Fast generalized multiwavelength ellipsometer

Abstract

An ellipsometer is provided that uses a broadband light source and a Fresnel cone to produce a simultaneous broadband polarization state generator without moving parts. The detector of the ellipsometer includes a diffractive element to spatially separate the wavelengths of light from the sample. The wavelengths can be sufficiently separated in space so that there is no overlap of wavelength bands when imaged by a two-dimensional sensor, or can be separated in time. In addition, the detector separates and simultaneously analyzes the polarization state of the light from the sample so that there is no overlap of polarization states when imaged by a two-dimensional sensor, and no moving parts are used. The resulting image with separated wavelengths and polarization states can be used to determine at least part of the Mueller matrix of the sample.

Description

[0001] Cross Reference to Related Patent Applications

[0002] This application claims priority under 35 USC 119 to U.S. Non-Provisional Application No. 16 / 796,648, filed February 20, 2020, entitled “FAST GENERALIZED MULTI-WAVELENGTH ELLIPSOMETER,” which is incorporated by reference herein in its entirety. BACKGROUND

[0003] An ellipsometer is an optical metrology device that detects changes in the polarization state of light reflected from the surface of a sample to measure properties of the sample. A conventional spectroscopic ellipsometer includes a broadband light source, a polarization state generator, a polarization state analyzer, and a detector. Spectroscopic ellipsometers can be used to produce generalized (e.g., full Mueller matrix) ellipsometric measurements at multiple wavelengths. Typically, rotating optics (e.g., one or more of a rotating polarizer, analyzer, or compensator) are used to generate the ellipsometric measurements. However, using rotating optics to generate the measurements is relatively slow.

[0004] One design that eliminates the need for rotating optics is a four-detector polarimeter, in which four independent polarization state detectors (PSDs) are used in conjunction with a beam splitter or modulation technique. Using four independent PSDs eliminates the need for rotating optics on the detection side of the ellipsometer and allows the entire polarization state of the light beam to be measured simultaneously after reflection from the sample. However, four-detector polarimeters have several drawbacks. For example, the initial polarization state is either 45° linearly polarized light, which limits the final measurements to 12 of the 16 Mueller elements, or is modulated in time through several input polarizations, which increases the measurement time and requires rotating optical elements. In addition, the instrument is either designed as a single-wavelength ellipsometer, or requires the use of 4 different spectrometers, one for each PSD, requiring complex calibration and computer control to operate. Furthermore, the tool uses 4 separate beam paths, one for each PSD, making the tool difficult to calibrate, difficult to align, and expensive.

[0005] It is desirable to have an improved ellipsometer that reduces the time required to complete generalized (full Mueller matrix) ellipsometric measurements at multiple wavelengths. SUMMARY

[0006] An ellipsometer uses a broadband light source and a Fresnel cone to produce a simultaneous broadband polarization state generator without moving parts. The detector of the ellipsometer includes a diffractive element to spatially separate the wavelengths of light from the sample. The wavelengths can be sufficiently separated in space so that there is no overlap of wavelength bands when imaged by a two-dimensional sensor, or can be separated in time. Additionally, the detector separates and simultaneously analyzes the polarization state of the light from the sample, so there is no overlap of polarization states when imaged by a two-dimensional sensor, and no moving parts are used. The resulting images with separated wavelengths and polarization states can be used to determine at least a partial Mueller matrix of the sample.

[0007] In one embodiment, an ellipsometer includes a light source that emits light having a plurality of wavelengths, a polarizer that polarizes the light to produce polarized light, a Fresnel cone that receives the polarized light and produces sample light having a plurality of polarization states at each of the plurality of wavelengths, a lens system that causes the sample light to be incident on a sample and receives reflected light from the sample, a detector that receives the reflected light, the detector including at least one diffractive element that separates wavelengths in the reflected light, a polarization separator that receives the reflected light and separates the reflected light into a plurality of polarization states, a two-dimensional sensor that receives images of the spatially separated wavelengths in each of the plurality of polarization states of the reflected light, and a processor that receives the images from the two-dimensional sensor and determines at least a partial Mueller matrix of the sample using the images of the spatially separated wavelengths in each of the plurality of polarization states of the reflected light.

[0008] In one embodiment, a method of characterizing a sample with an ellipsometer includes generating light having a plurality of wavelengths, polarizing the light, modifying the polarized light using a Fresnel cone to produce sample light having a plurality of polarization states at each of the plurality of wavelengths, causing the sample light to be incident on a sample, wherein the sample light interacts with the sample and is reflected by the sample, producing reflected light, separating wavelengths in the reflected light using at least one diffractive element, separating the reflected light into a plurality of polarization states using a polarization separator, imaging the spatially separated wavelengths in each of the plurality of polarization states of the reflected light using a two-dimensional sensor, and determining at least a partial Mueller matrix of the sample using the images of the spatially separated wavelengths in each of the plurality of polarization states of the reflected light.

[0009] In one implementation, an ellipsometer includes means for generating light having a plurality of wavelengths; means for polarizing the light; means for modifying the polarized light to produce sample light having a plurality of polarization states at each of the plurality of wavelengths; means for causing the sample light to be incident on a sample, wherein the sample light interacts with the sample and is reflected by the sample, producing reflected light; means for separating the wavelengths in the reflected light; means for separating the reflected light into the plurality of polarization states; means for capturing one or more images of the separated wavelengths in each of the plurality of polarization states of the reflected light; and means for determining at least a partial Mueller matrix of the sample using the one or more images of the separated wavelengths in each of the plurality of polarization states of the reflected light. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 An ellipsometer configured to measure at least a partial Mueller matrix of a sample across a plurality of wavelengths without using moving parts is shown.

[0011] Figure 2A And Figure 2B Perspective and side views of a Fresnel cone are shown.

[0012] Figure 3 is a plot showing the condition number of the inverse for each pixel of the simulated beam output by an unmodified Fresnel cone for a given wavelength.

[0013] Figure 4A , Figure 4B , Figure 4C And Figure 4D A simulated pupil plot of a Fresnel cone for each Stokes component at one wavelength is shown.

[0014] Figure 5A , Figure 5B , Figure 5C And Figure 5D A simulated pupil plot of a Fresnel cone for each Stokes component at a wavelength different from the wavelength used to generate Figure 4A , Figure 4B , Figure 4C And Figure 4D

[0015] Figure 6 is a plot showing the condition of the inverse of a polarized beam of light resulting from 45° TIR in a Fresnel cone.

[0016] Figure 7 is a plot showing the refractive index of a coating material on a Fresnel cone relative to wavelength to produce a constant phase shift for different wavelengths.

[0017] Figure 8 ​Analog images of reflected light after beam sorting performed by wavelength diffraction elements and polarization splitters in the detector of an ellipsometer are shown.

[0018] Figure 9 Mueller matrix elements for a rotating uniaxial Ti02 film used in an ellipsometer are shown.

[0019] Figure 10 is a diagram showing another embodiment of a detector that can be used with an ellipsometer.

[0020] Figure 11 A spectrum with multiple non-contiguous wavelength bands produced by a broadband frequency comb light source or a Fourier domain mode locked laser light source that can be used with an ellipsometer is shown.

[0021] Figure 12 An example of an echelette that can be used as a polarization splitter in an ellipsometer is shown.

[0022] Figure 13 A single phase shift element that can be present on an echelette is shown.

[0023] Figure 14 Multiple phase shift elements arranged in sub-wavelength spacing in a one-dimensional grating unit cell that can be used in an echelette are shown.

[0024] Figure 15A , Figure 15B and Figure 15C A vertex within a Poincare sphere is shown.

[0025] Figure 16 is a diagram showing another embodiment of a detector that can be used with an ellipsometer.

[0026] Figure 17A An embodiment of a micro-polarizer array and two-dimensional sensor that can be used with an ellipsometer is shown.

[0027] Figure 17B A unit cell of four micro-polarizer pixels in a micro-polarizer array is shown.

[0028] Figure 18A is a diagram showing another embodiment of a detector that can be used with an ellipsometer.

[0029] Figure 18B is a diagram showing another embodiment of a detector that can be used with an ellipsometer.

[0030] Figure 19 A continuous wavelength spectrum that can be produced by a broadband light source that can be used with an ellipsometer is shown.

[0031] Figure 20 FIG. 2 is a diagram illustrating another embodiment of a detector that can be used with an ellipsometer.

[0032] Figure 21 FIG. 2 is a diagram illustrating another embodiment of a detector that can be used with an ellipsometer.

[0033] Figure 22 FIG. 3 is a flowchart illustrating a method of characterizing a sample with an ellipsometer as disclosed herein. DETAILED DESCRIPTION

[0034] Spectroscopic ellipsometers are capable of measuring the full Mueller matrix of a sample across multiple wavelengths without using moving parts, using a single beam path or a limited number of beam paths. Ellipsometers capable of measuring the full Mueller matrix are sometimes referred to as “generalized” ellipsometers, while “standard” ellipsometers can measure only 6 of the 16 Mueller elements. The elimination of moving parts improves measurement speed relative to traditional ellipsometers, and the use of a single beam path (or limited number of beam paths) improves accuracy and ease of use relative to, for example, a four-detector polarimeter or similar device.

[0035] Ellipsometers use a broadband light source and a Fresnel cone to produce a simultaneous broadband polarization state generator without moving parts. The Fresnel cone can use a high refractive index optical coating to keep the induced phase constant over a wide wavelength range of interest. Through the Fresnel cone, each wavelength contains a large solid angle of a Poincare sphere in the pupil plane of the light beam. The Fresnel cone utilizes total internal reflection to produce different polarization structures for light of multiple wavelengths and acts as a fully simultaneous broadband polarization state generator.

[0036] The detector of the ellipsometer includes one or more diffractive elements that separate the wavelengths of light reflected from the sample. For example, if the light source produces a non-continuous spectrum, such as a frequency comb, the diffractive elements can spatially separate the wavelength bands so that there is no overlap when imaged by the two-dimensional sensor. If the light source produces a continuous spectrum, one or more wavelength filters can be used with the diffractive elements to spatially separate the wavelength bands so that there is no overlap when imaged by the two-dimensional sensor.

[0037] Furthermore, the detector separates and simultaneously analyzes multiple polarization states of light reflected from the sample without moving parts. For example, a polarization separator in the form of a meta-grating can be used. The meta-grating diffracts the light reflected from the sample into separate orders based on the polarization state. Alternatively, beam splitters and Fresnel cones can be used to generate multiple different polarization states. Analyzers, for example, in the form of a fixed polarizer or a micro-polarizer array, are used to simultaneously analyze light with separated polarization states; this analyzer is not superimposed on a two-dimensional sensor. The resulting image with separated wavelengths and polarization states can be used to determine at least a portion of the Mueller matrix of the sample.

[0038] Figure 1 An ellipsometer 100 is shown, configured to measure at least a portion of the Mueller matrix of a sample across multiple wavelengths without using moving parts. As shown, the ellipsometer 100 includes a light source 102, a polarization state generator (PSG) 110, a polarization state analyzer (PSA) 145, and a two-dimensional sensor 146. The light source 102 is a broadband light source emitting multiple wavelengths, for example, in one or more bands. In some embodiments, the light source 102 may generate multiple discontinuous wavelength bands. In some embodiments, the light source 102 may generate multiple wavelength bands simultaneously, while in other embodiments, the light source 102 may generate each of the multiple wavelength bands separately, for example, over a short time period. For example, the light source 102 may be a broadband frequency comb light source or a Fourier domain mode-locked laser light source. In some embodiments, the light source 102 may generate multiple consecutive wavelengths, for example, within a single broadband wavelength. For example, the light source 102 may be a thermal (halogen) bulb or a high-voltage arc discharge plasma lamp. One or more optical components 104 may be used to collimate the light 103 generated by the light source 102.

[0039] The polarization state generator 110 includes a polarizer 112, such as a linear polarizer, a beam splitter 114, and a Fresnel cone 116. The polarizer 112 receives collimated light and generates linearly polarized light 113. The beam splitter 114 receives the polarized light 113 and directs it toward the Fresnel cone 116. The Fresnel cone 116 is an optical prism that uses two total internal reflections (TIR) ​​to introduce a desired phase difference between the two vertical components of the polarization. The Fresnel cone 116 utilizes total internal reflection (TIR) ​​to generate multiple polarization states at each wavelength of the light 113.

[0040] Figure 2A It shows, for example, from Figure 1 The polarizer 112 in the image receives linearly polarized input light 202. The polarization of the output light 204 obtained from the Fresnel cone 116 depends on the initial polarization of the input light 202, the refractive index of the cone material at the wavelength of the light, and the angle of incidence θ when incident on the back surface 210 of the Fresnel cone 116.Figure 2B A side view of the Fresnel cone 116 is shown, showing the cone material with a first refractive index n1 and a coating material 212 on the back face 210 of the Fresnel cone with a second refractive index n2.

[0041] Not every wavelength experiences the same phase shift through the Fresnel cone. For example, Figure 3 The condition number of the inverse of the combined Stokes vector for each pixel of the simulated beam output by the unmodified Zr02 Fresnel cone 116 is shown for a given wavelength. The condition number of the inverse of the combined Stokes vector serves as a predictor of the quality of any resulting elliptical polarization data. At some wavelengths, the output beam consists of only one polarization, for example, at ~705 nm, and the condition number is then close to 0, as shown. At other wavelengths, the beam has a different polarization structure, for example, at ~530 nm, which will result in a high quality elliptical polarization measurement. As an example, Figure 4A , Figure 4B , Figure 4C and Figure 4D show the simulated pupil plots for the Fresnel cone for each Stokes component S0, S1, S2, and S3 at a wavelength of 530.8 nm, respectively, while Figure 5A , Figure 5B , Figure 5C and Figure 5D show the simulated pupil plots for the Fresnel cone for each Stokes component S0, S1, S2, and S3 at a wavelength of 705.7 nm, respectively. As Figure 4B to Figure 4D shown, the pupil plots at a wavelength of 530.8 nm show a more varied polarization structure than the corresponding pupil plots at a wavelength of 705.7 nm, shown in Figure 5B to Figure 5D for example, Figure 5D show that there is no polarization information for S3 at 705.7 nm, while Figure 4D in 530.8 nm provides both positive and negative polarization information for S3.

[0042] When the ratio of the refractive index of the Fresnel cone 116 to the outside changes, the phase shift caused by TIR also changes. Certain phase shifts result in different polarization structures and will provide good elliptical polarization measurements, while other phase shifts produce only one polarization state and are useless. For example, Figure 6 is a plot showing the condition number of the inverse of the polarized beam on the Y axis, and the various phase shifts produced by a 45° TIR in the Fresnel cone 116.

[0043] As Figure 2BAs shown, the coating material 212 on the outside of the Fresnel cone 116 can control the phase shift of each desired wavelength to produce different polarization structures. In other words, the coating material 212 can be selected to produce a constant phase shift across the desired wavelengths. The following expression controls the requirements on the coating material 212.

[0044]

[0045] In Equation 1, d s represents the phase shift introduced between p- and s-polarized light, which is referred to as the s-shift compared to p, and thus uses the subscript "s". Figure 6 Various phase shifts are shown to result in acceptable polarization diversity, and thus, d s may be selected according to the convenience of other parts of the system. Figure 7 is a plot showing the refractive index of the coating material 212 on the ZrO2 Fresnel cone 116 versus wavelength to produce a constant phase shift of d s 43.42° for wavelengths.

[0046] Referring to Figure 1 , the Fresnel cone 116 receives polarized light 113 from the polarizer 112 via a beamsplitter 114, which is a non-polarizing beamsplitter. Figure 1 The beamsplitter 114 is shown to transmit light to the Fresnel cone 116, but the beamsplitter 114 can reflect light to the Fresnel cone 116 if desired. As described above, the Fresnel cone 116 uses TIR to create different polarization structures for light of multiple wavelengths. By appropriately selecting and designing the coating material 212, as shown, the Fresnel cone 116 can produce a constant phase shift across the desired wavelengths, thereby producing light from the Fresnel cone 116 that has different polarization structures for the desired wavelengths. Figure 2B The beamsplitter 114 receives light from the Fresnel cone 116 and directs the light 117 toward the sample 130.

[0047] Optionally, as shown, the beamsplitter 114 can direct a portion of the polarized light 113 received from the polarizer 112 to an intensity monitor 118, which can be used to monitor fluctuations in the input light for normalization of the measurements.

[0048] Figure 1 The light 117 from the Fresnel cone 116 (via the beamsplitter 114) is shown to be directed toward the sample 130 by a folding mirror 120, but other arrangements of optical elements can be used. Focusing optics 122 focus the light 117 onto a structure 132 on the sample 130 held on a stage 134. Figure 1Focusing optics 122 are shown with a single refractive lens, but multiple optical elements / lenses, either refractive or reflective or a combination of them, can be used. Stage 134 is capable of motion to create relative motion between sample 130 and the optical system of ellipsometer 100 so that sample 130 can be placed at multiple locations for measurement of different locations on sample 130. For example, stage 134 can move sample 130 linearly, for example, within a Cartesian coordinate plane (X, Y) directions, or can rotate and linearly move sample 130, for example, within a polar coordinate plane (R, Θ). If desired, stage 134, one or more optical elements of ellipsometer 100, or both can be moved, for example, stage 134 can be rotated while more optical elements of ellipsometer 100 are linearly moved. Stage 134 or optical elements of ellipsometer 100 can also be capable of vertical motion, for example, for focusing.

[0049] Structure 132 on sample 130 will change the polarization state of light 117, and reflected light 133 from sample 130 is received by focusing optics 136, which can match focusing optics 122. For example, focusing optics 136 can include multiple optical elements / lenses, either refractive or reflective or a combination of them. Light 133 is directed to a detector 140 including, for example, a polarization state analyzer (PSA) 145 with folded mirrors 138, but other arrangements of optical elements can also be used.

[0050] Detector 140 includes a wavelength separator 142, a polarization separator 144, a PSA 145, and a two-dimensional sensor 146. Wavelength separator 142 can spatially separate wavelengths in reflected light 133, e.g., where light source 102 simultaneously produces multiple wavelengths. For example, wavelength separator 142 can be a diffractive element that spatially separates multiple wavelengths in reflected light 133, and thus, wavelength separator 142 can sometimes be referred to herein as a wavelength diffractive element 142. In implementations where wavelength separator 142 spatially separates wavelengths in reflected light 133, two-dimensional sensor 146 can be used to simultaneously capture wavelength and polarization information along the separated axes. In another example, wavelength separator 142 can temporally separate multiple wavelengths in reflected light 133, e.g., where light source 102 simultaneously or sequentially produces multiple wavelengths. For example, wavelength separator 142 can be an acousto-optic tunable filter that separates wavelengths in reflected light 133 (using diffraction in this case) into narrow wavelength bands and rapidly switches between each band, e.g., with a minimum switching time of 200 ns, to capture each wavelength band over time. Wavelength separator 142 can temporally separate wavelengths in other ways. For example, other types of tunable filters similar to acousto-optic tunable filters can be used. In another implementation, light source 102 can sequentially produce multiple wavelengths and a high-speed camera can be used as sensor 146 to collect the separated wavelengths, which collects multiple frames, each frame representing one wavelength. In this implementation, wavelength separator 142 can be considered to be light source 102 and high-speed sensor 146, and thus, Figure 1 The examples of wavelength separator 142 shown in FIGS. 1-3 can be considered to be functional, rather than physical. In implementations where wavelength separator 142 temporally separates wavelengths in reflected light 133, two-dimensional sensor 146 can capture multiple frames, where each frame captures polarization information for a different wavelength.

[0051] Polarization separator 144 receives reflected light 133 and separates the reflected light into multiple polarization states. PSA 145 can be, e.g., one or more polarizers that receive light having separated polarization states and transmit light having a known orientation. Two-dimensional sensor 146, which can be, e.g., a CCD or CMOS sensor array, receives light and images the separated wavelengths at each of the multiple polarization states of reflected light 133. The separated wavelengths (spatially separated or temporally separated) and the spatially separated polarization states are clearly imaged by two-dimensional sensor 146, e.g., without overlap.

[0052] As an example, Figure 8A simulated image 800 of reflected light after beam splitting by wavelength-diffraction element 142 and polarization splitter 144 and analyzer 145 is shown (assuming ideal optics and uncoated Fresnel cones), with wavelength varying along the X-axis and polarization state varying along the Y-axis, labeled as tetrahedron vertices within a Poincare sphere, and specular transmission labeled as N. The simulated image is applicable to a 100 nm uniaxial TiO2 film on Ni that has been grown at an odd angle to the lab frame to produce off-diagonal MM data. As shown, image 800 includes a plurality of diffracted "polarization orders," one of which is identified with box 802. For example, image 800 shows four polarization states for 30 individual wavelengths in separate polarization orders. For example, box 804 identifies a wavelength, e.g., about 531 nm, with a good polarization structure that will produce accurate Mueller matrix measurements. In contrast, box 806 identifies a wavelength, e.g., about 706 nm, with a relatively poor polarization structure. A hypothetical white noise of 1% of maximum intensity is added to the simulation to produce image 800 in order to test measurement robustness. Even with a relatively small number of pixels (25 x 25) dedicated to each polarization order, very high accuracy is possible even with 1% noise due to redundancy.

[0053] Detector 140 is coupled to a computer system 170, such as a workstation, personal computer, central processing unit, or other appropriate computer system or systems. Computer system 170 is preferably included in, or connected to or otherwise associated with ellipsometer 100. Computer system 170 can control movement of stage 134, and collect and analyze ellipsometer data obtained from detector 140, as discussed. For example, intensity of reflected light 133 received at different calibration positions on two-dimensional sensor 146 simultaneously provides spectral and polarization-related data from which ellipsometric parameters ψ and Δ for a wavelength of interest can be determined, and from which at least a partial Mueller matrix for structure 132 on sample 130 at the wavelength of interest can be determined, from which various parameters of sample 130 can be determined. As an example, Figure 9 Simulated Mueller matrix elements for a rotating uniaxial TiO2 film for ellipsometer 100 are shown, with circles representing simulated data and lines representing theoretical data.

[0054] The computer system 170 can analyze the ellipsometric data to determine one or more physical properties of the sample 130. The computer system 170 includes at least one processor 172 having a memory 174, and a user interface including, for example, a display 176 and an input device 178. A non-transitory computer-usable storage medium 182 having computer-readable program code embodied therein can be used by the at least one processor 172 to operate as a special purpose computer programmed to perform the techniques disclosed herein. In accordance with the present disclosure, one of ordinary skill in the art can implement the data structures and software code described in this DETAILED DESCRIPTION for automatically implementing one or more actions, and store the data structures and software code on, for example, the computer-usable storage medium 182, which can be any apparatus or medium that can store code and / or data for use by a computer system, such as the at least one processor 172. The computer-usable storage medium 182 can be, but is not limited to, magnetic storage devices and optical storage devices, such as disk drives, magnetic tapes, optical discs, and DVDs (digital versatile discs or digital video discs). A communications port 184 can also be used to receive instructions for programming the at least one processor 172 to perform any one or more of the functions described herein, and can represent any type of communication connection, such as a communication connection to the Internet or any other computer network. The communications port 184 can further export signals (e.g., having measurement results and / or instructions) to another system (such as an external processing tool) in a feed-forward or feedback process to adjust process parameters associated with a manufacturing process step of the sample based on the measurement results. Additionally, the functions described herein can be embodied in whole or in part in the circuitry of an application-specific integrated circuit (ASIC) or a programmable logic device (PLD), and the functions can be embodied in a computer understandable descriptor language that can be used to create an ASIC or a PLD that operates as described herein.

[0055] Thus, the determined one or more physical properties of the sample 130 can be determined by the computer system 170, and can be communicated and stored, for example, in a memory or database. The sample properties can be communicated to adjust one or more process tools associated with a particular manufacturing process step in a manufacturing sequence (e.g., a process tool responsible for or contributing to the sample properties) or to adjust the manufacturing sequence of the sample itself.

[0056] By calibrating each element between the PSG 110 and the PSA 145, the exact initial state of the PSG for each pixel within the two-dimensional sensor 146 can be determined, the ellipsometer can be operated. A single Stokes vector is a 4 x 1 matrix, which can fully describe the polarization state. The matrix of all polarization states generated by the PSG will be a 4 x n matrix, where n is the total number of pixels (in this example, n = 25*25 = 625). The PSD will then produce a corresponding matrix of measurements in an n x 4 matrix. This PSG matrix is then inverted at calibration time. When data is collected from a sample, a matrix multiplication is performed to produce a 4 x 4 Mueller matrix, from which any effects from the system optics are removed.

[0057] Figure 10 A is shown to illustrate that the detector 1040 can be used with a light source 102 that produces a plurality of non-contiguous wavelengths, such as a broadband frequency comb light source. Figure 1 A diagram of an embodiment of the detector 1040 of the detector 140 is shown. For example, the detector 1040 can be used with a light source 102 that produces a plurality of non-contiguous wavelengths, such as a broadband frequency comb light source. Figure 1 As shown, the reflected light 133 is received by a wavelength diffraction element 1042 (e.g., shown as a prism 1042). Other types of wavelength diffraction elements can be used, such as a diffraction grating, if desired. As shown, the prism 1042 separates the wavelengths of the light into separate non-contiguous beams 1043. In one embodiment, the separation of the light into beams having different wavelengths is due to the use of a light source 102 that produces non-contiguous wavelengths (shown), such as a broadband frequency comb light source. As an example, Figure 1 A light source spectrum 1100 produced, for example, by a broadband frequency comb light source is shown, which has a plurality of non-contiguous wavelength bands that can be used with an embodiment of the detector 1040 shown by A. Figure 11 A light source spectrum 1100 produced, for example, by a broadband frequency comb light source is shown, which has a plurality of non-contiguous wavelength bands that can be used with an embodiment of the detector 1040 shown by A. Figure 10 A plurality of non-contiguous wavelength bands that can be used with an embodiment of the detector 1040 shown by A.

[0058] Optical elements, such as a lens 1002 and a folding mirror 1004, direct the separated beams to a polarization splitter 1044. Although a single lens 1002 is shown, multiple optical elements can be used. Further, the lens elements can be refractive, reflective, or a combination thereof.

[0059] The polarization splitter 1044 includes a meta-grating 1046 on one side of a transparent substrate 1048 and a polarizer 1045 on the opposite side of the substrate 1048. The meta-grating diffracts the beams 1043 into polarization-based orders, similar to a blazed grating that separates wavelengths. For example, the meta-grating 1046 can be a sub-wavelength three-dimensional structure on a transparent substrate 1048, which can be, for example, glass.

[0060] Figure 12 A meta-grating 1046 is shown receiving, for example, the separated beams 1043 from the wavelength diffraction element (shown). Figure 11Figure 12 shows an example of two beams 1202 and 1204 of reflected light having different wavelengths received by the prism 1042 in Figure 10. The beam 1202 and the beam 1204 are each diffracted by the meta-grating 1046 into a specified polarization state on a diffractive order of the meta-grating 1046. The meta-grating 1046 can include a plurality of regions λ1, λ2... λ N each configured for a different wavelength λ1, λ2... λ N of input light to produce the same specified polarization state. The meta-grating 1046 can include sub-wavelength three-dimensional dielectric structures on a glass substrate.

[0061] For example, Figure 13 A single phase shifting element 1302 that can be present on the meta-grating 1046 is shown. Certain methods of fabricating metrology gratings are described, for example, in WO2019 / 147828, which is incorporated by reference herein and described as follows. The phase shifting element is made of a material that has a refractive index value significantly greater than that of a surrounding medium such as air at a particular wavelength, while not absorbing light of that length. Thus, the choice of material can depend on the desired wavelength value or range that the phase shifting element will be used for. In some embodiments, the phase shifting element can include one or more of: titanium dioxide, silicon nitride, an oxide, a nitride, a sulfide, a pure element, a metal or a non-metal oxide such as aluminum oxide (e.g., AI2O3), silicon dioxide (e.g., S1O2), hafnium oxide (e.g., HfCh), zinc oxide (e.g., ZnO), magnesium oxide (e.g., MgO), titanium dioxide (e.g., T1O2), a metal or non-metal nitride such as silicon nitride (e.g., S13N4), boron (e.g., BN), or tungsten (e.g., WN), a metal or non-metal sulfide, a pure element (e.g., Si or Ge, which can be used for longer wavelengths, such near-IR or mid-IR wavelengths).

[0062] The phase shifting element 1302 can be configured so that when illuminated with incident polarized light, the light intensity of each of a pre-selected number of diffractive orders is approximately equal to each other, while the light intensity of any other possible diffractive orders is much smaller, preferably at least one or at least several orders of magnitude smaller, and more preferably below the detection limit of the detection element, than the light intensity of the pre-selected diffractive orders.

[0063] The phase shifting element 1302 is shown as a rectangular columnar structure with two vertical mirror symmetry axes, having orthogonal dimensions w x and w y The phase shifting element can be configured to allow for independent phase delays φ x and φ yFor example, the phase shifting elements 1302 can be Ti02on glass (e.g., the transparent substrate 1048). If desired, shapes other than rectangular can be used for one or more of the phase shifting elements 1302 on the meta-grating 1046. Figure 14 Q phase shifting elements are shown arranged in a sub-wavelength spacing in a one-dimensional grating unit cell 1400. The phase shift experienced by x-polarized light at the qthposition in the unit cell can be denoted as φq= φ0+ qd x (q) As a function of the spatial coordinate x, the discrete phase function experienced by x-polarized light can be written as As a function of the spatial coordinate x, the discrete phase function experienced by x-polarized light can be written as Y-polarized light can be similarly treated, resulting in the vector The unit cell 1400 can be repeated on the meta-grating 1046, or within each particular wavelength region of the meta-grating 1046, to produce a particular periodic phase distribution for the orthogonal x and y polarizations.

[0064] Since the unit cell 1400 is periodic, the angular spectrum of the grating is discrete. By including the phase distributions and in the phase grating and The Fourier series of the phase grating can be calculated, and the projection onto the grating order m is given by:

[0065]

[0066] and

[0067]

[0068] The value d is the length of the unit cell 1400, and and are the Fourier coefficients of the grating experienced by the x and y polarizations, respectively.

[0069] Each coefficient is typically a complex number, and can be written as and A Jones matrix J(m) can be attributed to each order:

[0070]

[0071] The mthorder polarization properties contained in J(m) can be seen as equivalent to a cascade of two bulk optical elements: the first Jones matrix in the product is that of an attenuator, e.g., a defective polarization element that selectively attenuates light along the x and y directions, while the second Jones matrix is that of a phase retarder, e.g., a waveplate with a retardance Both have their characteristic axes mutually oriented along x and y. ​

[0072] If a beam with an electric field amplitude E0polarized at 45° is incident on the grating, the electric field on the mth grating order will be:

[0073]

[0074] In the special case of 45° polarized light, then the complex grating coefficients and directly produce the mth order polarization state. For a general input polarization, the output polarization state of each order can be understood in terms of the Poincare sphere.

[0075] Each wavelength region of the meta-grating can include different unit cells tailored to its specific wavelength. The phase profile vector and can be optimized to produce a desired polarization at each order. For example, the shape of each phase shifting element 1302 and the inter-element spacing of elements in the unit cell 1400 can be optimized for each desired wavelength to produce a consistent angular spacing of grating orders. More formally, one can desire to design a grating that produces a desired polarization state on a set of grating orders {l} when there is incident light polarized at 45°. The target Jones vector on each order m e {l} is given by:

[0076]

[0077] Light will generally be diffracted into all orders, not just those in {l}. To direct as much of the incident power into these desired orders as possible, one seeks to maximize

[0078]

[0079] Under the constraint

[0080]

[0081] and

[0082]

[0083] The constraint provides the desired polarization of each order, and the phase profile vector and are the quantities to be optimized. If the grating has Q constituent elements, the optimization will involve 2Q parameters. Q and the inter-element spacing dictate the grating period d, which together with the operating wavelength λ specify the angular spacing of the grating orders. Once the optimized and are obtained, one can use equations 6, 7, and 8 to mathematically evaluate the power in the desired orders and their correspondence to the target polarization.

[0084] The above constraints can be applied to perform a gradient descent optimization and randomly generate initial conditions. Once an optimized geometry of the phase shifters can be inferred. Once the operating wavelength and desired material platform are specified, the appropriate geometry of the phase shifters can be found from a library of simulated structures. For example, a search method can be used to maximize the amount of power delivered to the -2nd, -1st, 1st, and 2nd orders, e.g., using a seed value, varying the dimensions of the pillars, and simulating the results until the“best” set is found. Thus, the meta-grating 1046 can be configured for each desired wavelength to produce the vertices of the best measurement tetrahedron within the Poincare sphere 1500, as shown in FIG. 15, which ensures a high quality of elliptical polarization measurement.

[0085] Referring back to Figure 10 A, the beam of light sorted by wavelength and polarization state is received by a two-dimensional sensor 146, where the wavelength varies along one axis and the polarization state varies along the other axis.

[0086] Figure 16 is a diagram illustrating another embodiment of a detector 1640 that can be used as Figure 1 the detector 140 shown. For example, the detector 1640 can be used with a light source 102 (shown in Figure 1 ) that produces multiple discrete wavelengths, such as a broadband frequency comb light source or a Fourier domain mode locked laser light source, as described above. As shown, the reflected light 133 is received by a wavelength diffractive element, e.g., a prism 1042. Other types of wavelength diffractive elements can be used, such as a diffraction grating, if desired.

[0087] Optical elements, e.g., a lens 1002 and a folding mirror 1004, direct the separated beams to a polarization splitter 1644. While a single lens 1002 is shown, multiple optical elements can be used. Further, the lens elements can be refractive, reflective, or a combination thereof.

[0088] The polarization splitter 1644 includes a meta-grating 1046 on one side of a transparent substrate 1048. As described above, the meta-grating diffracts the beam 1043 into multiple orders based on polarization, similar to a blazed grating that separates wavelengths. For example, the meta-grating 1046 can be a sub-wavelength three-dimensional structure on a transparent substrate 1048, which can be, e.g., glass. As shown, there can be no polarizer on the substrate 1048.

[0089] The detector 1640 includes a micro-polarizer array 1645 aligned with the two-dimensional sensor 146, such as a 4D Polarcam produced by 4D Technologies of Onto Innovation. The micro-polarizer array 1645 includes a polarizer array to acquire multiple (e.g., four) polarization angles simultaneously. Each polarizer in the polarizer array is aligned with a detector pixel in the two-dimensional sensor 146. The micro-polarizer array 1645 and the echelette 1046 act as a polarizing state analyzer.

[0090] Figure 17A One embodiment of the micro-polarizer array 1645 is shown, which includes a plurality of micro-polarizer pixels 1702, each aligned with a detector pixel 1704 in the two-dimensional sensor 146. For example, Figure 17B A unit cell 1710 of four micro-polarizer pixels 1702A, 1702B, 1702C, and 1702D (collectively, micro-polarizer pixels 1702) is shown, each having a different polarization orientation. Each of the micro-polarizer pixels 1702 is, for example, a linear grating polarizer, held in a 2x2 array having four discrete polarizations (e.g., 0°, 45°, 90°, 135°) in the unit cell 1710. The unit cell 1710 is repeated across the micro-polarizer array 1645 such that the micro-polarizer array 1645 includes a repeating array of micro-polarizer pixels 1702 having discrete polarizations. The micro-polarizer pixels 1702 have a size and spacing that match the size and spacing of the detector pixels 1704 of the two-dimensional sensor 146, such that each detector pixel 1704 in the two-dimensional sensor 146 is matched, i.e., aligned, with a micro-polarizer pixel 1702.

[0091] With the polarization arrangement within the unit cell 1710 and the arrangement of the unit cells 1710 in the micro-polarizer array 1645 shown in Figure 17A and Figure 17B It will be appreciated that the two-dimensional sensor 146 will receive images of spatially separated wavelengths that can vary along one axis, but the variation in polarization state will not be identified along the other axis (as shown in Figure 8 ), but will be identified at the pixel level, e.g., based on the pixels aligned with the micro-polarizer pixels 1702. However, it will be appreciated that Figure 17A and Figure 17B One embodiment of the polarization arrangement within the unit cell 1710 and the arrangement of the unit cells 1710 in the micro-polarizer array 1645 is shown, and other arrangements are possible, including other arrangements that combine groups of pixels having similar polarization orientations.

[0092] In the current implementation, the micropolarizer array 1645 is replaced Figure 10 Polarizer 1045 is shown in Figure A. By using an array of different polarization orientations from the micro-polarizer array 1645 and light separated into multiple different polarization states from the elementary grating 1046, the measurement accuracy of the system can be improved, for example, by normalization of the measurements. For example, using four separate polarization states from the elementary grating 1046 and four separate polarizers in each unit cell 1710 of the micro-polarizer array 1645, sixteen measurement results (4×4=16) are generated. In one embodiment, instead of using the optimal measurement tetrahedron of the Poincaré sphere as described above, measurements can be performed using all six orthogonal states of the Poincaré sphere to accurately characterize the polarization states, such as... Figure 15B The Poincaré sphere 1510 is shown in the diagram. The PSA projects the polarization of the beam onto four optimal measurement vertices of the Poincaré sphere 1510. Since a single polarizer coupled to the metagrating 1046 will produce four vertices, one of the polarizer orientations in the micropolarizer array 1645 can produce four optimal measurement vertices. Other polarizer orientations in the micropolarizer array 1645 can be used to provide orthogonal points, which will improve the accuracy of polarization measurements.

[0093] Figure 18 shows what can be used as Figure 1 The diagram shows another embodiment of detector 1840 of detector 140. For example, detector 1840 can be used with a light source 102 that generates a continuous wavelength spectrum (such as...). Figure 1 (As shown) used together. As shown, reflected light 133 is received by a wavelength diffraction element (e.g., prism 1042 shown). Other types of wavelength diffraction elements, such as diffraction gratings, can be used if desired. Prism 1042 separates the wavelengths of light into individual wavelengths, but as shown, the resulting light 1843 is a continuous wavelength spectrum, i.e., multiple consecutive wavelengths. Prism 1042 produces continuous wavelengths, for example, because broadband light source 102 (such as...) Figure 1 (As shown) it produces a continuous spectrum. For example, Figure 19 An example of the spectrum 1900 generated by the light source 102 for the detector 1840 in the current embodiment is shown.

[0094] Optical elements, such as lens 1002 and folding mirror 1004, guide the separated light beams to polarization separator 1644. Although a single lens 1002 is shown, multiple optical elements can be used. Furthermore, the lens elements can be refractive, reflective, or a combination thereof.

[0095] The polarization separator 1044 includes a meta-grating 1046 on one side of a transparent substrate 1048 and a polarizer 1045 on the other side of the substrate 1048. As described above, the meta-grating diffracts the light beam 1043 into multiple orders based on polarization, similar to a blazed grating that separates wavelengths. For example, the meta-grating 1046 can be a sub-wavelength three-dimensional structure on a transparent substrate 1048, which can be, for example, glass.

[0096] The detector 1840 includes a wavelength filter 1802 between the two-dimensional sensor 146 and the polarization separator 1044. The wavelength filter 1802 can be one or more bandpass filters or etalon filters. For example, the wavelength filter 1802 can include a passband and a geometric width designed to match the light beam. The wavelength filter 1802 can be on the surface of the two-dimensional sensor 146 or on the polarizer 1045 or between the two. The wavelength filter 1802 receives light from the polarization separator 1044 and transmits different wavelength bands to produce multiple non-overlapping, non-contiguous wavelength bands imaged by the two-dimensional sensor 146.

[0097] Figure 18B is a diagram illustrating a detector 1840' that is another embodiment of a detector 1040 similar to that shown in Figure 10 A is a diagram of another embodiment of a detector 1840' similar to the detector 1040 shown in A, like designated elements are the same and can be used as Figure 1 the detector 140 shown in A. For example, the detector 1840' can be used with a light source 102 that produces multiple wavelengths simultaneously or sequentially, such as the light source 102 shown in Figure 1 As shown, the wavelengths in the reflected light 133 are separated in time by a wavelength separator 1042', which in one embodiment can be an acousto-optic tunable filter that separates the wavelengths in the reflected light 133 (using diffraction in this example) into narrow wavelength bands and rapidly switches between each band (e.g., 200 ns) to capture the wavelength bands over time. The wavelength separator 1042', such as an acousto-optic tunable filter, can be used with a light source that produces multiple wavelengths simultaneously. In another embodiment, the wavelengths in the reflected light 133 can be separated by the light source 102 (such as the light source 102 shown in Figure 1wavelengths, such as a Fourier domain mode locked laser source that sequentially produces multiple wavelengths. In this implementation, the wavelength separator 1042' is the light source 102, and the physical wavelength separator 1042' need not be present in the detector 1840' as shown by the dashed line. The two-dimensional sensor 146 need not include the wavelength filter 1802, but instead collects multiple frames at high speed in synchronization with the wavelength separator 1042' (e.g., an acousto-optic tunable filter or the light source 102) to capture the separated polarization states for different wavelengths in each frame. As shown, optical elements, such as the lens 1002 and the lens 1003 and the folding mirror 1004, direct the beams with the temporally separated wavelengths to the polarization separator 1044.

[0098] In some implementations, the detector can include a micro-polarizer array 1645, such as described in Figure 16 Figure 1 The detector can be used continuously with a light source 102 that produces a continuous spectrum of wavelengths, such as using a wavelength filter 1802, as described in Figure 18A Figure 16 In some implementations, the detector can include a micro-polarizer array 1645, such as described in Figure 18B

[0099] Figure 20 is a diagram showing another implementation of a detector 2040 that can be used as the detector 140 shown in Figure 1 Figure 1 ​​​​together, such as a broadband frequency comb light source, as described above. As shown, the reflected light is received by a beamsplitter 2002, which directs (e.g., reflects) a portion of the reflected light 133 into a first passageway toward a first diffractive element, shown as prism 2004. The remaining portion of the reflected light 133 from the beamsplitter 2002 is directed (e.g., transmitted) via a phase shifting optical element, shown as Fresnel prism 2006, toward a second passageway with a second diffractive element, shown as prism 2008. The Fresnel prism 2006, which includes an optical coating 2007, introduces a 90° phase shift between the linear polarization states of the reflected light 133. The Fresnel prism 2006 and optical coating 2007 can be similar to the Fresnel cone 116 and optical coating 212, for example. Other phase shifting optical elements can be used instead of the Fresnel prism, if desired. Thus, the light in the first passageway and the light in the second passageway have different polarization states. As shown, the prism 2004 and prism 2008 each separate the wavelengths of light into separate non-continuous beams 2005 and 2009, which are directed to a micro polarizer array 1645 aligned with the two-dimensional sensor 146, as Figure 16 As detailed above, the micro polarizer array 1645 and two-dimensional sensor 146 are used to determine the polarization state of the light in each of the first and second passageways. As shown, in the detector 2040, the micro grating 1046 in A is removed from the system, as it is functionally replaced by the beamsplitter 2002 and the Fresnel prism 2006, which direct light with different polarization states toward the micro polarizer array 1645 and combine to function as a polarization state analyzer. Figure 10 As detailed above, the micro polarizer array 1645 and two-dimensional sensor 146 are used to determine the polarization state of the light in each of the first and second passageways. As shown, in the detector 2040, the micro grating 1046 in A is removed from the system, as it is functionally replaced by the beamsplitter 2002 and the Fresnel prism 2006, which direct light with different polarization states toward the micro polarizer array 1645 and combine to function as a polarization state analyzer.

[0100] Optical elements, such as a lens 2010 and a folding mirror 2012 in the first passageway, and a lens 2014 and a folding mirror 2016 in the second passageway, direct the separated beams toward the two-dimensional sensor. While a single lens 2010 and 2014 are shown in each passageway, multiple optical elements can be used. Further, the lens elements can be refractive, reflective, or a combination thereof.

[0101] As shown, a single micro polarizer array 1645 and two-dimensional sensor 146 can be used, for example, by imaging the light from the first and second passageways in different areas of the micro polarizer array 1645 and two-dimensional sensor 146. If desired, two micro polarizer arrays 1645 / two-dimensional sensors 146 can be used, one for each passageway.

[0102] As detailed above, by Figure 17A and Figure 17BThe polarization arrangement within unit cell 1710 and the arrangement of unit cells 1710 in the micropolarizer array 1645 shown should be understood so that the two-dimensional sensor 146 in detector 2040 will receive images of spatially separated wavelengths. These spatially separated wavelengths can vary along one axis, but changes in polarization state will not be detected along another axis (e.g., ...). Figure 8 (As shown), instead, it will be identified at the pixel level, for example, based on pixels aligned with micro-polarizer pixel 1702. However, it should be understood that Figure 17A and Figure 17B The diagram illustrates one embodiment of the polarization arrangement within unit cell 1710 and the arrangement of unit cell 1710 in micropolarizer array 1645, and other arrangements are also possible, including combinations of pixel groups with similar polarization orientations and other arrangements of pixel groups.

[0103] In the current implementation, the meta-grating is removed from the system and functionally replaced by a phase-shifting optical element (Fresnel prism 2006) and a beam splitter 2002, which guide two different polarization states toward the micro-polarizer array 1645. By using an array of different polarization orientations from the micro-polarizer array 1645 and different polarization states provided by separate channels, the measurement accuracy of the system can be improved, for example, by normalizing the measurements. For example, with two separate polarization states from the Fresnel reflector 2006 and the beam splitter 2002, and four individual polarizers per unit cell 1710 in the micro-polarizer array 1645, eight measurements (2 × 4 = 8) are generated in six orthogonal polarization states, two of which are repeats. By repeating the measurements, one channel is normalized relative to the other to ensure accurate measurements, such as... Figure 15C The Poincaré sphere 1520 is shown in the diagram. This process achieves the same result as described above. Figure 15A The best measurement achieved is the same as that of tetrahedron 1500. In one embodiment, the orientation of the micropolarizer pixels 1702 in the micropolarizer array 1645 is configured relative to the Fresnel reflector 2006 such that the measured polarization state is traced using the separated wavelengths in the reflected light from prism 2004 and the separated wavelengths in the reflected light from prism 2008 to identify two orthogonal loops around the Poincaré sphere. For example, the intersection of the two orthogonal loops can be used by a two-dimensional sensor receiving two channels, or if more than one two-dimensional sensor is used, the first two-dimensional sensor can be referenced to the second two-dimensional sensor.

[0104] Figure 21 It shows what can be used as Figure 1 The diagram shows another embodiment of detector 2140 of detector 140. For example, detector 2140 can be used with a light source 102 that generates a continuous wavelength spectrum (such as...). Figure 1(As shown) used together, as described above. Detector 2140 is similar to Figure 20 The detector 2040 shown uses similar designated elements. As shown, in detector 2140, prisms 2004 and 2008 separate the wavelengths of light, but because light source 102 produces a continuous spectrum, the resulting light 2105 and light 2109 each include a continuous spectrum of wavelengths, i.e., multiple consecutive wavelengths. To generate multiple non-overlapping, discontinuous wavelength bands imaged by micropolarizer array 1645 and two-dimensional sensor 146, wavelength filter 2102 is used in detector 2140. Wavelength filter 2102 is placed, for example, between micropolarizer array 1645 and prisms 2004, 2008, and may be located, for example, on micropolarizer array 1645. Multiple wavelength filters may be used if desired, and in some embodiments, separate but matched wavelength filters may be located in a first channel, for example on folded mirror 2012, and in a second channel, for example on folded mirror 2016. The wavelength filter 2102 is configured to allow only the desired wavelength to reach the micropolarizer array 1645 and the two-dimensional sensor 146, so that the desired wavelength bands do not overlap.

[0105] Furthermore, in some embodiments, the detector may include a beam splitter 2002 and a phase-shifting optical element (Fresnel prism 2006), for example, such as Figure 20 and Figure 21 As discussed in [the document], but time-separated wavelengths can also be used, for example, using [a specific wavelength]. Figure 18B The wavelength splitter 1042' discussed above. As described above, the wavelength splitter 1042' can be an acousto-optic tunable filter that separates wavelengths in the reflected light 133, wherein the light source simultaneously generates multiple wavelengths, and the two-dimensional sensor 146 collects multiple frames synchronized with the acousto-optic tunable filter. In another embodiment, the light source can sequentially generate multiple wavelengths, such as a Fourier domain mode-locked laser source, and the wavelength splitter 1042' can be considered as a high-speed two-dimensional sensor 146 that collects multiple frames synchronized with the light source.

[0106] Figure 22is flowchart 2200, which illustrates a method of characterizing a sample with an ellipsometer disclosed herein, such as ellipsometer 100. As shown in first block 2202, light having a plurality of wavelengths is generated, for example, as discussed with reference to light source 102. At block 2204, the light is polarized, for example, as discussed with reference to polarizer 112. At block 2206, the polarized light is modified using a Fresnel cone (for example, as discussed with reference to Fresnel cone 116) to produce sample light having a plurality of polarization states at each of the plurality of wavelengths. At block 2208, the sample light is caused to be incident on a sample, where the sample light interacts with the sample and is reflected by the sample, producing reflected light, for example, as discussed with reference to optical elements 120, 122, 136, and 138. At block 2210, the wavelengths in the reflected light are separated, for example, as discussed with reference to wavelength separator 142, and wavelength separators 1042, 1042', 2004, and 2008. At block 2212, the reflected light is separated into a plurality of polarization states using a polarization separator, for example, as discussed with reference to polarization separator 144, and polarization separators 1044, 1644, 2002, and 2006. At block 2214, one or more images of the separated wavelengths at each of the plurality of polarization states of the reflected light are captured using a two-dimensional sensor, for example, as discussed with reference to two-dimensional sensor 146. At block 2216, at least a portion of a Mueller matrix of the sample is determined using the images of the spatially separated wavelengths at each of the plurality of polarization states of the reflected light, for example, as discussed with reference to computer system 170 having at least one processor 172 configured with computer-readable program code to operate as a special purpose computer.

[0107] In one implementation, separating the wavelengths in the reflected light can include spatially separating the wavelengths using a diffractive element, such as diffractive elements 1042, 2004, and 2008, where capturing one or more images includes capturing one image of the spatially separated wavelengths at each of the plurality of polarization states of the reflected light.

[0108] In one implementation, separating the wavelengths in the reflected light can include temporally separating the wavelengths in the reflected light, where capturing one or more images includes capturing a plurality of images, each having a different wavelength at each of the plurality of polarization states of the reflected light. Temporal separation of the wavelengths in the reflected light is performed, for example, by one of: an acousto-optic tunable filter, or a light source that emits each of a plurality of wavelengths separately. For example, the light source can be a Fourier domain mode locked laser light source.

[0109] In one implementation, the light having a plurality of wavelengths includes a plurality of non-contiguous wavelength bands, for example, as discussed with reference to light source 102. Figure 11The wavelengths in the reflected light are separated, as shown, and separating the wavelengths in the reflected light includes separating a plurality of non-contiguous wavelength bands, such as shown by the non-contiguous beams 1043, 2005, and 2009, such that the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor. For example, generating light having a plurality of wavelengths can be performed by a broadband frequency comb light source.

[0110] In one embodiment, the light having a plurality of wavelengths includes a continuous spectrum of wavelengths, such as shown by the light 1843, 2105, and 2109, and separating the wavelengths in the reflected light produces a spectrum of wavelengths, such as shown by the light 1843, 2105, and 2109. The method can further include filtering the spectrum of wavelengths to produce a plurality of non-contiguous wavelength bands, where the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor, such as discussed with reference to the filter 1802 and the filter 2102. For example, the spectrum of wavelengths can be filtered after separating the reflected light into a plurality of polarization states. Figure 19

[0111] In one embodiment, using a Fresnel cone to modify the polarized light to produce sample light having a plurality of polarization states at each of a plurality of wavelengths includes using total internal reflection (TIR) of the Fresnel cone with an optical coating having a refractive index selected to produce a constant phase shift for wavelengths of light imaged by the two-dimensional sensor, such as discussed with reference to the optical material 212.

[0112] In one embodiment, the polarization splitter separates the reflected light into a plurality of polarization states such that the polarization states do not overlap in the one or more images received by the two-dimensional sensor, such as discussed with reference to the polarization splitters 1044, 1644, 2002, and 2006.

[0113] In one embodiment, the polarization splitter separates the reflected light into a plurality of polarization states by producing polarization states that are vertices of an optimal measurement tetrahedron inside a Poincare sphere, such as discussed with reference to the polarization splitter 1044.

[0114] ​In an embodiment, the polarization separator that separates the reflected light into a plurality of polarization states is a grating before the two-dimensional sensor, where the grating is configured to diffract different polarization states to different transmission orders, e.g., as discussed with reference to meta-grating 1046. In addition, the different polarization states in the reflected light are analyzed, e.g., as discussed with reference to meta-grating 1046, polarizer 1045, and micro-polarizer array 1645. The grating can include a spaced array of phase shifting elements, e.g., as discussed with reference to meta-grating 1046 and phase shifting elements 1302. The different polarization states in the reflected light can be analyzed by diffracting different polarization states to different transmission orders with the grating and polarizing the different polarization states from the grating with a linear polarizer, e.g., as discussed with reference to polarizer 1045. The different polarization states in the reflected light can be analyzed by diffracting different polarization states to different transmission orders with the grating and polarizing the different polarization states from the grating with a micro-polarizer array that includes micro-polarizer pixels aligned with pixels of the two-dimensional sensor, where the micro-polarizer array includes a repeating array of micro-polarizer pixels with discrete polarizations, e.g., as discussed with reference to micro-polarizer array 1645.

[0115] In an embodiment, separating wavelengths in the reflected light is performed by a first diffractive element and a second diffractive element, and the reflected light is separated into a plurality of polarization states using a polarization separator by directing a first portion of the reflected light to the first diffractive element with a beamsplitter; and receiving a second portion of the reflected light from the beamsplitter with a phase shifting optical element and directing the second portion of the reflected light to the second diffractive element with the phase shifting optical element, where the first portion of the reflected light has different polarization states than the second portion of the reflected light, e.g., as discussed with reference to beamsplitter 2002 and phase shifting optical element (Fresnel prism 2006). The wavelengths in the reflected light are separated by separating wavelengths in the first portion of the reflected light with the first diffractive element and separating wavelengths in the second portion of the reflected light with the second diffractive element, e.g., as discussed with reference to prisms 2004 and 2008. The different polarization states in the first portion of the reflected light and the second portion of the reflected light are analyzed with a micro-polarizer array that includes micro-polarizer pixels aligned with pixels of the two-dimensional sensor, where the micro-polarizer array includes a repeating array of micro-polarizer pixels with discrete polarizations, e.g., as discussed with reference to micro-polarizer array 1645. The micro-polarizer array can be configured to produce two orthogonal rings around a Poincare sphere using the separated wavelengths in the reflected light from the first diffractive element and the separated wavelengths in the reflected light from the second diffractive element, e.g., as discussed with reference to micro-polarizer array 1645. An intersection of the two orthogonal rings around the Poincare sphere can be used to reference a first two-dimensional sensor to a second two-dimensional sensor.

[0116] In one implementation, an ellipsometer can include a means for generating light having a plurality of wavelengths, which can be, for example, the light source 102, which can emit a plurality of non-contiguous wavelength bands, such as a broadband frequency comb light source or a Fourier domain mode locked laser light source, or can emit a plurality of contiguous wavelengths, such as a thermal (halogen) light bulb or a high pressure arc discharge plasma lamp. A means for polarizing the light can be, for example, the polarizer 112. A means for modifying the polarized light to produce sample light having a plurality of polarization states at each of the plurality of wavelengths can be the Fresnel cone 116. A means for causing the sample light to be incident on a sample can be focusing optics, such as focusing optics 122 and focusing optics 136, which can include a plurality of optical elements / lenses that are refractive or reflective or a combination thereof, where the sample light interacts with and is reflected by the sample, producing reflected light. A means for separating the wavelengths in the reflected light can be, for example, the wavelength separator 142, 1042, 1042', 2004, 2008, or the light source 102 and the sensor 146. A means for separating the reflected light into a plurality of polarization states can be, for example, the polarization separator 144, 1044, 1644, 2002, and 2006. A means for capturing one or more images of the separated wavelengths at each of the plurality of polarization states of the reflected light can be, for example, the two-dimensional sensor 146. A means for determining at least a portion of the Mueller matrix of the sample using the one or more images of the separated wavelengths at each of the plurality of polarization states of the reflected light can be, for example, the computer system 170 having at least one processor 172 configured with computer-readable program code to operate as a special purpose computer using an algorithm, such as the algorithms disclosed herein.

[0117] In one implementation, a means for separating the wavelengths in the reflected light can spatially separate the wavelengths using a diffractive element, such as the diffractive elements 1042, 2004, and 2008, where a means for capturing one or more images captures one image of the spatially separated wavelengths at each of the plurality of polarization states of the reflected light.

[0118] In one implementation, a means for separating the wavelengths in the reflected light can temporally separate the wavelengths in the reflected light, for example, using an acousto-optic tunable filter 1042' or the light source 102, such as a Fourier domain mode locked laser light source that emits each of a plurality of wavelengths, respectively, where a means for capturing one or more images captures a plurality of images, each having a different wavelength at each of the plurality of polarization states of the reflected light.

[0119] In one embodiment, the light has a plurality of non-contiguous wavelength bands, and the means for separating wavelengths in the reflected light (which can be, for example, a broadband frequency comb light source) separates the plurality of non-contiguous wavelength bands such that the plurality of non-contiguous wavelength bands do not overlap in the one or more images.

[0120] In one embodiment, the light has a continuous wavelength spectrum, and the means for separating wavelengths in the reflected light (which can be, for example, wavelength separators 1042, 2004, 2008) produces the wavelength spectrum, and the ellipsometer can further comprise means for filtering the wavelength spectrum to produce a plurality of non-contiguous wavelength bands, which can be, for example, filter 1802 or filter 2102, wherein the plurality of non-contiguous wavelength bands do not overlap in the one or more images. The means for filtering the wavelength spectrum can be in the beam path after the means for separating the reflected light into a plurality of polarization states.

[0121] In one embodiment, the means for modifying the polarized light to produce sample light having a plurality of polarization states at each of a plurality of wavelengths comprises means for total internal reflection (TIR) having an optical coating with an index of refraction selected to produce a constant phase shift for wavelengths of light imaged by the two-dimensional sensor, which can be, for example, optical material 212 on Fresnel cone 116.

[0122] In one embodiment, the means for separating the reflected light into a plurality of polarization states separates the reflected light into a plurality of polarization states such that the polarization states do not overlap in the one or more images, which can be, for example, polarization separators 1044, 1655, 2002, and 2006.

[0123] In one embodiment, the means for separating the reflected light into a plurality of polarization states can produce polarization states that are vertices of an optimal measurement tetrahedron inside a Poincare sphere, which can be, for example, polarization separator 1044.

[0124] In one implementation, the means for separating wavelengths in the reflected light can include a first diffractive element and a second diffractive element, such as prisms 2004 and 2008, and the means for separating the reflected light into a plurality of polarization states using a polarization splitter can include means for directing a first portion of the reflected light to the first diffractive element, which can be beam splitter 2002, and means for receiving a second portion of the reflected light and directing the second portion of the reflected light to the second diffractive element, which can be, for example, a phase shifting optical element such as Fresnel prism 2006, wherein the first portion of the reflected light has a different polarization state than the second portion of the reflected light. The means for separating wavelengths in the reflected light can include a first diffractive element that separates wavelengths in the first portion of the reflected light and a second diffractive element that separates wavelengths in the second portion of the reflected light. The ellipsometer can further include means for analyzing polarization states in the first portion of the reflected light and the second portion of the reflected light, which can be, for example, a micro polarizer array 1645 having micro polarizer pixels aligned with pixels of a two-dimensional sensor, wherein the micro polarizer array includes a repeating array of micro polarizer pixels having discrete polarizations. The means for analyzing polarization states can be configured to use the separated wavelengths in the reflected light from the first diffractive element and the separated wavelengths in the reflected light from the second diffractive element to produce two orthogonal loops around a Poincare sphere. An intersection of the two orthogonal loops around the Poincare sphere is used to reference a first two-dimensional sensor to a second two-dimensional sensor.

[0125] In one implementation, the means for separating wavelengths in the reflected light can include a first diffractive element and a second diffractive element, such as prisms 2004 and 2008, and the means for separating the reflected light into a plurality of polarization states using a polarization splitter can include means for directing a first portion of the reflected light to the first diffractive element, which can be beam splitter 2002, and means for receiving a second portion of the reflected light and directing the second portion of the reflected light to the second diffractive element, which can be, for example, a phase shifting optical element such as Fresnel prism 2006, wherein the first portion of the reflected light has a different polarization state than the second portion of the reflected light. The means for separating wavelengths in the reflected light can include a first diffractive element that separates wavelengths in the first portion of the reflected light and a second diffractive element that separates wavelengths in the second portion of the reflected light. The ellipsometer can further include means for analyzing polarization states in the first portion of the reflected light and the second portion of the reflected light, which can be, for example, a micro polarizer array 1645 having micro polarizer pixels aligned with pixels of a two-dimensional sensor, wherein the micro polarizer array includes a repeating array of micro polarizer pixels having discrete polarizations. The means for analyzing polarization states can be configured to use the separated wavelengths in the reflected light from the first diffractive element and the separated wavelengths in the reflected light from the second diffractive element to produce two orthogonal loops around a Poincare sphere. An intersection of the two orthogonal loops around the Poincare sphere is used to reference a first two-dimensional sensor to a second two-dimensional sensor.

[0126] References throughout this specification to "one example," "an example," "certain examples," or "exemplary implementation" mean that a particular feature, structure, or characteristic described in connection with the feature and / or example can be included in at least one feature and / or example of claimed subject matter. Thus, the appearance of the phrase "in one example" or "an example" or "in certain examples" or "in certain implementations" or other similar phrases in various places throughout this specification are not necessarily all referring to the same feature, example, and / or limitation. Furthermore, the particular features, structures, or characteristics can be combined in one or more examples and / or features.

[0127] Some portions of the detailed description contained herein are presented in terms of algorithms or symbolic representations of operations on binary digital signals stored within memories of specific electronic devices or special purpose computing devices or platforms. In the context of this particular specification, the term specific device or the like refers to a general purpose computer once it is programmed to perform particular operations pursuant to instructions from program software. Algorithmic descriptions or symbolic representations are examples of techniques used by those of ordinary skill in the signal processing or related arts to convey the substance of their work to others skilled in the art. An algorithm is here, and generally, is considered to be a self-consistent sequence of operations or similar signal processing leading to a desired result. In this context, operations or processing involves physical manipulation of physical quantities. Typically, but not necessarily, such quantities can take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared or otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to such signals as bits, data, values, elements, symbols, characters, terms, numbers, numerals, or the like. It should be understood, however, that all of these or similar terms are to be associated with appropriate physical quantities and are merely convenient labels. Unless specifically stated otherwise, as apparent from the discussion herein, it is appreciated that throughout this specification discussions utilizing terms such as "processing," "computing," "calculating," "determining" or the like refer to the action or processes of a specific device, such as a special purpose computer, special purpose computing apparatus or a like special purpose electronic computing device. In the context of this specification, therefore, a special purpose computer or a like special purpose electronic computing device is capable of manipulating or transforming signals, typically, represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the special purpose computer or like special purpose electronic computing device.

[0128] In the foregoing detailed description, numerous specific details are set forth in order to provide a thorough understanding of the claimed subject matter. However, those skilled in the art will understand that the claimed subject matter can be practiced without these specific details. In other instances, methods and devices that would be known by one of ordinary skill have not been described in detail in order not to obscure the claimed subject matter.

[0129] The terms "and", "or", and "and / or" as used herein can include a variety of meanings that also are at least partially dependent on the context in which such terms are used. Typically, "or" if used to associate a list, such as A, B, or C, is intended to mean A, B, and C, here used in the inclusive sense, as well as A, B or C, here used in the exclusive sense. In addition, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular or can be used to describe a plurality or some other combination of features, structures or characteristics. However, it should be noted that this is merely an illustrative example and claimed subject matter is not limited to this example.

[0130] While there have been illustrated and described what are presently considered to be example features, it will be understood by those skilled in the art that various other modifications can be made, and that the subject matter should not be limited to the precise examples described herein, and that such other modifications can be made without departing from the scope of the claimed subject matter. Additionally, numerous other modifications can be made to adapt the precise examples to the circumstances to which the claimed subject matter is applied without departing from the central concept of the claimed subject matter.

[0131] Accordingly, it is therefore intended that the claimed subject matter not be limited to the particular examples disclosed, but that such claimed subject matter also include all aspects falling within the scope of the appended claims, and equivalents thereof.

Claims

1. An ellipsometer comprising: a light source that emits light having a plurality of wavelengths; a polarizer that polarizes the light to produce polarized light; a Fresnel cone that receives the polarized light and produces sample light having a plurality of polarization states at each of the plurality of wavelengths, wherein the Fresnel cone produces a plurality of polarization states at each wavelength of the polarized light using total internal reflection; a two-dimensional sensor that receives reflected light from a sample in one or more images of separated wavelengths at each of a plurality of polarization states of the reflected light, the two-dimensional sensor outputting data from the one or more images.

2. The ellipsometer of claim 1, further comprising a diffractive element that spatially separates the wavelengths in the reflected light, wherein the two-dimensional sensor receives one image of spatially separated wavelengths at each of the plurality of polarization states of the reflected light.

3. The ellipsometer of claim 1, further comprising a wavelength separator that temporally separates the wavelengths in the reflected light, wherein the two-dimensional sensor receives a plurality of images, each image having a different wavelength at each of the plurality of polarization states of the reflected light.

4. The ellipsometer of claim 3, wherein the wavelength separator comprises one of an acousto-optic tunable filter, or a light source that emits light of each of the plurality of wavelengths separately.

5. The ellipsometer of claim 4, wherein the light source is a Fourier domain mode locked laser light source.

6. The ellipsometer of claim 1, wherein the light having a plurality of wavelengths comprises a plurality of non-contiguous wavelength bands, the ellipsometer further comprising a wavelength separator that separates the plurality of non-contiguous wavelength bands such that the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor.

7. The ellipsometer of claim 6, wherein the light source is a broadband frequency comb light source.

8. The ellipsometer of claim 1, wherein the light having a plurality of wavelengths comprises a continuous wavelength spectrum, the ellipsometer further comprising a wavelength separator that separates the wavelengths in the reflected light and a wavelength filter positioned to receive the separated wavelengths from the wavelength separator and produce a plurality of non-contiguous wavelength bands, wherein the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor.

9. The ellipsometer of claim 8, wherein the wavelength filter is on the two-dimensional sensor.

10. The ellipsometer of claim 8, wherein the wavelength filter is between the wavelength separator and the two-dimensional sensor.

11. The ellipsometer of claim 1, wherein the Fresnel cone comprises an optical coating having a refractive index selected to produce a constant phase shift for the wavelength of light in the one or more images received by the two-dimensional sensor.

12. The ellipsometer of claim 1, further comprising a polarization separator that separates the reflected light into the plurality of polarization states such that the polarization states do not overlap in the one or more images received by the two-dimensional sensor.

13. The ellipsometer of claim 1, further comprising a polarization separator that separates the reflected light into the plurality of polarization states and is configured to produce polarization states that are vertices of an optimal measurement tetrahedron inside a Poincare sphere.

14. The ellipsometer of claim 1, further comprising a grating that separates the reflected light into the plurality of polarization states, the grating configured to diffract different polarization states into different transmission orders, the ellipsometer further comprising a second polarizer that analyzes the different polarization states in the reflected light.

15. The ellipsometer of claim 14, wherein the grating comprises a spaced array of phase shifting elements.

16. The ellipsometer of claim 14, wherein the second polarizer is a linear polarizer between the grating and the two-dimensional sensor.

17. The ellipsometer of claim 14, wherein the second polarizer comprises a micro-polarizer array comprising micro-polarizer pixels aligned with pixels of the two-dimensional sensor, wherein the micro-polarizer array comprises a repeating array of micro-polarizer pixels having discrete polarizations.

18. The ellipsometer of claim 1, further comprising a first diffractive element and a second diffractive element, and further comprising: a beam splitter that receives the reflected light and directs a first portion of the reflected light to the first diffractive element; a phase shifting optical element that receives a second portion of the reflected light from the beam splitter and directs the second portion of the reflected light to the second diffractive element, wherein the first portion of the reflected light has different polarization states than the second portion of the reflected light; wherein the first diffractive element separates the wavelengths in the first portion of the reflected light and the second diffractive element separates the wavelengths in the second portion of the reflected light, and the ellipsometer further comprising a micro-polarizer array comprising micro-polarizer pixels aligned with pixels of the two-dimensional sensor, wherein the micro-polarizer array comprises a repeating array of micro-polarizer pixels having discrete polarizations, wherein the micro-polarizer array analyzes the polarization states in the first portion of the reflected light and the second portion of the reflected light.

19. The ellipsometer of claim 18, wherein the array of micro polarizers is configured to use the separated wavelengths in the reflected light from the first diffractive element and the separated wavelengths in the reflected light from the second diffractive element to produce two orthogonal rings around a Poincare sphere.

20. The ellipsometer of claim 19, wherein an intersection of the two orthogonal rings around the Poincare sphere is used to reference a first two-dimensional sensor to a second two-dimensional sensor.

21. A method of characterizing a sample with an ellipsometer, the method comprising: generating light having a plurality of wavelengths; polarizing the light; modifying the polarized light using a Fresnel cone to produce sample light having a plurality of polarization states at each of the plurality of wavelengths, wherein the Fresnel cone produces a plurality of polarization states at each wavelength of the polarized light using total internal reflection; detecting, using a two-dimensional sensor, reflected light from a sample in each of a plurality of polarization states of the reflected light from the sample in one or more images of separated wavelengths and outputting data from the one or more images.

22. The method of claim 21, further comprising spatially separating the wavelengths using a diffractive element, wherein detecting one or more images comprises detecting one image of spatially separated wavelengths at each of the plurality of polarization states of the reflected light.

23. The method of claim 21, further comprising temporally separating the wavelengths in the reflected light, wherein detecting one or more images comprises detecting a plurality of images, each image having a different wavelength at each of the plurality of polarization states of the reflected light.

24. The method of claim 23, wherein temporally separating the wavelengths in the reflected light is performed by one of: an acousto-optic tunable filter, or a light source that emits each of the plurality of wavelengths separately.

25. The method of claim 24, wherein the light source is a Fourier domain mode locked laser light source.

26. The method of claim 21, wherein the light having a plurality of wavelengths comprises a plurality of non-contiguous wavelength bands, the method further comprising separating the plurality of non-contiguous wavelength bands such that the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor.

27. The method of claim 26, wherein generating light having a plurality of wavelengths comprises using a broadband frequency comb light source to generate the light.

28. The method of claim 21, wherein the light having a plurality of wavelengths comprises a continuous wavelength spectrum, the method further comprising separating the wavelengths in the reflected light to produce a wavelength spectrum; and filtering the wavelength spectrum to produce a plurality of non-contiguous wavelength bands, wherein the plurality of non-contiguous wavelength bands do not overlap in the one or more images received by the two-dimensional sensor.

29. The method of claim 28, wherein filtering the wavelength spectrum is performed after separating the reflected light into the plurality of polarization states.

30. The method of claim 21, wherein modifying the polarized light using the Fresnel cone to produce the sample light having the plurality of polarization states at each of the plurality of wavelengths comprises using total internal reflection of a Fresnel cone having an optical coating with a refractive index selected to produce a constant phase shift for wavelengths of light imaged by the two-dimensional sensor.

31. The method of claim 21, further comprising separating the reflected light into the plurality of polarization states such that the polarization states do not overlap in the one or more images received by the two-dimensional sensor.

32. The method of claim 21, further comprising separating the reflected light into a plurality of polarization states that are vertices of a best-measurement tetrahedron within a Poincare sphere.

33. The method of claim 21, further comprising separating the reflected light into the plurality of polarization states using a grating before the two-dimensional sensor, the grating configured to diffract different polarization states to different transmission orders, the method further comprising analyzing the different polarization states in the reflected light.

34. The method of claim 33, wherein the grating comprises a spaced array of phase- shifting elements.

35. The method of claim 33, wherein analyzing the different polarization states in the reflected light comprises diffracting the different polarization states to different transmission orders with the grating and polarizing the different polarization states from the grating with a linear polarizer.

36. The method of claim 33, wherein analyzing the different polarization states in the reflected light comprises diffracting the different polarization states to different transmission orders with the grating and polarizing the different polarization states from the grating with a micro-polarizer array comprising micro-polarizer pixels aligned with pixels of the two-dimensional sensor, wherein the micro-polarizer array comprises a repeating array of micro-polarizer pixels having discrete polarizations.

37. The method of claim 21, further comprising separating the wavelengths in the reflected light with a first diffractive element and a second diffractive element, and further comprising: directing a first portion of the reflected light to the first diffractive element with a beam splitter; receiving a second portion of the reflected light from the beam splitter with a phase- shifting optical element and directing the second portion of the reflected light to the second diffractive element with the phase-shifting optical element, wherein the first portion of the reflected light has a different polarization state than the second portion of the reflected light; wherein separating the wavelengths in the reflected light comprises separating the wavelengths in the first portion of the reflected light with the first diffractive element and separating the wavelengths in the second portion of the reflected light with the second diffractive element; and The method further includes analyzing the polarization state in the first portion of the reflected light and the second portion of the reflected light with a micro-polarizer array, the micro-polarizer array including micro-polarizer pixels aligned with pixels of the two-dimensional sensor, wherein the micro-polarizer array includes a repeating array of micro-polarizer pixels having discrete polarizations.

38. The method of claim 37, wherein the micro-polarizer array is configured to use the separated wavelengths in the reflected light from the first diffractive element and the separated wavelengths in the reflected light from the second diffractive element to produce two orthogonal rings around a Poincare sphere.

39. The method of claim 38, wherein an intersection of the two orthogonal rings around the Poincare sphere is used to reference a first two-dimensional sensor to a second two-dimensional sensor.

40. An ellipsometer, the ellipsometer comprising: means for generating light having a plurality of wavelengths; means for polarizing the light; means for modifying the polarized light using a Fresnel cone to produce sample light having a plurality of polarization states at each of the plurality of wavelengths, wherein the Fresnel cone utilizes total internal reflection to produce a plurality of polarization states at each wavelength of the polarized light; means for detecting reflected light from a sample in each of a plurality of polarization states of the reflected light from the sample in one or more images of separated wavelengths and outputting data from the one or more images.

Images