WO2009030889A1

WO2009030889A1 - Imaging ellipsometer

Info

Publication number: WO2009030889A1
Application number: PCT/GB2008/002966
Authority: WO
Inventors: Matthew David Gunn; Tudor Emlyn Jenkins
Original assignee: Aberystwyth University
Priority date: 2007-09-04
Filing date: 2008-09-02
Publication date: 2009-03-12

Abstract

An imaging ellipsometer for imaging a substantially planar reflecting surface, the surface defining a surface plane. The ellipsometer comprises: a focussing element for focusing electromagnetic radiation specularly reflected from said surface, the focussing element having a focussing element plane; a detector for detecting specularly reflected electromagnetic radiation focussed by the focussing element at a detector plane; and a stage for supporting said surface; at least one constraining device for constraining the movement of the ellipsometer such that: the detector plane, the focussing element plane and said surface plane are arranged either to intersect along a single line or to be parallel to one another. Furthermore, the focussing element is arranged such that it is tiltable with respect to a principal axis such that the magnitude of an angle between a focussing element axis and the principal axis is able to be greater than 0 radians.

Description

Imaging Ellipsometer

The present invention relates generally to imaging. Embodiments of the present invention provide an imaging ellipsometer for imaging a substantially planar reflecting surface and a method for arranging an imaging ellipsometer to image a substantially planar reflecting surface. Further embodiments provide an automated control system adapted to constrain the arrangement of at least one of: a detector, a focusing element and a stage of an imaging ellipsometer. Yet further embodiments provide a method of determining the ellipsometric angles Ψ and Δ of a substance. Yet further embodiments provide an algorithm for determining the appropriate arrangement of at least one of: a detector, a focusing element and a stage of an imaging ellipsometer.

Ellipsometry is a well established technique for the non-destructive analysis of chemical and biological thin films on either solid or liquid substrates. Properties of a thin film sample, such as its thickness and refractive index, can be determined by using an ellipsometer to measure the change in polarization of light specularly reflected from the surface of the sample and applying computational models, for example involving Fresnel's equation, to the measurements. Measurements can be made in any situation where light can reach and return from the sample and so ellipsometry is ideally suited to in situ sample surface analysis.

Imaging ellipsometry has been developed to map or image the surface of a sample. This technique involves replacing the conventional detector of a typical ellipsometer with an electronic image sensor such as a CCD camera and imaging lens. High spatial, temporal and ellipsometric resolutions have been separately achieved in previous imaging ellipsometers but improvements in all three resolutions have not been achieved simultaneously. This is principally due to problems encountered with obtaining sharp/optimally focused and undistorted images of the whole of the surface of the sample. Because of these problems, imaging ellipsometry has not achieved wide-spread use. In previous arrangements of the components of an imaging ellipsometer, an image of a sample's surface is detected at an oblique angle, i.e. the sample, lens and detector are not all parallel to one another. As will be discussed in greater detail below, with previous arrangements of the sample, lens and detector of an imaging ellipsometer, it is not possible to bring the entirety of a real image of the surface of the sample into optimal focus, or at least an acceptable level of focus, over the whole of the surface of the detector. Only a small region of the detected image is brought into optimal focus at the detector whilst large regions of the detected image are brought into sub-optimal focus at the detector. This results in a detected image, as exemplified in figure 1 C, where only a central linear narrow strip-shaped region of the detected image of the surface of the sample is in-focus or at least within an acceptable level of focus. Large regions of the detected image, both above and below the central narrow strip-shaped in- focus region, are not brought into sharp focus at the detector and are thus detected and imaged at sub-optimal focus.

The problem of sub-optimal focus of detected images suffered by previous arrangements of the components of imaging ellipsometers has been dealt with in various ways. Common approaches include ignoring it and putting up with sub-optimally focused images providing a poor spatial resolution of the detected image. Alternatively an image capture technique known as 'focus stacking' is utilised. With this technique a composite image is created from a number of separately detected sub-images. Each sub-image comprises the narrow strip-shaped in-focus, or at least an acceptable level of focus, region of a detected image. The regions of the detected image which are sub-optimally focussed are discarded. The sample or optical components are re-aligned between the detection of each sub-image so that a new strip-shaped region of the sample is imaged at optimal focus. This process is repeated until sub- images have been detected for the whole area of the surface of the sample. An in-focus composite image of the entire surface of the sample is then created from the plurality of detected sub-images.

Since each sub-image only provides a narrow strip-shaped region of an in-focus detected image, a large number of sub-images are required where a relatively large surface area of a sample is to be analysed. Consequently, a large number of re-alignments of the sample or the components are required to image the entire surface of the sample and to create the composite image. Accordingly, such an imaging technique using a conventional imaging ellipsometer 100 has a low measurement rate due to the length of time required to create the in-focus composite image of sub-images of the surface of the sample, for example around 2.5 seconds per image. The conventional imaging ellipsometer 100 is also inefficient in collecting images and data since images and data relating to the out of focus regions of each detected image is simply discarded.

An additional problem with this technique is that a composite image of a surface of a sample having dynamic thin film phenomena thereon would have dislocations where each sub-image adjoins its adjacent sub-image. This is because the dynamic phenomena would change during the time between the detection of each in-focus sub-image. Hence scanning through the focus is not suited to real time imaging or measurements of dynamic phenomena as this technique has a low temporal resolution.

Figure IA is a cross-sectional view of a conventional imaging ellipsometer 100. The imaging ellipsometer 100 comprises a light source 101, a polarizer 105, a thin film sample to be analysed 102, an analyser 107 to analyse the polarization state of the reflected light, an imaging lens 103 and a detector 104 to measure the intensity of the detected light. Such a configuration is known as PSA (Polarizer, Sample and Analyser) optionally, a Compensator 106 can be added either before (as shown in figure 1) or after the sample to alter the polarization state of the light, resulting in a PCSA or PSCA configuration respectively. The optical components of the ellipsometer are aligned along the beams of incident and reflected light.

Referring now to figure IB, the detector 104 of the conventional imaging ellipsometer 100 is parallel to the lens 103. The sample 102 defines a surface plane 112 which is coplanar with the sample 102. The detector 104 defines a detector plane 109 coplanar with the detector 104. The imaging lens 103 defines a lens plane 108, coplanar with the lens 103. The lens 103 further defines an image plane 110, the image plane 110 being the plane whereby objects located along an object plane 111 of the lens 103 are brought into focus by the lens 103. The lens 103 is arranged such that the object plane 111 intersects the sample 102 along intersection line 113. The detector 104 and lens 103 are arranged such that the detector plane 109 coincides with the image plane 110. Figure 1C shows a detected image 114 detected with the conventional imaging ellipsometer 100. A real image of the sample 102 is only brought into optimal sharp focus at the detector 104 for a region of the real image which corresponds to an area of the surface of the sample where the object plane 111 coincides with the surface plane 112. With the conventional ellipsometer 100, this condition is only met along the line of intersection 113, where the object plane 111 intersects the surface plane 112. Accordingly, the only region of the detected image 114 which is brought into optimal focus is a region of the detected image that corresponds to the section of the surface of the sample along the line of intersection 113. However, due to the effects of depth of field and depth of focus, the region of the detected image 114 in acceptable focus is a 2 dimensional narrow strip-shaped region 115 rather than merely a 1 dimensional line 116. The level of focus of the detected image decreases with increasing distance from the line 116. It is an object of embodiments of the present invention to improve the focus of a detected image of a sample and specifically to increase the size of the region of a sample which is brought into optimal or at least an acceptable level of focus at the detector. Embodiments also seek to reduce image distortion of the detected image. Embodiments also seek to enable measurements to be taken over a range of angles of incidence of electromagnetic radiation thereby providing an additional degree of freedom when taking measurements. Yet further, embodiments also seek to provide the ability to vary the magnification of the detected image whilst maintaining improved focus and reduced image distortion.

Prior art relating to imaging ellipsometry including: Beaglehole, D. (1988), "Performance Of A Microscopic Imaging Ellipsometer" Review Of Scientific Instruments 59(12): 2557-2559; US patent application 2005/0134860 Al and US patent application 2004/0142482, describe the use of the

Scheimpflug geometry or Scheimpflug's principle to obtain focussed images of a sample surface. This is achieved by tilting the plane of the detector such that the sample surface, focussing element and detector planes intersect along a single line. However, the degree of magnification achievable using this technique is limited by the achievable detector tilt. In practice, as the magnification is increased above 1 the light falls on the detector at grazing incidence and so the proportion of reflected light from the detector increases and thus the sensitivity decreases. This significantly limits the'applicability of this method to imaging ellipsometry and similar techniques and only instruments with a magnification of around 1 can be implemented effectively. US patent 2,963,326 mentions the use of an afocal lens system which does not produce a real image of the sample on the detector and instead projects the reflected light onto the detector surface forming a virtual image. The present invention is set out in the claims.

According to an aspect of the disclosure there is provided an imaging ellipsometer for imaging a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element for focusing electromagnetic radiation specularly reflected from said surface, the focussing element having a focussing element plane; a detector for detecting specularly reflected electromagnetic radiation focussed by the focussing element at a detector plane; and a stage for supporting said surface; at least one constraining device for constraining the movement of the ellipsometer such that: the detector plane, the focussing element plane and said surface plane are arranged to intersect along a single line.

There is also provided an automated control system adapted to constrain the arrangement of at least one of: the detector, the focussing element and the stage of the imaging ellipsometer as mentioned above.

There is yet further provided a first method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane; a detector having a detector plane; and a stage for supporting said surface; the method comprising the step of: causing the detector plane, the focussing element plane and said surface plane to intersect along a single line.

There is yet further provided a second method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane, the focussing element defining an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the focussing element along the image plane; a detector having a detector plane; and a stage for supporting said surface; the method comprising the steps of: causing: the detector plane, the focussing element plane and said surface plane to intersect along a single line; the object plane, at least substantially, to coincide with said surface plane; and the detector plane, at least substantially, to coincide with the image plane.

There is yet further provided a third method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane, the focussing element defining an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the focussing element along the image plane, the focussing element further defining a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects a principal axis; a detector having a detector plane; and a stage for supporting said surface; the method comprising the steps of: causing: the detector plane, the focussing element plane and said surface plane to intersect along a single line; the object plane, at least substantially, to coincide with said surface plane; the detector plane, at least substantially, to coincide with the image plane; the detector, the focussing element and said surface, at least substantially, to align along a straight line defining the principal axis; and an angle of incidence, θ, of electromagnetic radiation incident on said surface, at least substantially, to be equal to an angle, α, between a normal to the detector plane and the principal axis. There is yet further provided a fourth method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane, the focussing element defining an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the focussing element along the image plane, the focussing element further defining a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects a principal axis; a detector having a detector plane; and a stage for supporting said surface; the method comprising the steps of: causing: the detector plane, the focussing element plane and said surface plane to intersect along a single line; the object plane, at least substantially, to coincide with said surface plane; the detector plane, at least substantially, to coincide with the image plane; the detector, the focussing element and said surface, at least substantially, to align along a straight line defining the principal axis; and an angle, δ, between the focussing element axis and the principal axis to be greater than 0 radians.

There is yet further provided a method of determining the ellipsometric angles Ψ and Δ of a substance using each of the first, second, third and fourth method as mentioned above.

There is yet further provided an algorithm for determining the appropriate arrangement of at least one of: a detector, a focussing element and a stage of an imaging ellipsometer, wherein the algorithm is adapted to output signals representing the rotational orientation and translational position of the at least one of: the detector, the focussing element and the stage to implement each of the first, second, third and fourth method for arranging an imaging ellipsometer as mentioned above.

According to another aspect of the disclosure there is provided an imaging ellipsometer for imaging a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element for focusing electromagnetic radiation specularly reflected from said surface, the focussing element having a focussing element plane; a detector for detecting specularly reflected electromagnetic radiation focussed by the focussing element at a detector plane; and a stage for supporting said surface; at least one constraining device for constraining the movement of the ellipsometer such that: the detector plane, the focussing element plane and said surface plane are arranged so as to be aligned parallel to one another. There is also provided an automated control system adapted to constrain the arrangement of at least one of: the detector, the focussing element and the stage of the imaging ellipsometer as mentioned above.

There is yet further provided a fifth method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane; a detector having a detector plane; and a stage for supporting said surface; the method comprising the steps of: causing the detector plane, the focussing element plane and said surface plane to be aligned parallel to one another. There is yet further provided a method of determining the ellipsometric angles Ψ and Δ of a substance using the fifth method as mentioned above.

There is yet further provided an algorithm for determining the appropriate arrangement of at least one of: a detector, a focussing element and a stage of an imaging ellipsometer, wherein the algorithm is adapted to output signals representing the rotational orientation and translational position of the at least one of: the detector, the focussing element and the stage to implement the fifth method for arranging an imaging ellipsometer as mentioned above.

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Figure IA is a schematic cross-sectional view of a conventional imaging ellipsometer;

Figure IB is a schematic cross-sectional view of the relevant planes of the conventional imaging ellipsometer; 1 Figure 1C is an example of a detected image obtained by the conventional imaging ellipsometer;

Figure 2 is a schematic cross-sectional view of an embodiment of an imaging ellipsometer; Figure 3A is a schematic cross-sectional view of a focussing element of an embodiment of an imaging ellipsometer;

Figure 3B is an example of a detected image obtained by an embodiment of an imaging ellipsometer;

Figure 4A is a schematic cross-sectional view of an embodiment of an imaging ellipsometer;

Figure 4B is a schematic cross-sectional view of a detector and sample of an embodiment of an imaging ellipsometer;

Figure 5A is a schematic cross-sectional view of an embodiment of an imaging ellipsometer; Figure 5B is a plot of detected image magnification versus the angle of incidence for an embodiment of an imaging ellipsometer;

Figure 6A is a schematic cross sectional view of an embodiment of an imaging ellipsometer;

Figure 6B is a schematic cross sectional view of an embodiment of an imaging ellipsometer;

Figure 7 is a plot of detected image resolution versus detected image magnification for an embodiment of an imaging ellipsometer;

Figure 8 is a schematic cross-sectional view of an embodiment of a constraining device; and Figure 9 is a schematic diagram of another embodiment of a constraining device.

Referring to figure 2, the imaging ellipsometer 200 detects images of a sample's substantially planar reflecting surface 201. The upper reflecting surface 201 of a sample to be imaged defines a surface plane 207 which is coplanar with the reflecting surface 201 of the sample. The sample is mounted on a stage 202. Incident electromagnetic radiation (not shown), such as light in the visible part of the spectrum, is directed on to the sample's reflecting surface 201 at an angle oblique to the normal to the reflecting surface 201. The incident light is specularly reflected from the surface 201 towards a focussing element 203. The focussing element 203, such as a lens, mirror or other device suitable for focussing electromagnetic radiation, focuses the light specularly reflected from the surface 201 at a detector 204. The detector 204 detects the intensity of the reflected light, i.e. the square of the amplitude of the electronic field of the electromagnetic radiation focussed by the focussing element 203 at the detector 204.

The focussing element 203 has a focussing element plane 205 coplanar with the focussing element 203. The detector 204 has a detector plane 206 coplanar with the detector 204. At least one constraining device (not shown) is provided to constrain the movement of the components of the ellipsometer, i.e. the stage 202, the focussing element 203 and the detector 204, such that the detector plane 206, the focussing element plane 205 and the surface plane 207 are arranged to intersect along a single common line 208. A direction, p, is defined as a direction parallel to the plane of incidence of the incident light. An orthogonal direction, s, is defined as a direction perpendicular to the plane of incidence and parallel to the surface plane 207.

As shown in Figure 3A, the focussing element 203 defines an image plane 301 that corresponds to an object plane upon which objects 302, e.g. surface features, are arranged along. The objects 302 on the object plane 303 are brought into focus by the focussing element 203 along the image plane 301 when the objects 302 are located at a distance greater than the focal length, f, 305 of the focussing element 203. As will be understood by those skilled in the art, the relationship between the image plane 301 and the object plane 303 is dependent upon the focal length 305 of the focussing element 203. As an example, the middle object of 302, having an object distance, R₃ in front of the focussing element, will be brought into focus at 304 at an image distance, B, behind the focussing element at: B = / - (1 - M) = ^-J-

R -f where

M = Magnification of the optical system

The ellipsometer 200 is configured such that the object plane 303 is made to coincide with the reflecting surface plane 207 and the image plane 301 is made to coincide with the detector plane 206. Such a configuration makes use of a little known principal sometimes referred to as 'Scheimpflug's principal' which states that the object plane, focussing element plane and image plane of an off-axis optical system (i.e. where the object plane 303, focussing element plane 205 and image plane 301 are not parallel with one another) will all intersect along a common line 208, called the Scheimpflug Line.

Sharp focus at the detector of a real image of the sample is only achieved in the region where the object plane coincides with the surface plane 207 and the image plane 301 coincides with the detector plane 206. Accordingly, in embodiments of the present invention, since the object plane 303 is coplanar with the surface plane 207, i.e. the two planes lie on the same plane, and the image plane 301 is coplanar with the detector plane 206, sharp focus of the real image is achieved over the entire surface of the detector. Thus the detected image is entirely in- focus.

An ellipsometer configured with the plane alignments as described above enables the whole of the real image to be brought to optimal focus at the detector 204. The whole of the sample, or a least a significantly increased width of the region of the sample is able to be imaged in-focus with a single image capturing exposure, thereby providing a high efficiency of in-focus image capture and data acquisition. By contrast, in conventional ellipsometers, the object plane and surface planes only coincide along a single intersection line, thus sharp focus is only achieved along this line resulting in only a narrow strip-shaped region of the detected image which is in an acceptable level of focus. Embodiments of imaging ellipsometers not only substantially increase the imaging and data collection efficiency but also reduce the amount of redundant data collection and unnecessary data processing. Also embodiments provide a significant increase in the temporal resolution of the imaging Ellipsometer since a larger sized region of in-focus detected image can be obtained with a single image capturing exposure. This allows real time imaging of dynamic phenomena to be performed. Furthermore, by providing a detected image of the sample that is in-focus throughout the whole of the image (and not merely in a narrow strip-shaped region) the spatial resolution of the images is improved as well as the ellipsometric resolution of the values of Ψ and Δ calculated from measurements of the detected image. The calculation of Ψ and Δ is discussed later.

The limiting factor of the size or dimension of the sample that is able to be imaged in-focus with a single image exposure capture process is no longer restricted by the amount of depth of field and depth of focus. Instead the dimension of the detected image of the sample, which is in-focus across the entirety of the detected image, is merely dependent upon the dimensions of the beam of incident light, the dimensions of the focussing element, the dimensions of the detector and the magnification of the optical system.

Figure 3B shows an indication of the improvement in the focus of a detected image. The entirety of the detected image is in-focus, as opposed to merely a narrow strip-shaped portion of detected image of the sample being in- focus as in figure 1C. The correction and improvement of the focus of the detected image is due to the configuration of the components of the ellipsometer and the alignment of the relevant planes, namely: the coincidence of the surface plane 207 with the object plane 303; the coincidence of the detector plane 206 with the image plane 301; and the alignment of the detector plane 206, the focussing element plane 205 and the surface plane 207 such that the planes intercept along a single line 208.

Figure 4A shows an embodiment of an imaging ellipsometer 400 having a principal axis 401. The ellipsometer 400 is set up such that the above mentioned alignment of the planes is adopted. The principal axis 401 is defined as a straight line which passes through each of: the surface of the sample 201, the focussing element 203 and the detector 204. Preferably, the principal axis 401 passes through the optical centre of the focussing element

203 and the central area of the region under analysis of the reflecting surface 201. The principal axis 401 is aligned along the plane of incidence. The focussing element 203 has a focussing element axis 402. This is defined as an axis perpendicular to the focussing element plane 205 which passes through the optical centre of the focussing element 203. Furthermore, the focussing element axis 402 intersects the principal axis 401 at the optical centre or front nodal point of the lens. In the embodiment shown in figure 4A, the focussing element 203 is fixed such that the focussing element axis 402 is coincident with the principal axis 401.

A detector angle, a, is defined as the angle between a normal to the detector 204 and the principal axis 401. An angle of incidence, θ, is defined as the angle between a normal to the reflecting surface 201 and an incident ray of light 403. For imaging ellipsometers, it is common that the angle of incidence is oblique, i.e. not parallel, to the normal to the reflecting surface 201. Accordingly, ellipsometers are typically configured 'off-axis', i.e. the detector 204, focussing element 203 and surface 201 are not parallel with one another and perpendicular to the principal axis 401.

Two types of image distortion are evident in images detected for such off- axis configurations: a) Keystone distortion occurring due to the object surface and detector plane not being parallel to one another b) Perspective projection distortion due to the projection of a three dimensional system onto a two dimensional plane.

Keystone distortion occurs whenever the object plane is not parallel to the detector plane. As an example, where a sample to be imaged comprises a series of lines each parallel to the plane of incidence these lines, when imaged, are no longer parallel but appear to converge. This is due to a slight variation of magnification along the image in a direction parallel to the plane of incidence because the distance between the focussing element and points along the surface/object plane and the distance between the focusing element and the corresponding image points on the detector/imaging plane vary along the length of the detected image. This results in a slight variation of magnification in the detected image and so an apparent convergence of imaged lines which correspond to the parallel lines on the sample. The keystone distortion is not as significant or pronounced as the perspective projection distortion since it is only noticeable for large sized samples and their corresponding detected images. Thus the converging parallels distortion that occurs in relatively small samples is tolerable. However, in order to reduce the keystone distortion imaging ellipsometer embodiments could employ image processing algorithms to correct the distortion or the 'focus stacking' imaging technique to create a composite image formed from sub-images of wide band shaped regions of a detected sub- image of the surface of the sample. The width of the band would be determined such that an acceptable level of converging parallels distortion takes place. This would be particularly applicable for imaging of non-dynamic phenomena. Embodiments would require fewer sub-images than conventional ellipsometers since a wider in- focus band of each detected sub-image could be used. Perspective projection distortion occurs when a planar surface is projected onto a second planar surface that is not parallel to the first. This is caused by the fact that the projection of the real image of the sample on the object plane onto the image plane will be compressed in a direction parallel to the plane of incidence, whereas there is no corresponding compression in the orthogonal s direction. This can result in, for example the effective magnification in the p direction being half that in the s direction. Perspective projection leads to a distortion of the resulting image, for example a detected image of a circular sample would be distorted such that it would be compresses along the p direction resulting in an oval shaped detected image of the circular sample. With conventional imaging ellipsometers, the degree of perspective projection distortion of a detected image varies with the angle of incidence of the incident electromagnetic radiation used. Accordingly, images detected at different angles of incidence would have different levels of image distortion and thus such images would not be suitable for being directly compared with one another as the area of the real image of the sample that is detected in each image will differ. As an example, the eccentricity of a real image of a circular sample detected at the detector would vary according to the angle of incidence at which the image was detected. Accordingly, images detected at different angles of incidence would have differently shaped images of the circular sample and therefore, such detected images could not be directly compared with each other.

Figure 4B shows a detector 204 and a surface of the sample 201 (the focussing element is not shown) in an off-axis ellipsometer. Here the sample has a length x. The length V₁ is given by y_λ = x ^■ cos(<9) . The projected length of the sample imaged at the detector 204 y₂ is given by: y_{x =} x -cos(0) cos(or) cos(cc)

Inclining the detector 204 with respect to the principal axis 401 such that the detector angle is equal to the angle incidence, i.e. a = θ , eliminates the perspective projection distortion since y₂ = x.

It can be shown that the magnification, M, of the ellipsometer shown in Figure 4A can be defined as:

_ tan(αr) _ B tan(0) ^~ R In order to eliminate the perspective projection distortion, the condition

OF¹Q must be met. In this case, the magnification of an ellipsometer so configured is limited to a fixed value of M = - 1.

However, under this condition even images taken at different angles of incidence would not suffer from perspective projection distortion. Such images would appear substantially the same and would appear as if the image was captured from the normal to the sample plane. Accordingly, such images could be directly compared with one another. This enables the angle of incidence to be freely altered providing the user with an additional degree of freedom. For instance the angle of incidence could be used as a control variable in addition to the wavelength of the incident electromagnetic radiation. Using the angle of incidence as a control variable is not possible with conventional imaging ellipsometers since varying the angle of incidence varies the amount of perspective projection distortion and thus the level of image compression.

If it is not necessary to completely eliminate the perspective projection distortion then it is not necessary to maintain the condition a = θ and so larger values of the angle a can be used to allow the magnification to be increased. However if images taken from different angles of incidence are to be directly comparable then the ratio — — can be kept constant so that the amount of cos(or) perspective projection distortion is constant.

Figure 5A shows an embodiment of an imaging ellipsometer 500 in which the focussing element 203 is tiltable, i.e. a lens tilt configuration. Again, the various plane orientation constraints are employed, namely: the detector plane 206, the focussing element plane 205 and the surface plane 207 are arranged such that they intersect one another along a single line 208; the object plane 303 is arranged to coincide with the surface plane 207; and the image plane 301 is arranged to coincide with the detector plane 206.

However, in the embodiment of figure 5, the focussing element 203 is tillable such that the focussing element axis 402 is not fixed so as to be coincident with the principal axis 401. The focussing element 203 is able to be inclined with respect to the principal axis to provide a non-zero focussing element angle, δ. The focussing element angle δ is defined as the angle between the focussing element axis 402 and the principal axis 401. In the ellipsometer 500, the magnification M is given by: M = ^cos(^θ) - ^sin(^{a + δ}) cos(or) • sin(6> - δ)

Thus by providing the ability to vary the focussing element angle δ it is possible to alter the magnification of the ellipsometer whilst maintaining the plane alignment requirements necessary to improve the focus of a detected image as well as the a = θ requirement necessary to correct for perspective projection distortion. In this case the equation for the magnification reduces to: sin(or + δ) sin(# + δ)

M = - sin(αr - δ) sin(# - δ) If the focussing element is tilted relative to the principal axis then its focal length measured along the principal axis is greater than the focal length, / , measured along the focussing element axis. In this case the effective focal length, /' , i.e. the focal length along the principal axis, may be determined as:

cos(<5)

Figure 5B provides a plot of ellipsometer magnification versus the angle of incidence θ where the ellipsometer is arranged to correct for focus correction and the ellipsometer is further arranged under the condition a = θ for eliminating perspective projection distortion. This plot shows that whilst maintaining optimum focus and the condition a = θ , the magnification can be increased if δ is increased. The maximum magnification at which focus correction and the elimination of distortion can both be achieved is determined by the maximum focussing element angle δ_max. In practice, δ_max is limited by the coverage angle of the focussing element. With modern computer designed wide angle camera lenses, a coverage angle in excess of 100° can be achieved and thus focussing element angles in excess of ± 45° would be possible.

Figure 6A shows an alternative embodiment of the invention in which the detector plane 206 is tilted in the opposite direction to that shown previously. The required geometry for the alternative embodiment may be described by the equation: cos(<9) • sin(α + S)

M = — - cos(α) • sin((9 - o)

In the embodiment shown in figure 6 A, if the detector plane 206 is tilted in a clockwise direction and the lens plane 205 is tilted sufficiently then the Scheimpflug intersection line 208 will move further and further to the left. In the limit that δ = θ = -a , the modulus of the magnification M will tend towards infinity. Figure 6B shows that in this alternative lens tilt configuration, where S = θ = -a ; the detector plane 206, lens plane 205 and surface plane 207 are all parallel to one another then the Scheimpflug intersection line converges at infinity. The geometry resembles that of a conventional camera except that the lens 203 and detector 206 are shifted laterally with respect to the surface plane so that the principal axis 401 is not perpendicular to the surface plane 207, lens plane 205 or detector plane 206. Accordingly, the principal axis is oblique to a normal to the surface plane 207.

In this geometry the locations of the focussing element 203 and the detector 204 along the principal axis 401 are linear distances and the image plane 206 and focussing element plane 205 are parallel to the surface plane 207 associated with the sample 201.

The distance B along the principal axis 401 between the detector 204 and the focussing element 203 is given by: 5_{= /}' .₍₁_M) = ^ζ- = -4--(l-M) = ^{R '}f

R - f COS(£) R - cos(δ) - f

The distance R along the principal axis 401 between the focussing element 203 and the intersection of the principal axis with the surface plane 207 is given by:

^ _{= /},₍₁-±_{) =} ^l ₌ ^-.₍₁-±_{) =} ^B-f

M B -f' cos(8) M B - cos(δ) -f In this embodiment the magnification achievable whilst optimally focussed images are achievable is unlimited.

/ f - RcOS(S)

Furthermore, as the condition a = -θ is met, the perspective projection distortion will be completely eliminated. Additionally as the object and detector planes are parallel than the keystone distortion will be completely eliminated. The above mentioned embodiment may be implemented provided that the available tilt angle of the lens δ is greater than the required angle of incidence θ . Where the angle of incidence required is less than the available lens tilt angle, this embodiment is preferable as the magnification is unlimited 5 and greater overall distortion correction is possible. When the required angle of incidence is greater than the available lens coverage angle the previous embodiment, shown in figure 5A, is preferably used.

The spatial resolution achievable with an imaging ellipsometer with a CCD detector is limited by three factors: 0 the diffraction limited resolution of the focussing element, s^; the CCD' s pixel limited resolution, s_p; and the focus limited resolution.

The diffraction limited resolution of the focussing element will impose the ultimate limit on the resolution attainable. If this is expressed in terms of5 the optical magnification and the focal ratio of the focussing element then it will take the form:

where:

F is the focal ratio of the focussing element defined as F=f/d and0 d is the diameter of the focussing element. λ= wavelength of incident electromagnetic radiation For any given focussing element s_d this will be minimized when the magnification is high and the focal ratio is low.

The maximum achievable resolution of the ellipsometer will also be5 affected by the size of the pixels in the CCD array and the magnification at which the ellipsometer is used. If two closely spaced spots on the sample are viewed by the CCD detector such that the real images of each spot both fall on the same pixel then they will not be resolved. However, if the magnification of

1019752v1 the ellipsometer is increased or the dimensions of the pixels reduced so that the images fall on separate pixels separated by an intermediate pixel (as required by Nyquist-Shanon sampling theory) then they will be resolved. The pixel limited resolution s_p can therefore be given as:

s - ^hph

" 2 -M where: h_pix is the dimension of a pixel

The maximum resolution of the imaging ellipsometer will be achieved only if the system is perfectly focused. When the surface of the sample to be imaged does not precisely coincide with the object plane or the image plane does not precisely coincide with the detector plane, then the detected image consists of a number of overlapping circles of confusion, χ, which will reduce the maximum resolution achievable. The size of the circles of confusion, χ, relate to the focus limited resolution. The size of the circle of confusion χ on the detector as a function of position v along the detector can be given by: cos(α) a - f z⁽y) = 1 - c -v-R -b + (R -f) - a

- B F - (I -M) v- tan(θ- S) + (R -f) - a where α = cos(#) + sin(0) • tan(0 - δ) b = cos(<9) + sin(<9) • tan(<9 + ά) c = tan(6> - δ) - tan(6> + α)

If a complete focus correction is not possible and the depth of field is used to render the image in apparent focus then the resolution will be lower at the extremes of the image than in the centre where a perfect focus is achieved. Figure 7 shows a comparison of the diffraction, pixel and focus limited resolution limits of an embodiment of an imaging ellipsometer by plotting the resolution limits against the magnification. Under the condition cc = θ the maximum value of v is obtained from v = - h_CCD/2M , where h_CCD is the dimension of the CCD array. This plot shows that the three resolutions are heavily dependant on the magnification of the ellipsometer. For conventional ellipsometers, at the centre of the detected image where the focus is perfect, the resolution is limited at low magnifications by the pixel resolution and at higher magnifications by the diffraction resolution. The plot shows the focus limited resolution, which is related to the circle of confusion, calculated at an extreme top region of a detected image for an ellipsometer according to embodiments of the present invention as well as a conventional ellipsometer. It is clearly shown that, in the region of a magnification of 1 , the focus limited resolution is smaller for the ellipsometers according to the embodiment.

Typically, ellipsometers are used to measure the two ellipsometric angles Ψ and Δ. These are related to the electronic field reflectivity of the sample in the p and s directions, R_p and R_s respectively, by:

D

~^ = tan(ψ) - e^iA

^Rs where:

Ψ is a measure of the ratio of the reflectivities of the sample in the p and s directions

Δ = δ_p - δ_s , Δ is a measure of the change of phase between the electronic field in the p direction and the electronic field in s direction following reflection from the sample δ_p = change in phase of electronic field in the p direction following reflection from the sample δ_s = change in phase of electronic field in the s direction following reflection from the sample A variable to be determined in an imaging ellipsometer is typically film thickness but could also equally well be the refractive index of the film or surface roughness etc. N parameters may theoretically be determined simultaneously if N sets of Ψ-Δ values are obtained corresponding to N values of a control variable. Control variables include: the wavelength and angle of incidence of the incident electromagnetic radiation.

If all other film parameters remain constant, then Ψ and Δ will vary periodically with increasing film thickness. The trace obtained by plotting Ψ and Δ for an increasing film thickness is referred to as a Ψ-A trajectory.

If the absorption of the film is zero then Ψ and Δ will return to their initial values as the film thickness tends towards its periodicity thickness or an integer multiple thereof. If the absorption of the film is non-zero then Ψ and Δ will not return to their initial values. If the absorption is small Ψ and Δ will vary in a cyclic fashion. The periodicity thickness, dp_er, for a film is calculated from:

where: ni is refractive index to the ambient medium n₂ is the refractive index of the sample film λis the wavelength of the incident light

The accuracy with which Ψ and Δ can be determined is dependant on the method by which they are found and the accuracy of the ellipsometer. If the uncertainty in Ψ and Δ is fixed then the accuracy with which the film thickness can be determined will be maximized when the Ψ-Δ trajectory occupies the maximum proportion of the Ψ-Δ space. It is found that this condition occurs when the angle of incidence of the incident electromagnetic radiation is equal to the Brewster angle of the sample.

Referring now to figure 8, this shows a constraining device 800 suitable for mounting and moving the sample stage 202, the focussing element 203 and the detector 204 such that the detector plane 206, the focussing element plane 205 and the surface plane 207 are arranged to intersect along a single line 208. Each of the detector 204, focussing element 203 and sample stage 202 are mechanically connected together. An elongate supporting member 801, upon which the detector 204 is mounted at a distal end, is arranged to rotate, as indicated by arrow 802, about a hinge located at a proximal end. The hinge is located such that the supporting member pivots about a pivot point at 208. Likewise, an elongate supporting member 803 is provided to support the focussing element 203 mounted at a distal end. The member 803 is arranged to pivot about a pivot point 208 as indicated by arrow 804 via a hinge. Also, a supporting member 805 is provided to support the stage 202 which is mounted at a distal end of the member 805. The member is arranged to pivot about a pivot point at 208 as indicated by arrows 806 via a hinge. The hinges for each of the detector, the focussing element and the stage are arranged such that the respective pivot points are located on a point on the line 208 where the detector plane, the focussing element plane and the surface plane intersect. Furthermore, the components, i.e. the detector, focussing element and stage, are mounted on their respective support members such that the components are aligned along the plane of the incident light and the principal axis. To provide further degrees of freedom of movement of the components, each support member 801, 803 and 805 is provided with a device for allowing translational movement of its component along the length of the member as indicated by arrows 807, 808 and 809 respectively. The lens angle δ between the principal axis and the normal to the lens plane can be altered by rotating the lens support member 803 about point 208, as shown by arrow 804. This results in the lens plane 205 also rotating about point 208 and thus changing the angle of the lens plane with respect to the principal axis. In order to keep the lens 203 appropriately aligned on the principal axis, the lens 203 is moved along the length of the support 803, as shown by arrow 808, until the centre of the lens 203 lies on the principal axis.

Figure 9 shows an alternative constraining device 900 in which each component is provided with its own adjustment device 901, such as an actuator, that is arranged to adjust the rotational orientation and/or translational position of the component. A controller 903 provides controlling signals to a processor 902 which in turn provides signals to the adjustment devices 901 such that each adjustment device 901 is able to appropriately adjust the translational position and rotational orientation of its respective component such that the detector plane, the focussing element plane and surface plane are suitably arranged so as to meet the various alignment constraints as discussed above with regards to either the embodiment shown in Figure 5 A or the embodiment shown in figure 6B. For example, the controller 903 is operable to cause the adjustment devices 901 to adjust their respective component such that the detector plane, the focussing element plane and surface plane all intercept along a single line or alternatively are all parallel to one another. Furthermore, the controller 903 is operable to cause the adjustment devices 901 to adjust their respective component such that the object plane coincides with the surface plane and the detector plane coincides with the image plane.

According to a further embodiment of the present invention, an algorithm is provided to determine the appropriate arrangement of each of the detector, the focussing element and the stage. As an example, a user of a given ellipsometer is able to input a desired magnification and a desired angle of incidence, such as the Brewster angle for the sample to be analysed. The algorithm, with knowledge of the initial relative position and orientation of each of the components of the given ellipsometer, is arranged to calculate and output signals representing the appropriate rotational orientation and translational position of each of the components such that the various planes and axes are appropriately arranged as previously discussed.

As will be well known to those skilled in the art, an imaging ellipsometer according to embodiments of the present invention is able to be used to determine the ellipsometric angles Ψ and Δ. Measurement techniques devised for conventional imaging ellipsometers such as null ellipsometry, off- null ellipsometry and radiometric ellipsometry are readily applicable to embodiments of the present invention. Preferably, radiometric ellipsometry is used. One of many possible techniques that could be employed is Dynamic Imaging Microellipsometry, DIM, whereby several images are taken with the polarization state of the light being varied between each image. This can be achieved by altering the polarizer or analyser azimuth angles or altering the phase of the incident light. As previously discussed, imaging ellipsometer embodiments allow for the use of the angle of incidence to be a possible control variable which was not possible for conventional ellipsometers. The intensities of the electromagnetic radiation detected at the detector for a given pixel of the detector's CCD in a set of images are then processed to obtain Ψ and Δ for that pixel. The resulting images of Ψ and Δ calculated for each pixel are termed an ellipsogram. Preferably a phase modulation technique is used such that the control variable is the phase of the light. Previous rotating element DIM systems required a rotating polarizer or a rotating analyser to alter the phase of the light. However, physically rotating an element of the optical system is undesirable since any such rotation introduces vibration into the optical components thereby introducing uncertainties and inaccuracies in the measurements. Accordingly, it is preferable to fix all optical components during the capture of images and when making measurements for determining Ψ and Δ. An improved and non-mechanical way of altering the phase of the light is to use a liquid crystal such as a twisted nematic liquid crystal cell to alter the phase of the electromagnetic radiation. The retardence of the liquid crystal is a function of the voltage applied across it. Such a liquid crystal can be used as a variable compensator. Using an algorithm making use of a Fourier series enables Ψ and Δ to be determined. As an example, in a PSCA imaging ellipsometer the following equations provide expressions for determining Ψ and Δ from measurements of intensities obtained by imaging ellipsometer embodiments. 1

where:

1 N-I

N ά

2 ^₁ ¹ _ ^2^^ v = — > / • cos

N ά " I N J

2 fc^» . (2m) w = — > / • sm N ώ " I N J

^/. =^/(4.⁾

_^4_π = 2 -π - n/N (the control variable phase angles) n = 0,1,2...(N-I)

Ν = total number of measurements per ellipsogram

Although the invention has been described with regards to imaging ellipsometers, it is equally applicable for Brewster Angle Microscopy or

Surface Plasma Resonance imaging. Preferably, electromagnetic radiation from the visible, infrared and ultraviolet parts of the electromagnetic spectrum is used.

Embodiments are particularly suitable to the field of Biosensors and Biochips where a high throughput of screening and analysis of a plurality of samples is desirable, i.e. a wide imaging field is required.

The invention is not restricted to the features of the described embodiments. It will be readily apparent to those skilled in the art that it is possible to embody the invention into specific forms other than those of the preferred embodiments described above.

Claims

1. An imaging ellipsometer for imaging a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising:

5 a focussing element for focusing electromagnetic radiation specularly reflected from said surface, the focussing element having a focussing element plane; wherein the focussing element defines a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects a principal axis; 0 a detector for detecting specularly reflected electromagnetic radiation focussed by the focussing element at a detector plane; and a stage for supporting said surface; at least one constraining device for constraining the movement of the ellipsometer such that: 5 the detector plane, the focussing element plane and said surface plane are at least substantially arranged to intersect along a single line; the detector, the focussing element and said surface at least substantially align along a straight line defining the principal0 axis; and the focussing element is tiltable with respect to the principal axis such that the magnitude of an angle, δ, between the focussing element axis and the principal axis is able to be greater than 0 radians. 5

2. The ellipsometer claimed in claim 1 wherein the focussing element defines an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is

1019752v1 greater than a focal distance of the focussing element, are focussed by the focussing element along the image plane; and the at least one constraining device is operable such that: the object plane at least substantially coincides with said surface plane; 5 and the image plane at least substantially coincides with the detector plane.

3. The ellipsometer claimed in claims 1 or 2 wherein the at least one constraining device is operable such that: 0 an angle of incidence, θ, of electromagnetic radiation incident on said surface is at least substantially equal to an angle, α, between a normal to the detector plane and the principal axis.

4. The ellipsometer claimed in claim 2 wherein the at least one5 constraining device is operable such that, for a given desired imaged magnification, M: an angle of incidence, θ, of electromagnetic radiation incident on said surface and an angle, α, between a normal to the detector plane and the0 principal axis satisfy: tan(cκ)

M = - tan(6>) ^'

5. The ellipsometer claimed in any previous claim wherein the at least one constraining device is operable such that, for a given desired magnification, M:5 an angle of incidence, θ , of electromagnetic radiation incident on said surface, an angle, α, between a normal to the detector and the principal axis and

1019752V1 the angle, δ, between the focussing element axis and the principal axis satisfy: cos(#) • sin(« + S) cos(α) • sin(# - S)

5 6. The ellipsometer claimed in any previous claim wherein the at least one constraining device is operable such that: an angle of incidence, θ, of electromagnetic radiation incident on said surface is at least substantially equal to a Brewster angle of the reflecting surface. 0

7. The ellipsometer claimed in any previous claim wherein the focussing element, the detector and the stage are mechanically connected, the mechanical connection forming the constraining device. 5

8. The ellipsometer claimed in any previous claim wherein the constraining device comprises: at least one adjustment device for adjusting a rotational orientation or a translational position of at least one of: the detector, the focussing element and the stage. 0

9. The ellipsometer claimed in claim 8 further comprising an automated control system comprising a processor under control of a controller, the system adapted to control the at least one adjustment device. 5 10. An automated control system adapted to constrain the arrangement of at least one of: the detector, the focussing element and the stage of the imaging ellipsometer claimed in any previous claim.

1019752V1

11. A method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane, the focussing 5 element defining a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects a principal axis; a detector having a detector plane; and a stage for supporting said surface; 0 the method comprising the steps of: causing the detector, the focussing element and said surface to align, at least substantially, along a straight line defining the principal axis; causing the detector plane, the focussing element plane and said surface plane to intersect, at least substantially, along a single line; and 5 causing an angle, δ, between the focussing element axis and the principal axis to be greater than 0 radians.

12. The method claimed in claim 11 wherein the focussing element further defines an image plane, the image plane being the plane whereby objects0 located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the focussing element along the image plane; and the method further comprises the steps of causing: the object plane, at least substantially, to coincide with said5 surface plane; and the image plane, at least substantially, to coincide with the detector plane.

1019752V1

13. The method claimed in claims 11 or 12 further comprising the step of causing: an angle of incidence, θ, of electromagnetic radiation incident on said surface, at least substantially, to be equal to an angle, α, 5 between a normal to the detector plane and the principal axis.

14. The method claimed in any of claims 11 to 13 further comprising the step of causing, for a given desired imaged magnification, M: an angle of incidence, θ, of electromagnetic radiation incident on 10 said surface and an angle, α, between a normal to the detector plane and the principal axis to satisfy:

_{M =} _ tan(«) tan(6>)

15

15. The method claimed in any of claims 11 to 14 further comprising the step of causing, for a given desired magnification, M: an angle of incidence, θ , of electromagnetic radiation incident on said surface,

20 an angle, α, between a normal to the detector and the principal axis and the angle, δ, between the focussing element axis and the principal axis to satisfy:

_{Λ c} , _ cos(<9) • sin(or + δ)

25 M = — - cos(or) • sin((9 - δ)

1019752v1

16. The method claimed in any of claims 11 to 15 further comprising the step of causing: an angle of incidence, θ, of electromagnetic radiation incident on said surface to be at least substantially equal to a Brewster angle of the reflecting 5 surface.

17. A method of determining the ellipsometric angles Ψ and Δ of a substance using the method as claimed in any of claims 11 to 16. 0

18. An algorithm for determining the appropriate arrangement of at least one of: a detector, a focussing element and a stage of an imaging ellipsometer, wherein the algorithm is adapted to output signals representing the rotational orientation and translational position of the at least one of: the detector, the focussing element and the stage to implement the method as claimed in any of5 claims 11 to 17.

19. An imaging ellipsometer for imaging a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element for focusing electromagnetic radiation specularly0 reflected from said surface, the focussing element having a focussing element plane; a detector for detecting specularly reflected electromagnetic radiation focussed by the focussing element at a detector plane; and a stage for supporting said surface; 5 at least one constraining device for constraining the movement of the ellipsometer such that: the detector plane, the focussing element plane and said surface plane are arranged so as to be aligned parallel to one another.

1019752V1

20. The ellipsometer claimed in claim 19 wherein the focussing element defines an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the

5 focussing element along the image plane; and the at least one constraining device is operable such that: the object plane at least substantially coincides with said surface plane; and the image plane at least substantially coincides with the detector plane.0

21. The ellipsometer claimed in claims 19 or 20 wherein the at least one constraining device is operable such that: the detector, the focussing element and said surface align at least substantially along a straight line defining a principal axis. 5

22. The ellipsometer claimed in claim 21 wherein the at least one constraining device is operable such that the principal axis is oblique to a normal to said surface plane. 0 23. The ellipsometer claimed in any of claims 21 to 22 wherein: the focussing element defines a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects the principal axis; and: an angle, δ, between the focussing element axis and the principal5 axis; an angle of incidence, θ, of electromagnetic radiation incident on said surface; and an angle, α, between a normal to the detector plane and the principal axis satisfy:

1019752V1 S = θ = -a

24. The ellipsometer claimed in any of claims 21 to 23 wherein: the focussing element defines a focussing element axis, the focussing 5 element axis being an axis perpendicular to the focussing element plane and which intersects the principal axis; and at least one constraining device is operable such that, for a given desired imaged magnification, M: a separation distance, B, along the principal axis between the0 focussing element and the detector; an angle, δ, between the focussing element axis and the principal axis; and a focal length, f, along the focussing element axis satisfy:

M = I - l 5

25. The ellipsometer claimed in any of claims 21 to 23 wherein: the focussing element defines a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects the principal axis; and 0 the at least one constraining device is operable such that, for a given desired imaged magnification, M: a separation distance, R, along the principal axis between the focussing element and the surface plane; an angle, δ, between the focussing element axis and the principal5 axis; and a focal length, f, along the focussing element axis satisfy:

M =- / f -Rcos(S)

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26. The ellipsometer claimed in any of claims 19 to 25 wherein the at least one constraining device is operable such that: an angle of incidence, θ, of electromagnetic radiation incident on said surface is at least substantially equal to the Brewster angle of the reflecting 5 surface.

27. The ellipsometer claimed in any of claims 19 to 26 wherein the focussing element, the detector and the stage are mechanically connected, the mechanical connection forming the constraining device. 0

28. The ellipsometer claimed in claim in any of claims 19 to 27 wherein the constraining device comprises: at least one adjustment device for adjusting a rotational orientation or a translational position of at least one of: the detector, the focussing 5 element and the stage.

29. The ellipsometer claimed in claim 28 further comprising an automated control system comprising a processor under control of a controller, the system adapted to control the at least one adjustment device. 0

30. An automated control system adapted to constrain the arrangement of at least one of: the detector, the focussing element and the stage of the imaging ellipsometer claimed in any of claims 19 to 29. 5 31. A method for arranging an imaging ellipsometer to image a substantially planar reflecting surface, the surface defining a surface plane, the ellipsometer comprising: a focussing element having a focussing element plane; a detector having a detector plane; and

1019752v1 a stage for supporting said surface; the method comprising the steps of: causing the detector plane, the focussing element plane and said surface plane to be aligned at least substantially parallel to one another. 5

32. The method claimed in claim 31 wherein the focussing element further defines an image plane, the image plane being the plane whereby objects located along an object plane, at a distance from the focussing element that is greater than a focal distance of the focussing element, are focussed by the0 focussing element along the image plane; and the method further comprises the steps of causing: the object plane, at least substantially, to coincide with said surface plane; and the image plane, at least substantially, to coincide with the5 detector plane.

33. The method claimed in claims 31 or 32 further comprising the step of causing the detector, the focussing element and said surface to align at least substantially along a straight line defining a principal axis. 0

34. The method claimed in claim 33 further comprising the step of causing the principal axis to align obliquely to a normal to said surface plane.

35. The method claimed in any of claims 33 to 34 wherein the focussing5 element defines a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects the principal axis and further comprising the step of causing: an angle, δ, between the focussing element axis and the principal axis;

1019752V1 an angle of incidence, θ, of electromagnetic radiation incident on said surface; and an angle, α, between a normal to the detector plane and the principal axis 5 to satisfy:

S = θ = -a

36. The method claimed in any of claims 33 to 35 wherein the focussing element defines a focussing element axis, the focussing element axis being an0 axis perpendicular to the focussing element plane and which intersects the principal axis and further comprising the step of causing, for a given desired imaged magnification, M: a separation distance, B, along the principal axis between the focussing element and the detector; 5 an angle, δ, between the focussing element axis and the principal axis; and a focal length, f, along the focussing element axis to satisfy.

f 0

37. The method claimed in any of claims 33 to 35 wherein the focussing element defines a focussing element axis, the focussing element axis being an axis perpendicular to the focussing element plane and which intersects the principal axis and further comprising the step of causing, for a given desired5 imaged magnification, M: a separation distance, R, along the principal axis between the focussing element and the surface plane;

1019752V1 an angle, δ, between the focussing element axis and the principal axis; and a focal length, f, along the focussing element axis to satisfy:

5 M = £- f ~Rcos(δ)

38. The method claimed in any of claims 31 to 37 further comprising the step of causing: an angle of incidence, θ, of electromagnetic radiation incident on said0 surface to be at least substantially equal to a Brewster angle of the reflecting surface.

39. A method of determining the ellipsometric angles Ψ and Δ of a substance using the method as claimed in any of claims 31 to 38. 5

40. An algorithm for determining the appropriate arrangement of at least one of: a detector, a focussing element and a stage of an imaging ellipsometer, wherein the algorithm is adapted to output signals representing the rotational orientation and translational position of the at least one of: the detector, the0 focussing element and the stage to implement the method as claimed in any of claims 31 to 39.

1019752v1