CN112540460A - Optical system design method based on combination of TIR and microlens array - Google Patents
Optical system design method based on combination of TIR and microlens array Download PDFInfo
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Abstract
The invention provides a design method of an LED high-uniformity and high-efficiency optical system based on TIR and micro-lens array combination. Microlens arrays have not only the optical properties of conventional lenses but also many unique optical properties, and have been widely used in LED light sources in recent years. However, most studies focus on the manufacturing process, and a complete mathematical model for designing a free-form surface is not established. Therefore, a complete set of free-form surface micro-lens mathematical model is established according to the TIR characteristic and the refraction law. And solving a set of differential equations through numerical values to obtain the contour of the free-form surface micro-lens. Finally, the microlens array was simulated using ray tracing software TracePro in the near field and far field cases, respectively, and the effect of microlens array characteristics on illumination performance was discussed. The result shows that the smaller the radius of the micro lens is, the better the illumination effect is, the uniformity and the efficiency can reach more than 90%, and the prospect of the micro lens array in practical application can be effectively widened.
Description
Technical Field
The invention belongs to the technical field of optics and illumination, and particularly relates to a free-form surface of a micro-lens for redistributing energy of an LED light source to realize uniform illumination and high efficiency.
Background
As a fourth generation illumination light source, a Light Emitting Diode (LED) has many advantages such as small size, fast response, long service life, and no pollution, and as the light efficiency of LEDs is continuously improved, LEDs are increasingly widely used in various aspects such as indoor illumination and outdoor illumination. However, since the spatial light intensity of the LED is approximately lambertian cosine distributed, the LED is directly used for illumination without secondary light distribution, a circular light spot with a bright center and gradually darkened periphery is formed on the target surface, the uniformity is poor, the large-field-angle light is difficult to irradiate on the target surface, the energy utilization rate is low, glare is easy to generate, and the actual illumination requirement is difficult to meet. Therefore, in the application of actual LED lighting, secondary light distribution design needs to be performed on the LED, so that the light energy distribution can meet the actual lighting requirement. In recent years, the research of LED lighting has been greatly advanced, particularly in the fields of reflective lighting and refractive lighting. Catadioptric redistribution of the emitted light is an effective way to improve illumination performance. However, the conventional mirror or refractive lens requires high processing accuracy and material. Microlens arrays, which have not only the optical properties of conventional lenses but also many unique optical properties, are now also used in LED lighting systems. By adjusting the shape, arrangement and duty ratio of the microlenses in the microlens array, modulation such as diffusion of incident light, uniform distribution of light, and the like can be realized, thereby realizing a specific optical function. However, the application of the microlens array in the LED light source is relatively little studied, and most of the research is heavily focused on the manufacturing process of the microlens, so that the complete design of the free-form surface of the microlens is lacked. Based on the problems, the invention provides a design method for the free-form surface micro-lens, a set of complete mathematical model is established, the illumination uniformity of a specific area of a target plane is improved, and meanwhile, the illumination efficiency is improved to a certain extent.
Disclosure of Invention
The invention aims to establish a free-form surface design method based on TIR and micro-lens combination, designs a free-form surface micro-lens illumination system for redistributing the energy of an LED light source, and meets the requirement of uniform illumination in a specific target area. The invention is realized by the following technical scheme:
(1) and establishing an LED optical system model based on the free-form surface micro-lens array, wherein the LED optical system model comprises an LED light source, a TIR lens, the free-form surface micro-lens array and a target detection surface.
(2) The single LED is used as a point light source, light rays of the point light source are collimated, a Cartesian coordinate system is established, a single free-form surface micro lens used for redistributing light source energy is in a central axis symmetrical shape, a section passing through a free-form surface rotating central axis is used as a reference plane, a z axis is used as a rotating central axis, a direction passing through an origin of the coordinate system and perpendicular to the central axis is used as a y axis, the top end of the free-form surface micro lens is located at the origin of the center of the coordinate system, and a target detection plane is parallel to a light emitting plane of the LED light source and is in the.
(3) The method comprises the steps of constructing a mathematical model of the free-form surface micro-lens for secondary light distribution, firstly collimating LED light rays by the TIR lens to obtain parallel light rays parallel to a z axis, and carrying out secondary uniform distribution on the parallel light rays after passing through the free-form surface micro-lens, so that reasonable control and distribution of light intensity are realized, and uniform illumination is formed on a target detection surface.
(4) And rotating the free curve obtained by the free-form surface micro-lens on the YOZ plane for one circle around the rotation central axis z which is the normal of the light emitting surface of the LED light source to obtain the surface profile of the free-form surface micro-lens.
The LED light source is used for emitting light rays with different wave bands. A TIR lens for collimating light emitted by the LED light source. And the free-form surface micro-lens array is used for redistributing the light rays collimated by the TIR lens. And the target detection surface is used for receiving the light rays after the diffuse reflection of the free-form surface.
The free-form surface micro-lens for redistributing the light source energy is in a central axis symmetrical shape, and a section passing through the rotating central axis of the free-form surface micro-lens is taken as a reference surface to establish a Cartesian coordinate system: the rotating central shaft is taken as a Z axis, the direction which passes through the origin of a coordinate system and is vertical to the central shaft is taken as a Y axis, the free-form surface micro-lens is arranged right above the LED light source, and a target plane to be illuminated is parallel to a light emitting plane of the LED light source and is in the positive direction of the Z axis;
in the invention, the TIR lens firstly collimates the light emitted by a single LED light source, and then the collimated light is uniformly distributed on a target plane by the free-form surface micro lens, thereby realizing reasonable control and distribution of light intensity and forming a uniform illumination area on a target detection plane. The lighting system is shown in cross-section in fig. 1 and 2.
Based on the rotational symmetry principle, the free-form surface curve obtained by the obtained free-form surface micro-lens on the YOZ plane rotates for one circle around the axis Z of the normal line of the light emitting surface of the LED light source, namely the rotation central axis, so that the required surface profile of the multiple diffuse reflection free-form surface with high diffuse reflectivity can be obtained.
The free curve is determined by the programmed calculation of the following steps:
1. the method comprises the steps of constructing a TIR lens to horizontally disperse light rays of an LED light source based on characteristics of the LED light source and a specular reflection surface, constructing a mathematical simulation algorithm of a free-form surface micro-lens for representing target plane irradiance based on the TIR characteristic and a refraction law, and using coordinates of discrete points on a free-form curve as unknowns.
The irradiance distribution of an ideal lambertian LED point source can be expressed by a cosine function:
wherein
In order to be the intensity of the radiation,
the emergent light intensity of the LED light source along the direction of the optical axis thereof,dis the distance between the LED light source and the detection target,
the angle between the actual outgoing ray and the optical axis,mis equal to the LED half-decay angle
The numerical value of (c).
The vector form of the law of refraction can be expressed as:
where n is the refractive index of the free-form surface lens,Nfrom the normal direction of the curved surface at the incident point A of the light ray,INandOUTrespectively, an incident ray and an emergent ray, wherein the emergent ray intersects the target plane at point B.
Coordinates of the set point A are
The coordinates of B are
，OUT、INAndNcan be expressed as:
wherein
And
the derivatives of the free-form surface component in the Y and Z directions, respectively. By substituting formula (3) for formula (2), it is possible to obtain:
wherein A, B, C, D are respectively:
by substituting formula (5) for formula (4), an angle can be obtained
And the slope of the surface of the microlens
The relationship between:
2. according to the irradiation distribution requirement of the target surface in the actual LED optical system and the geometric relation in the established Cartesian coordinate system, the method further obtains
、 
And
the relationship between the two components, thereby establishing a series of differential equations:
and is
And
the following relationships exist:
wherein
And
the radii of the free-form surface microlens and the target surface, respectively.
The final differential equation is obtained by substituting equations (7) and (8) into equation (6):
3. programming and solving an equation set by using a numerical method, introducing a smoothing algorithm into the obtained discrete point coordinates, and fitting to obtain a free curve; the method specifically comprises the following steps:
1) setting initial conditions
Setting the initial point coordinate of the free curve as
The change step lengths of the horizontal and vertical coordinates are respectively
、
(ii) a The value of the initial point coordinate and the step length thereof depends on the size of the free-form surface micro-lens;
2) solving equation set by using numerical method
Based on a numerical method, obtaining a free curve of the micro-lens by an expression, then bringing an initial value of each discrete point coordinate on the free curve into a formula (9), and programming and iterating to solve the free curve of the micro-lens by taking a vertical coordinate of the free curve as an unknown variable;
3) fitting smooth curve
Fitting the coordinate data of the discrete points on the free curve obtained by calculation to obtain a smooth curve; correcting the initial value of the vertical coordinate of each discrete point on the arc segment of the free curve by adopting a trial and error method, and repeating the solving process in the step 2) until a curved surface profile which is convenient to process and manufacture is obtained.
The invention provides a design method of an LED high-uniformity and high-efficiency optical system based on TIR and micro-lens array combination. First, the TIR lens part collimates the light of the LED, and then the micro lens array part collimates the lightIs redistributed to the target plane. Compared with some existing lighting systems, the lighting system has the following advantages and effects: a set of complete mathematical model is established, and the target detection plane receives the light rays passing through the free-form surface micro-lens array, so that the irradiation uniformity is high, the light rays are soft, and the illumination efficiency is high. Good illumination results are exhibited in both near field and far field illumination. In addition, in the design scheme of the invention, the radius of the target illumination surface
And the distance between the target surface and the micro lens is used as the structural parameter of the micro lens array optical system. And proper parameters of the lighting system can be selected according to the requirements of actual application occasions, so that the actual indirect lighting prospect is expanded.
Drawings
Fig. 1 is a design diagram of a free-form surface microlens.
Fig. 2 is a single free-form surface microlens model in Solidworks software and Tracepro software, respectively.
Fig. 3 is a 13 × 13 microlens array model.
Detailed Description
The following detailed description of the embodiments of the invention is provided in connection with the accompanying drawings. As shown in fig. 1, the details of the free-form surface microlens optical path of the present invention are described. When the light emitted from the LED light source passes through the TIR lens, the light becomes totally parallel to the optical axis, and the parallel light is redistributed through the micro-lens array again and finally uniformly distributed on the target plane. The shape of the free-form surface micro-lens is determined by the following scheme:
in the present embodiment, a cartesian coordinate system is established with a cross section passing through the rotational center axis of the free-form surface microlens as a reference plane, and the rotational center axis is defined as a Z axis, and a direction passing through the origin of the coordinate system and perpendicular to the center axis is defined as a Y axis. Based on the rotational symmetry principle, in order to simplify the calculation problem and convert three dimensions into two-dimensional conditions, the free-form surface micro-lens solving diagram is shown in fig. 1.
The irradiance distribution of an ideal lambertian LED point source can be expressed by a cosine function:
wherein
In order to be the intensity of the radiation,
the emergent light intensity of the LED light source along the direction of the optical axis thereof,dis the distance between the LED light source and the detection target,
the angle between the actual outgoing ray and the optical axis,mis equal to the LED half-decay angle
The value of (d);
the vector form of the law of refraction can be expressed as:
where n is the refractive index of the free-form surface lens,Nfrom the normal direction of the curved surface at the incident point A of the light ray,INandOUTincident rays and emergent rays are respectively, wherein the emergent rays are intersected with the target plane at a point B;
coordinates of the set point A are
The coordinates of B are
，OUT、INAndNcan be expressed as:
wherein
And
the derivatives of the free-form surface component in the Y and Z directions, respectively. By substituting formula (3) for formula (2), it is possible to obtain:
wherein A, B, C, D are respectively:
by substituting formula (5) for formula (4), an angle can be obtained
And the slope of the surface of the microlens
The relationship between:
according to the irradiation distribution requirement of the target surface in the actual LED optical system and the geometric relation in the established Cartesian coordinate system, the method further obtains
、 
And
the relationship between the two components, thereby establishing a series of differential equations:
and is
And
the following relationships exist:
wherein
And
the radii of the free-form surface microlens and the target surface, respectively.
The final differential equation is obtained by substituting equations (7) and (8) into equation (6):
the equation for limiting the curve shape of the free-form surface established in the invention is a nonlinear algebraic equation, and in order to simplify the calculation difficulty and convert three dimensions into two dimensions, the coordinate of the initial point of the free-form surface is firstly set as
And the change step length of the horizontal and vertical coordinates
、
(ii) a Based on a numerical method and by means of MATLAB programming iterative solution, coordinate values of a series of discrete points on the free curve are obtained. And performing smooth fitting on the obtained coordinate data by using a least square method, correcting the coordinate values of each discrete point on the arc segment of the free curve by using a trial-and-error method if necessary, and repeating the solving process until a free-form surface micro-lens profile convenient to process and manufacture is obtained.
In the implementation method, the coordinates of the initial point of the free curve are set as follows: (0, 0, 0) having vertical and horizontal coordinate change step lengths of
,
The number of discrete points N =41 defining the arc segment of the free curve sought. According to the steps, the equation set is iteratively solved by means of MRTLAB programming, and coordinate data obtained by smooth fitting are obtained, so that coordinate values of a series of discrete points on the arc segment of the free curve are finally obtained. The free-form surface micro-transmission surface profile with high uniformity and high efficiency can be obtained by rotating the free-form curve for one circle around the normal line of the light emitting surface center of the LED light source, namely the Z axis of the rotating central shaft (as shown in figures 2 and 3).
The entity model of the light source system designed by the invention is led into optical simulation software TracePro for non-sequence light ray tracing, and a plurality of groups of optical systems with different parameters are selected for simulation experiment, wherein when the distance L =500mm and the radius of an illumination surface
The lighting effect is best when the thickness is not less than 100 mm. As can be seen from the irradiation distribution simulation diagram in the circular illumination area of the target illumination surface, after the technical scheme is implemented, the irradiation uniformity and the efficiency of the target illumination surface can reach more than 90 percent, and the reasonable control and distribution of light energy distribution are realized. Can meet the requirements of color vision measurement, indoor illumination and the likeHigh uniformity illumination is required in many areas.
Claims (1)
1. The free-form surface design method based on the TIR and the micro-lens array is characterized by comprising the following steps:
s1, establishing an LED optical system model based on a free-form surface micro-lens array, which comprises an LED light source, a TIR lens, a free-form surface micro-lens array and a target detection surface;
s2, using a single LED as a point light source and collimating the light of the point light source, establishing a Cartesian coordinate system, wherein a single free-form surface micro-lens for redistributing the energy of the light source is in a central axis symmetrical shape, the cross section passing through the free-form surface rotation central axis is taken as a reference plane, the z axis is taken as a rotation central axis, the direction passing through the origin of the coordinate system and vertical to the central axis is taken as the y axis, the top end of the free-form surface micro-lens is positioned at the origin of the center of the coordinate system, and a target detection plane is parallel to the light emitting plane of the LED light;
s3, constructing a mathematical model of a free-form surface micro-lens for secondary light distribution, firstly, collimating LED light rays by a TIR lens to obtain parallel light rays parallel to a z axis, and carrying out secondary uniform distribution on the parallel light rays after passing through the free-form surface micro-lens, so that reasonable control and distribution of light intensity are realized, and uniform illumination is formed on a target detection surface;
s4, rotating a free curve obtained by the free-form surface micro-lens on the YOZ plane around the normal line of the light emitting surface of the LED light source, namely the rotation central axis z axis for one circle to obtain the surface profile of the free-form surface micro-lens, wherein the free curve is determined by the following steps:
s41, constructing a TIR lens to horizontally disperse the light of the LED light source based on the characteristics of the LED light source and the specular reflection surface, and constructing a mathematical simulation algorithm for representing the target plane irradiance of the free-form surface micro-lens based on the TIR characteristics and the refraction law, wherein the algorithm takes the coordinates of each discrete point on the obtained free-form curve as unknown quantity;
the irradiance distribution of an ideal lambertian LED point source can be expressed by a cosine function:
wherein
In order to be the intensity of the radiation,
the emergent light intensity of the LED light source along the direction of the optical axis thereof,dis the distance between the LED light source and the detection target,
the angle between the actual outgoing ray and the optical axis,mis equal to the LED half-decay angle
The value of (d);
the vector form of the law of refraction can be expressed as:
where n is the refractive index of the free-form surface lens,Nfrom the normal direction of the curved surface at the incident point A of the light ray,INandOUTincident rays and emergent rays are respectively, wherein the emergent rays are intersected with the target plane at a point B;
coordinates of the set point A are
The coordinates of B are
，OUT、INAndNcan be expressed as:
wherein
And
the derivatives of the free-form surface component in the Y and Z directions, respectively, can be obtained by substituting equation (3) for equation (2):
wherein A, B, C, D are respectively:
by substituting formula (5) for formula (4), an angle can be obtained
And the slope of the surface of the microlens
The relationship between:
s42, obtaining the irradiation distribution demand of the target surface in the actual LED optical system and the geometric relation in the established Cartesian coordinate system
、 
And
the relationship between the two components, thereby establishing a series of differential equations:
and is
And
the following relationships exist:
wherein
And
the radii of the free-form surface micro lens and the target surface are respectively;
the final differential equation is obtained by substituting equations (7) and (8) into equation (6):
s43, programming and solving an equation set by using a numerical method, introducing a smoothing algorithm into the obtained discrete point coordinates, and fitting to obtain a free curve; the method specifically comprises the following steps:
s43.1 setting initial conditions
Setting the initial point coordinate of the free curve as
The change step lengths of the horizontal and vertical coordinates are respectively
，
(ii) a The value of the initial point coordinate and the step length thereof depends on the size of the free-form surface micro-lens;
s43.2 solving equation set by using numerical method
Based on a numerical method, obtaining a free curve of the micro-lens by an expression, then bringing an initial value of each discrete point coordinate on the free curve into a formula (9), and programming and iterating to solve the free curve of the micro-lens by taking a vertical coordinate of the free curve as an unknown variable;
s43.3 fitting smooth curve
Fitting the coordinate data of the discrete points on the free curve obtained by calculation to obtain a smooth curve; and (4) correcting the initial value of the vertical coordinate of each discrete point on the arc segment of the free curve by adopting a trial and error method, and repeating the solving process in the step S43.2 until a curved surface profile which is convenient to process and manufacture is obtained.
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Effective date of abandoning: 20240308 |