventh example

Fig. 24a to 24c relate to an eleventh real example of a coating according to the invention. The coating of this eleventh example comprises 24 alternating layers of SiO2 and TiO 2. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, and L23) are SiO2 layers. The even number of layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22 and L24) are TiO2 layers. Fig. 24a shows the SiO2 layer (i.e. the odd layer). Fig. 24b shows a TiO2 layer (i.e., even layer).

The first subset of layers of fig. 24a has a first value of percent thickness change represented by continuous lines. The second subset of layers has a second value of percent thickness variation represented by the dashed line. The first value of the percent change is 10% +/-1%. The second value of the percent change is-50% +/-5%.

All layers of fig. 24b have a third value for the percent thickness change, represented by a continuous line. The third value of the percent change is +20++/-2%. Thus, the tenth example differs from the previous examples in that there are three different (discrete) layer thickness percentages instead of four.

Fig. 24c shows how the waveguide of the eleventh example provides acceptable transmission performance at each of the three wavelengths. The solid line 2402 of fig. 24c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 24c relate to blue 2404, green 2406 and red 2408 lasers, respectively.

Twelfth example

Fig. 25a to 25c relate to a twelfth real example of a coating according to the invention. The twelfth example coating includes 30 alternating layers of SiO2 and Nb 205. The layers are numbered from 1 to 24 such that light emitted from the waveguide passes sequentially through each of the layers 1 to 24. The odd layers (layers L1, L3, L5, L7, L9, L11, L13, L15, L17, L19, L21, L23, L25, L27, and L29) are SiO2 layers. The even layers (layers L2, L4, L6, L8, L10, L12, L14, L16, L18, L20, L22, L24, L26, L28, and L30) are Nb2O5 layers. Fig. 25a shows the SiO2 layer (i.e. the odd layer). Fig. 25b shows NbO5 (i.e. even layers).

The first subset of layers of fig. 25a has a first value of percent thickness change represented by continuous lines. The second subset of layers has a second value of percent thickness variation represented by the dashed line. The first value of the percent change is-55% +/-5%. The second value of the percent change is-80% +/-5%.

All layers of fig. 25b have a third value for the percent thickness change, represented by the continuous line. The third value of the percent change is +35++/-5%. Thus, the twelfth example is another example that includes three different (discrete) layer thickness percentages.

Fig. 25c shows how the waveguide of the twelfth example provides acceptable transmission performance at each of the three wavelengths. The solid line 2502 of fig. 25c represents the ideal transmission behavior. The three dashed lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in fig. 25c relate to blue 2504, green 2506 and red 2508 lasers, respectively.

Additional features

Embodiments relate, by way of example only, to electrically activated LCOS spatial light modulators. The teachings of the present disclosure can equally be implemented on any spatial light modulator capable of displaying a computer-generated hologram according to the present disclosure, such as any electrically activated SLM, optically activated SLM, digital micro-mirror device or micro-electromechanical device.

In some embodiments, the light source is a laser, such as a laser diode. In some embodiments, the detector is a photodetector, such as a photodiode. In some embodiments, the light receiving surface is a diffuser surface or screen, such as a diffuser. The holographic projection systems of the present disclosure may be used to provide improved heads-up displays (HUDs). In some embodiments, a vehicle is provided that includes a display system mounted in the vehicle to provide a HUD. The vehicle may be a motor vehicle such as an automobile, truck, van, cargo truck, motorcycle, train, aircraft, boat or ship.

The quality of the holographic reconstruction may be affected by the so-called zero order problem, which is a result of the diffractive properties of the use of a pixelated spatial light modulator. Such zero order light may be considered "noise" and include, for example, specularly reflected light as well as other unwanted light from the SLM.

In the example of fourier holography, this "noise" is concentrated at the focus of the fourier lens, resulting in a bright spot at the center of the holographic reconstruction. The zero order light can simply be blocked, however this means that the bright spot is replaced by a dark spot. Some embodiments include an angularly selective filter to remove only zero order collimated light rays. Embodiments also include the method of managing zero order described in European patent 2030072, which is incorporated herein by reference in its entirety.

In some embodiments, the size of the hologram (number of pixels in each direction) is equal to the size of the spatial light modulator, such that the hologram fills the spatial light modulator. I.e. the hologram uses all pixels of the spatial light modulator. In other embodiments, the hologram is smaller than the spatial light modulator. More specifically, the number of hologram pixels is less than the number of light modulation pixels available on the spatial light modulator. In some of these other embodiments, a portion of the hologram (i.e., a contiguous subset of the pixels of the hologram) is repeated in unused pixels. This technique may be referred to as "tiling" in which the surface area of the spatial light modulator is divided into a plurality of "tiling" each representing at least a subset of the holograms. Thus, the size of each tile is smaller than the size of the spatial light modulator. In some embodiments, a "tiling" technique is implemented to improve image quality. In particular, some embodiments implement tiling techniques to minimize the size of image pixels while maximizing the amount of signal content that enters the holographic reconstruction. In some embodiments, the holographic pattern written to the spatial light modulator comprises at least one complete tile (i.e., a complete hologram) and at least a small portion of the tile (i.e., a contiguous subset of the pixels of the hologram).

In an embodiment only the main playback field is utilized and the system comprises physical blocks, such as baffles, arranged to limit the propagation of the higher order playback field through the system.

In an embodiment, the holographic reconstruction is colored. In some embodiments, a method called spatially separated color "SSC" is used to provide color holographic reconstruction. In other embodiments, a method called frame sequential color "FSC" is used.

The SSC method uses three spatially separated arrays of light modulating pixels for three monochromatic holograms. The advantage of the SSC method is that the image can be very bright, since all three holographic reconstructions can be formed simultaneously. However, if three spatially separated arrays of light modulating pixels are provided on a common SLM due to spatial constraints, the quality of each monochrome image will be sub-optimal because each color uses only a subset of the available light modulating pixels. Thus, a relatively low resolution color image is provided.

The FSC method can use all pixels of a common spatial light modulator to display three monochromatic holograms in sequence. The monochrome reconstruction cycle (e.g., red, green, blue, etc.) is fast enough that a human viewer perceives a multicolor image from the integration of three monochrome images. The advantage of FSC is that the entire SLM can be used for each color. This means that the quality of the three color images produced is optimal, since all pixels of the SLM are used for each color image. However, the disadvantage of the FSC method is that the brightness of the composite color image is about 3 times lower than the SSC method because only one third of the frame time can occur per single color illumination event. This disadvantage can be addressed by overdriving the laser or using a more powerful laser, but this requires more power, resulting in higher costs and increased system size.

The examples describe illuminating the SLM with visible light, but those skilled in the art will appreciate that the light source and SLM may equally be used to direct infrared or ultraviolet light, for example as disclosed herein. For example, those skilled in the art will recognize techniques for converting infrared and ultraviolet light into visible light in order to provide information to a user. For example, the present disclosure extends to the use of phosphor and/or quantum dot technology for this purpose.

Some arrangements describe 2D holographic reconstruction by way of example only. In other arrangements, the holographic reconstruction is a 3D holographic reconstruction. That is, in some arrangements, each computer generated hologram forms a 3D holographic reconstruction.

The methods and processes described herein may be embodied on a computer readable medium. The term "computer readable medium" includes media arranged to temporarily or permanently store data such as Random Access Memory (RAM), read Only Memory (ROM), cache memory, flash memory, and cache memory. The term "computer-readable medium" shall also be taken to include any medium or combination of media that is capable of storing instructions for execution by a machine such that the instructions, when executed by one or more processors, cause the machine to perform any one or more of the methodologies described herein, in whole or in part.

The term "computer-readable medium" also encompasses cloud-based storage systems. The term "computer-readable medium" includes, but is not limited to, one or more tangible and non-transitory data stores (e.g., data volumes) in the example form of solid state memory chips, optical disks, magnetic disks, or any suitable combination thereof. In some example embodiments, the instructions for execution may be conveyed by a carrier medium. Examples of such carrier media include transient media (e.g., propagated signals conveying instructions).

It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. The disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.

Claims

1. A waveguide comprising a pair of complementary surfaces arranged to provide a waveguide therebetween, wherein a first surface of the pair of complementary surfaces comprises a plurality of first layers and a plurality of second layers, each first layer comprising a first dielectric and each second layer comprising a second dielectric, wherein each of the first and second layers has a first end and a second end, wherein a percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowable values; wherein the total number of first and second layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

2. The waveguide of claim 1, wherein the plurality of discrete allowed values consists of two to six discrete values, optionally two to four discrete values, optionally four discrete values.

3. The waveguide of claim 1 or 2, wherein the plurality of discrete allowed values includes a first value, a second value, and a third value, and wherein the percent change in thickness of each layer of the first dielectric is equal to the first value or the second value, and wherein the percent change in thickness of at least one layer of the second dielectric is equal to the third value.

4. The waveguide of any of the preceding claims, wherein the plurality of discrete allowed values includes first through fourth values, and wherein the percent thickness change of each layer of the second dielectric is equal to a third value or a fourth value.

5. The waveguide of any of the preceding claims, wherein the rate of change of thickness of each layer of the first and second dielectrics is constant.

6. The waveguide of any of the preceding claims, wherein the first surface is partially reflective-transmissive and/or the second surface of the pair of complementary surfaces is substantially fully reflective, and wherein the first surface provides a plurality of n light emitting regions for light being waveguide between the first and second surfaces, optionally wherein an internal angle of incidence at each emitting region is in the range of 0 to 70 degrees, optionally 10 to 50 degrees.

7. The waveguide of claim 6, wherein the transmittance of the first surface at the first, second, and third visible wavelengths increases with distance from the first light-emitting region to the nth light-emitting region to maintain the intensities of the plurality of light emissions substantially constant at the first, second, and third wavelengths.

8. The waveguide of claim 7, wherein the first wavelength is in the range of 630-670nm, the second wavelength is in the range of 500-540nm, and the third wavelength is in the range of 430-470 nm.

9. The waveguide of claim 7 or 8, wherein the transmittance T (n) of the first surface at each emission point satisfies the following equation:where L is the optical loss factor of the waveguide material.

10. A waveguide as claimed in any preceding claim, wherein the first dielectric is a first oxide, fluoride, sulphide or nitrate of a first transition metal or semiconductor and the second dielectric is a second oxide, fluoride, sulphide or nitrate of a second transition metal or semiconductor.

11. A waveguide according to any preceding claim, wherein the thickness of each layer is in the range 2 to 300nm, optionally between 20 and 200 nm.

12. A waveguide according to any preceding claim, wherein at least one of the first to fourth values of the ratio is positive and at least one of the first to fourth values of the percent change in thickness.

13. A waveguide according to any preceding claim, wherein each of the first to fourth values of percent change in thickness is in the range-150% to +150%.

14. A waveguide according to any preceding claim, wherein the percentage change in thickness of the respective layers is at least one of: the percent change in physical thickness or the percent of optical thickness.

15. A holographic system, comprising:

a first waveguide arranged to receive light encoded with a hologram output by the display device at a second surface of the pair of complementary surfaces;

wherein a first surface of the pair of complementary surfaces comprises a plurality of first layers of a first dielectric and a plurality of second layers of a second dielectric, wherein each of the first and second layers has a first end and a second end, wherein a percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowed values; wherein the total number of first and second layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

16. The holographic system of claim 15, further comprising a second waveguide comprising a pair of complementary surfaces arranged to provide a waveguide therebetween.

17. The holographic system of claim 16, wherein the first surface of the first waveguide is arranged to provide a plurality of n light emitting regions for light being guided between the first surface and the second surface, and the second surface of the second waveguide is arranged to receive light from the n light emitting regions of the first waveguide.

18. The holographic system of claim 15 or 16, wherein the second waveguide is a waveguide as claimed in any preceding claim.

19. The holographic system of any one of claims 15 to 18, wherein the first waveguide is substantially elongate, and wherein the first and second surfaces are elongate surfaces.

20. The holographic system of any one of claims 16 to 18, wherein the second waveguide is planar, and wherein the first and second surfaces are major surfaces of the planar second waveguide.

21. A method of waveguiding an optical field, the method comprising:

directing light into a first waveguide comprising a pair of complementary surfaces; and

directing light by internal reflection between the pair of complementary surfaces;

Wherein a first surface of the pair of complementary surfaces comprises a plurality of first layers comprising a first dielectric and a plurality of second layers comprising a second dielectric, wherein each of the first and second layers has a first end and a second end, wherein a percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowed values; wherein the total number of first and second layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.

22. A waveguide according to any preceding claim, wherein the first surface provides a plurality, n, of light emitting regions for light being guided between the first and second surfaces, optionally wherein the internal angle of incidence at each emitting region is in the range 10 to 50 degrees.

23. A method of providing a waveguide, the method comprising:

providing a waveguide substrate comprising a pair of complementary surfaces arranged to provide a waveguide therebetween;

wherein a first surface of the pair of complementary surfaces comprises a plurality of layers of first dielectrics and a plurality of layers of second dielectrics arranged in an alternating configuration, wherein each layer of the first and second dielectrics has a first end and a second end, wherein a percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete allowed values; wherein the total number of first and second layers is greater than the total number of discrete allowed values; and wherein the refractive index difference between the first dielectric and the second dielectric is greater than 0.4.