Double-frequency comb-shaped imaging spectrum ellipsometer

Abstract

A measurement system may direct an illumination beam including at least one of a first frequency comb or a second frequency comb to a sample and generate a sequence of images of the sample based on the first frequency comb and the second frequency comb. The system may include one or more coding optical elements to encode data associated with one or more transfer matrix elements into the sequence of images of the sample. The system may further generate a transfer matrix dataset including measurements of at least one of the one or more transfer matrix elements associated with the sample based on at least one of a spectral, spatial, or temporal analysis of the sequence of images, and generate one or more measurements of the sample based on the transfer matrix data set.

Description

Cross-reference of related applications

[0001] This application claims the right to U.S. Provisional Application No. 63 / 531,473, filed August 8, 2023, entitled “Dual Frequency Comb Imaging Spectroscopic Ellipsomer”, by inventors Chao Chang, Jongjin Kim, and David Zimdars, pursuant to 35 USC §119(e), the entire contents of which are incorporated herein by reference. Technical Field

[0002] This disclosure generally relates to spectral elliptography, and more specifically, to imaging spectral elliptography. Background Technology

[0003] Semiconductor manufacturing processes have become exceptionally complex. For example, as nodes continue to expand in semiconductor devices, logic device manufacturing technology is shifting from FinFETs to gate-all-around (GAA) nanosheets and will continue the trend from nanosheets to forked wafers, from forked wafers to complementary FETs (where nFETs are 3D “folded” in-line within pFETs), and so on. As another example, DRAM manufacturing technology could eventually move to 3D-DRAM structures similar to 3D-NAND, while EUV continuously reduces the size of current 2D-DRAM.

[0004] Therefore, there is an increasing demand for measurement tools suitable for characterizing such small and complex structures. Mueller matrix ellipsometry (MMSE) is one promising technique because the Mueller matrix contains information about the change in polarization state after light interacts with complex 3D structures patterned on a semiconductor wafer. However, conventional MMSE techniques cannot meet the requirements for processing power and dot size.

[0005] Therefore, it is necessary to develop systems and methods to overcome the above-mentioned shortcomings. Summary of the Invention

[0006] In an embodiment, the technology described herein relates to a measurement system comprising: a first frequency comb source configured to generate a first frequency comb; a second frequency comb source configured to generate a second frequency comb having a repetition rate different from the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources; an illumination subsystem comprising one or more illumination lenses to guide an illumination beam comprising at least one of the first or second frequency combs to a sample; an imaging subsystem comprising one or more imaging lenses and a detector configured to generate an image sequence of the sample based on the first and second frequency combs; one or more coding optical elements comprising at least one of one or more optical retarders or one or more polarizers, wherein at least one of the one or more coding optical elements is located in the illumination subsystem, wherein the one or more At least one of the coding optics is located in the imaging subsystem, wherein the coding optics encode data associated with one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial, spectral, or temporal domains of the image sequence; and a controller comprising one or more processors configured to execute program instructions that cause the one or more processors to generate a transfer matrix dataset containing measurements of at least one of the one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence, wherein the transfer matrix dataset is at least one of spatial, spectral, or temporal resolution; and to generate one or more measurements of the sample based on the transfer matrix dataset.

[0007] In embodiments, the techniques described herein relate to a measurement system in which the measurement of at least one of the one or more transition matrix elements associated with the sample is generated based on at least one of spatial, spectral, or temporal analyses of the image sequence, and the at least one of the one or more transition matrix elements is decoded from the image sequence based on at least one of spatial, spectral, or frequency analyses of the image sequence.

[0008] In embodiments, the techniques described herein relate to a measurement system in which one or more transition matrix elements comprise Mueller matrix elements.

[0009] In embodiments, the techniques described herein relate to a measurement system in which one or more transition matrix elements comprise Jones matrix elements.

[0010] In an embodiment, the technology described herein relates to a measurement system, wherein the illumination subsystem further includes a beam combiner configured to combine the first frequency comb and the second frequency comb into a single illumination beam, wherein the one or more imaging lenses of the illumination subsystem guide the single illumination beam to the sample.

[0011] In an embodiment, the technology described herein relates to a measurement system in which the image sequence corresponds to a multi-pixel image of the sample, wherein the transfer matrix dataset contains the measurement of at least one of the one or more transfer matrix elements as a function of wavelength and spatial location on the sample.

[0012] In an embodiment, the technology described herein relates to a measurement system in which the image sequence corresponds to a single-pixel image of the sample, wherein the transfer matrix dataset contains the measurement of at least one of the one or more transfer matrix elements as a function of the wavelength at a single spatial location on the sample.

[0013] In embodiments, the technology described herein relates to a measurement system in which one or more coding optics include a generator in an illumination subsystem, the generator including one or more beam clippers to generate two or more clipped beams with different polarization states, wherein the one or more illumination lenses of the illumination subsystem guide the two or more clipped beams to a common point on the sample; and an analyzer in an imaging subsystem, the analyzer including one or more additional beam clippers to cut the two or more clipped beams into additional clipped beams with different polarization states, wherein the one or more imaging lenses of the imaging subsystem interfere with the additional clipped beams on the detector.

[0014] In embodiments, the techniques described herein relate to a measurement system in which the measurement of at least one of the one or more transfer matrix elements associated with the sample is generated based on at least one of spectral or spatial frequency analysis of the image sequence; and one or more transfer matrix element datasets are generated based on the one or more channel images, wherein the transfer matrix dataset contains the one or more transfer matrix element datasets.

[0015] In embodiments, the techniques described herein relate to a measurement system in which the image sequence comprises multi-pixel images, and the one or more transfer matrix element datasets comprise a sequence of spatially resolved transfer matrix element images; wherein the transfer matrix dataset, which generates the measurement comprising at least one of the one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence, further comprises extracting spectrally resolved transfer matrix element data for at least some pixels in the image sequence using time-frequency analysis techniques, wherein the transfer matrix dataset contains the spectrally resolved transfer matrix element data.

[0016] In an embodiment, the technology described herein relates to a measurement system in which one or more write-optical elements comprise a series of cascaded spectral-dependent phase retarders to encode the data associated with the one or more transfer matrix elements into the spectral domain of a series of images.

[0017] In an embodiment, the technology described herein relates to a measurement system in which the measurement of at least one of the one or more transition matrix elements at each location on the sample is decoded by spectral analysis of the image sequence.

[0018] In embodiments, the techniques described herein relate to measurement systems, wherein the one or more coding optics comprise one or more rotating optics of at least one of the illumination subsystem or the imaging subsystem.

[0019] In an embodiment, the technology described herein relates to a measurement system in which one or more rotating optical elements include a first rotating quarter-wave plate in the illumination subsystem and a second rotating quarter-wave plate in the imaging subsystem, wherein the first and second rotating quarter-wave plates rotate at different speeds, and wherein the data associated with the one or more transfer matrix elements is encoded into the time domain of the image sequence.

[0020] In an embodiment, the technology described herein relates to a measurement system in which the measurement of at least one of the one or more transition matrix elements at each location on the sample is decoded by time-frequency analysis of the image sequence.

[0021] In an embodiment, the technology described herein relates to a measurement system in which the imaging subsystem provides the image sequence via electro-optic sampling.

[0022] In the embodiments described herein, the technology relates to a measurement system, wherein the one or more measurements comprise one or more metric measurements.

[0023] In the embodiments described herein, the technology relates to a measurement system, wherein the one or more measurements include one or more inspection measurements.

[0024] In an embodiment, the technology described herein relates to a measurement system comprising: a controller including one or more processors configured to execute program instructions that cause the one or more processors to: generate a transfer matrix dataset containing one or more transfer matrix elements associated with a sample based on at least one of spatial, spectral, or temporal analysis of an image sequence, wherein the transfer matrix dataset is at least one of spatial resolution or spectral resolution, wherein the image sequence is generated by a measurement subsystem, the measurement subsystem comprising: a first frequency comb source configured to generate a first frequency comb; and a second frequency comb source configured to generate a second frequency comb having a repetition rate different from the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources. The system includes an illumination subsystem comprising one or more illumination lenses to direct an illumination beam containing at least one of the first frequency comb or the second frequency comb onto the sample; an imaging subsystem comprising one or more imaging lenses and a detector configured to generate the image sequence of the sample based on the first frequency comb and the second frequency comb; and one or more coding optics comprising one or more optical delayers, wherein the coding optics encode data associated with the one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial domain, spectral domain, or temporal domain of the image sequence; and one or more measurements of the sample based on the transfer matrix dataset.

[0025] In embodiments, the techniques described herein relate to a measurement system in which the measurement of the one or more transition matrix elements associated with the sample is generated based on at least one of spatial, spectral, or temporal analysis of the image sequence, and the one or more transition matrix elements are decoded from the image sequence based on at least one of spatial, spectral, and frequency analysis of the image sequence.

[0026] In embodiments, the techniques described herein relate to a measurement system in which one or more transition matrix elements comprise Mueller matrix elements.

[0027] In an embodiment, the technology described herein relates to a measurement system in which one or more transition matrix elements comprise Jones matrix elements.

[0028] In an embodiment, the technology described herein relates to a measurement system, wherein the illumination subsystem further includes a beam combiner configured to combine the first frequency comb and the second frequency comb into a single illumination beam, wherein the one or more imaging lenses of the illumination subsystem guide the single illumination beam to the sample.

[0029] In an embodiment, the technology described herein relates to a measurement system in which the image sequence corresponds to a multi-pixel image of the sample, wherein the transfer matrix dataset contains the measurements of one or more transfer matrix elements as a function of wavelength and spatial location on the sample.

[0030] In an embodiment, the technology described herein relates to a measurement system in which the image sequence corresponds to a single-pixel image of the sample, wherein the transfer matrix dataset contains the measurements of one or more transfer matrix elements as a function of the wavelength at a single spatial location on the sample.

[0031] In an embodiment, the technology described herein relates to a measurement system in which one or more coding optics include: a generator in an illumination subsystem, the generator including one or more beam clippers to generate two or more clipped beams with different polarization states, wherein the one or more illumination lenses of the illumination subsystem guide the two or more clipped beams to a common point on the sample; and an analyzer in an imaging subsystem, the analyzer including one or more additional beam clippers to cut the two or more clipped beams into additional clipped beams with different polarization states, wherein the one or more imaging lenses of the imaging subsystem interfere with the additional clipped beams on the detector.

[0032] In an embodiment, the technology described herein relates to a measurement system in which the measurement of the transfer matrix dataset, which includes one or more transfer matrix elements associated with the sample, is generated based on at least one of spectral or spatial frequency analysis of the image sequence. This includes: generating one or more channel images for specific images of the image sequence based on spatial frequency filtering techniques; and generating one or more transfer matrix element datasets based on the one or more channel images, wherein the transfer matrix dataset includes the one or more transfer matrix element datasets.

[0033] In embodiments, the techniques described herein relate to a measurement system in which the image sequence comprises multi-pixel images, and the one or more transfer matrix element dataset comprises a sequence of spatially resolved transfer matrix element images; wherein the transfer matrix dataset, which generates the measurement containing the one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence, further comprises extracting spectrally resolved transfer matrix element data for at least some pixels in the image sequence using time-frequency analysis techniques, wherein the transfer matrix dataset contains the spectrally resolved transfer matrix element data.

[0034] In an embodiment, the technology described herein relates to a measurement system in which one or more coding optics comprise a series of cascaded spectral-dependent phase retarders to encode the data associated with the one or more transfer matrix elements into the spectral domain of a series of images.

[0035] In an embodiment, the technology described herein relates to a measurement system in which one or more transition matrix elements at each location on the sample are decoded by spectral analysis of the image sequence.

[0036] In embodiments, the technology described herein relates to a measurement system in which the one or more coding optics comprise one or more rotating optics of at least one of the illumination subsystem or the imaging subsystem.

[0037] In an embodiment, the technology described herein relates to a measurement system in which one or more rotating optical elements comprise: a first rotating quarter-wave plate in the illumination subsystem; and a second rotating quarter-wave plate in the imaging subsystem, wherein the first and second rotating quarter-wave plates rotate at different speeds, and wherein the data associated with the one or more transfer matrix elements is encoded into the time domain of the image sequence.

[0038] In an embodiment, the technique described herein relates to a measurement system in which one or more transition matrix elements at each location on the sample are decoded by time-frequency analysis of the image sequence.

[0039] In an embodiment, the technology described herein relates to a measurement system in which the imaging subsystem provides the image sequence via electro-optic sampling.

[0040] In the embodiments described herein, the technology relates to a measurement system, wherein the one or more measurements comprise one or more metric measurements.

[0041] In the embodiments described herein, the technology relates to a measurement system, wherein the one or more measurements include one or more inspection measurements.

[0042] In embodiments, the technology described herein relates to a measurement method comprising: generating a transfer matrix dataset containing one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of an image sequence of the sample, wherein the transfer matrix dataset is at least one of spatial, spectral, or temporal resolution, wherein the image sequence is generated by a measurement subsystem comprising: a first frequency comb source configured to generate a first frequency comb; a second frequency comb source configured to generate a second frequency comb having a repetition rate different from the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources; and an illumination subsystem comprising one or more illumination lenses for... The system includes: an illumination beam comprising at least one of the first frequency comb or the second frequency comb, directed to the sample; an imaging subsystem comprising one or more imaging lenses and a detector configured to generate the image sequence of the sample based on the first frequency comb and the second frequency comb; and one or more coding optics comprising one or more optical delayers, wherein the coding optics encode data associated with the one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial, spectral, or temporal domains of the image sequence; and one or more measurements of the sample generated based on the transfer matrix dataset.

[0043] It should be understood that the above general description and the following detailed description are for illustrative and explanatory purposes only and do not necessarily limit the invention. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. Attached Figure Description

[0044] Those skilled in the art can better understand the many advantages of this disclosure by referring to the accompanying drawings.

[0045] Figure 1A A block diagram illustrating a spectral transfer matrix measurement system according to one or more embodiments of the present disclosure.

[0046] Figure 1B A flowchart illustrating the steps performed in a method for generating at least one of spectral or spatially resolved transfer matrix data, according to one or more embodiments of the present disclosure.

[0047] Figure 2 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0048] Figure 3A A schematic diagram illustrating a BSP according to one or more embodiments of the present disclosure.

[0049] Figure 3B A schematic diagram illustrating a BSA according to one or more embodiments of the present disclosure.

[0050] Figure 4 This describes an optical chain of a measurement system according to one or more embodiments of the present disclosure, having a generator before the sample and an analyzer after the sample, wherein both the generator and the analyzer are configured to have, as Figure 3B The half-wave plate 316 depicted in the text.

[0051] Figure 5 A simplified diagram illustrating various channels in the spatial frequency plane of an image according to one or more embodiments of the present disclosure.

[0052] Figure 6 This describes different sampling states using a dual-frequency comb according to one or more embodiments of the present disclosure.

[0053] Figure 7 This describes a series of steps for generating spatially and spectrally resolved Mueller matrix data according to one or more embodiments of the present disclosure.

[0054] Figure 8 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0055] Figure 9A A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0056] Figure 9B Description of one or more embodiments according to this disclosure Figure 9A The optical chain of the measurement system in the middle.

[0057] Figure 10 This describes a series of steps for generating spatially and spectrally resolved Mueller matrix data based on spectral coding, according to one or more embodiments of the present disclosure.

[0058] Figure 11 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0059] Figure 12 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0060] Figure 13A A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0061] Figure 13B Description of one or more embodiments according to this disclosure Figure 13AThe optical chain of the measurement system described in the figure.

[0062] Figure 14 This describes a series of steps for generating spatially and spectrally resolved Mueller matrix data based on time-polarized coding according to one or more embodiments of the present disclosure.

[0063] Figure 15 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0064] Figure 16 A schematic diagram illustrating a measurement system according to one or more embodiments of the present disclosure.

[0065] Figure 17 Description of one or more embodiments according to this disclosure Figure 2 A schematic diagram of the changes in the measurement system depicted in the figure.

[0066] Figure 18 Description of one or more embodiments according to this disclosure Figure 9A A schematic diagram of the changes in the measurement system depicted in the figure.

[0067] Figure 19 Description of one or more embodiments according to this disclosure Figure 13A A schematic diagram of the changes in the measurement system depicted in the figure. Detailed Implementation

[0068] The disclosed subject matter will now be described in detail with reference to the accompanying drawings. Specific embodiments and features of this disclosure are particularly shown and described below. The embodiments set forth herein should be considered illustrative rather than restrictive. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail may be made without departing from the spirit and scope of this disclosure.

[0069] Embodiments of this disclosure pertain to systems and methods for providing an imaging metric system with per-pixel transfer matrix spectral elliptic polarization measurements. As used herein, the transfer matrix can refer to any type of matrix describing the properties of light transformed by a sample, such as (but not limited to) a Mueller matrix or a Jones matrix. In this manner, transfer matrix spectral elliptic polarization measurements of the entire imaging field (e.g., an image of samples from one or more detectors located at a field plane conjugate to the sample) are simultaneously generated at pixel-level resolution to produce a real-time metric map. The imaging field can be adjusted to cover a dies, sub-dies regions, or any selected point size.

[0070] In an embodiment, an imaging spectral elliptic polarization measurement system includes: one or more frequency comb generators for generating two frequency combs with different repetition rates; an imaging subsystem for imaging a sample using the two frequency combs; and one or more coding optics designed to code data associated with transfer matrix elements into an image generated by the imaging subsystem in any combination of the spatial, spectral, or temporal domains. Therefore, based on the coding induced by the coding optics, spectral, spatial, and / or temporal frequency analysis of the image generates transfer matrix elements as a function of wavelength (or a spectral Mueller matrix measure in the case of a Mueller matrix) for each pixel or combination of pixels. For example, the coding element may comprise a combination of optical retarders and / or polarizers located before and after the sample, which code data or combinations thereof associated with various transfer matrix elements into the spatial, spectral, and / or temporal domains of the image, allowing spectral transfer matrix data to be extracted during post-processing based on corresponding spatial, spectral, and / or temporal techniques. Furthermore, the imaging spectral elliptic polarization measurement system can operate in either reflection or transmission mode.

[0071] A dual-frequency comb, combined with coding optics, was carefully considered to provide spectral transfer matrix measurements with fixed elements. In other words, the dual-frequency comb provides spectral transfer matrix measurements without requiring element movement during detection. This configuration thus provides stable and robust measurements. For example, guiding dual-frequency combs with different repetition rates to a sample can generate time-difference beat signals that provide spectral data similar to time-domain spectra or dispersed Fourier transform spectra or heterodyne spectra in the frequency domain, where each pair of comb teeth contributes to a heterodyne signal at a specific radio frequency (RF) value.

[0072] After further careful consideration, it has been found that various techniques can be used to write data associated with elements or combinations thereof of a transfer matrix into the spatial, spectral, and / or temporal domains within the spirit and scope of this disclosure. Therefore, it should be understood that the specific examples disclosed herein are provided for illustrative purposes only and should not be construed as limiting the scope of this disclosure.

[0073] Referring now to Figures 1 to 19, systems and methods for providing real-time spectral transfer matrix measurements according to one or more embodiments of the present disclosure are described.

[0074] Figure 1A A block diagram illustrating a measurement system 100 (e.g., a spectral transfer matrix measurement system) according to one or more embodiments of the present disclosure.

[0075] In an embodiment, the measurement system 100 includes one or more frequency comb sources 102 for generating two phase-locked frequency combs 104 with different repetition rates, an illumination subsystem 106 for directing at least one of the two frequency combs 104 to a sample 108, an imaging subsystem 110 for collecting light emitted from the sample 108, and a detector 112 located in an image plane to generate one or more images of the sample 108 based on the frequency combs 104. As used herein, an image of the sample 108 may refer to any data generated by the detector 112 in a field plane conjugate to the sample 108. Furthermore, the detector 112 may comprise a single-pixel sensor or a multi-pixel sensor. For example, a single-pixel detector 112 located in the field plane may provide single-pixel image data (e.g., a single-pixel image) associated with the sample 108. As another example, a multi-pixel detector 112 located in the field plane may provide multi-pixel image data (e.g., a multi-pixel image) associated with the sample 108.

[0076] The measurement system 100 may further include one or more write-code optical elements 114 to write data associated with transfer matrix elements (e.g., Mueller matrix elements, Jones matrix elements, or the like) representing the modification of light by the sample 108 into at least one of the spatial, spectral, or temporal domains associated with a sequence of one or more images of the sample 108 captured by the detector 112.

[0077] The measurement system 100 may further include a controller 116 having one or more processors 118 configured to execute program instructions stored (e.g., maintained) on memory 120 or a memory device. Furthermore, the controller 116 may be communicatively coupled to any component of the measurement system 100, such as (but not limited to) detector 112. In this way, the one or more processors 118 of the controller 116 may directly or indirectly perform any of the various process steps described throughout this disclosure. For example, the controller 116 may perform at least one of spatial, spectral, or temporal analyses of a sequence of one or more images from detector 112 to extract transfer matrix data associated with sample 108. In other words, the controller 116 may decode transfer matrix data from a sequence of one or more images encoded by write-code optics 114. Specifically, the controller 116 may generate transfer matrix elements as a function of wavelength for each pixel or combination of pixels (e.g., providing a spectral Mueller matrix metric in the case of a Mueller matrix). In this way, the controller 116 can generate real-time spectral transfer matrix metric data of samples having spatial resolution associated with the image provided by the imaging subsystem 110.

[0078] A transfer matrix can represent how an object (e.g., sample 108) modifies the polarization state of incident light. For example, the polarization state of light can be characterized by a quaternary Stokes vector. The Mueller matrix is ​​a 16-element transfer matrix representing the manipulation of the Stokes vector of light by the object. As another example, the Jones matrix can be a quaternary transfer matrix representing the transformation of the Jones vectors of the incident and outgoing light from the sample, where the Jones vectors describe the amplitude and phase of the electric field of the light in orthogonal directions.

[0079] Specifically, Mueller matrix elliptic polarization (MMSE) is a promising technique for generating measurements related to the physical and / or chemical structure of a target object using collected Mueller matrix data. Conventional MMSE techniques generate data associated with the entirety or a portion of the target object's Mueller matrix based on a sequence of elliptic polarization measurements, where the polarization states of the incident and collected light are controlled by rotating the polarizer and / or waveplate. However, this technique is unsuitable for high-volume measurements due to the limited spatial resolution associated with the size of the illumination beam and the relatively low throughput associated with the physical rotation of the polarizing elements required for the series of measurements.

[0080] In an embodiment, the measurement system 100 generates spectral and spatially resolved transfer matrix data associated with sample 108 by encoding data indicating transfer matrix elements into the spatial, spectral, and / or temporal aspects of a series of images generated by the imaging subsystem 110 based on a dual-frequency comb 104 as an illumination source. Specifically, one or more coding optics 114 of the measurement system 100 include polarization manipulation optics to encode different polarization states into one or more frequency combs 104 for imaging sample 108 in any combination of spatial, spectral, or temporal domains. These coding optics 114 can be located anywhere in the measurement system 100, included in the illumination subsystem 106 to manipulate the frequency combs 104 before sample 108 and / or in the imaging subsystem 110 to manipulate the frequency combs 104 after interaction with sample 108. It should be noted that this configuration can provide data associated with transfer matrix elements without requiring moving parts, achieving a processing power generally higher than existing MMSE techniques.

[0081] In a broad sense, the coding optics 114 may comprise any combination of one or more polarization manipulation elements (e.g., but not limited to, waveplates or polarizers). In some embodiments, the coding optics 114 comprises a beam shearing plate (BSP) formed by two (or more) birefringent plates at different orientations to produce a spatially varied polarization distribution. In some embodiments, the coding optics 114 comprises a beam shearing analyzer (BSA) formed by two (or more) BSPs separated by waveplates to further provide a spatially varied polarization distribution. The combination of BSPs and / or BSAs to manipulate the polarization of light before and after interaction with sample 108 can thus provide spatial encoding of transfer matrix element data into one or more images of sample 108. Specifically, data associated with transfer matrix elements can be encoded into the spatial frequencies of the images so that spatial frequency filtering techniques on the images (e.g., spatial domain Fourier transform techniques) can be used to extract data associated with a particular transfer matrix element (or combination thereof).

[0082] Furthermore, a dual-frequency comb 104, combined with the coding optics 114, is used to provide encoding of data associated with elements of the transfer matrix in the spectral and / or time domains. For example, the interaction of combs 104 with different repetition rates can generate time-difference beat signals, which provide spectral data similar to time-domain spectra or dispersed Fourier transform spectra in the time domain or heterodyne spectra in the frequency domain, wherein each pair of comb teeth contributes to the heterodyne signal at a specific radio frequency (RF) value.

[0083] In this manner, time-frequency analysis techniques (e.g., time-Fourier transform) can be used to extract spectral-resolved data associated with the elements (or combinations thereof) of the transfer matrix from an image sequence. It should be noted that this time-frequency analysis can be applied to each pixel of the image sequence to provide spatial and spectral-resolved data associated with the elements (or combinations thereof) of the transfer matrix. This data can then be used to generate spatially resolved measurements of the physical and / or chemical properties of sample 108 at a resolution defined by imaging subsystem 110.

[0084] Figure 1B A flowchart illustrating the steps performed in method 122 for generating spectral and / or spatially resolved transfer matrix data according to one or more embodiments of this disclosure. The embodiments and enabling techniques previously described herein in the context of measurement system 100 should be interpreted as extending to method 122. For example, processor 118 of controller 116 of measurement system 100 may execute program instructions that cause processor 118 to perform various steps of method 122 directly or indirectly (e.g., by generating control signals for directing additional components in measurement system 100). As another example, various components of measurement system 100 may implement various steps of method 122. However, it should be further noted that method 122 is not limited to the architecture of measurement system 100.

[0085] In an embodiment, method 122 includes step 124 of generating an image sequence of samples, wherein data associated with the transition matrix of the samples (e.g., Mueller matrix, Jones matrix, or the like) is written into at least one of the spatial, spectral, or temporal domains of the image sequence.

[0086] In an embodiment, method 122 includes step 126 of generating a transfer matrix dataset containing measurements of one or more elements (e.g., transfer matrix elements) of the transfer matrix based on the image sequence. For example, measurements of the transfer matrix elements may be generated based on at least one of spectral or spatial frequency analysis of the image sequence. The transfer matrix dataset may be spectral and / or spatially resolved. For example, the transfer matrix data may be formed as a tensor spatially resolved image associated with the values ​​of one or more transfer matrix elements along one dimension and spectral resolved data associated with one or more Mueller matrix elements along another dimension. As an illustration, the transfer matrix data of the Mueller matrix may be written as:

[0087] (1)

[0088] in For each individual element of the transition matrix, x and y are spatial coordinates, and λ represents the wavelength (or more generally, the spectral coordinates).

[0089] However, it should be noted that in all embodiments, the transfer matrix data does not require spectral and spatial resolution. In some embodiments, only spectral resolution is performed on the transfer matrix data. For example, this configuration can be generated using a single-pixel detector that produces a single-pixel image. In some embodiments, only spatial resolution is performed on the transfer matrix data. In this configuration, the transfer matrix data can be generated using a single wavelength.

[0090] In an embodiment, method 122 includes step 128 of generating one or more measurements of the sample based on the transfer matrix dataset. Because the Mueller matrix data characterizes how the sample 108 manipulates light, this transfer matrix data can serve as the basis for a wide range of measurements. For example, one or more models can correlate the transfer matrix data with metric measurements (e.g., performing inverse measurements based on the transfer matrix data), such as (but not limited to) superposition measurements, critical dimension (CD) measurements, edge placement error (EPE) measurements, film metric measurements (e.g., film thickness, refractive index, composition, or the like), local variation (e.g., average value) and / or locality (3σ) measurements, pad measurements, or wafer edge-to-wafer center uniformity measurements (e.g., superposition, CD, or any other uniformity measurement). As another example, the transfer matrix data can serve as the basis for inspection measurements used for defect identification and / or characterization.

[0091] For reference Figures 2 to 17The figures illustrate various non-limiting configurations of the measurement system 100 according to one or more embodiments of the present disclosure. In a broader sense, the measurement system 100 may, upon careful consideration, include any combination of write optics 114 suitable for writing data associated with one or more transition matrix elements representing sample 108 into one or more images of sample 108, representing spatial, spectral, and / or temporal properties.

[0092] It should be noted that Figures 2 to 17 The focus is on using the Mueller matrix as the transition matrix. However, this is merely illustrative and should not be construed as limiting the scope of this disclosure. Specifically, the systems and methods disclosed herein encode Jones matrix data in the spatial, temporal, and / or spectral domains of the image sequence of sample 108 and then extract one or more Jones matrix elements associated with sample 108 from the image sequence.

[0093] The measurement system 100 can guide one or more frequency combs 104 to the sample 108. For example, in some embodiments, two frequency combs 104 are aligned to form a single collinear beam guided to the sample 108. As another example, in some embodiments, a first frequency comb 104 is guided to the sample 108 and interferes with a second frequency comb 104 within the imaging subsystem 110 before the detector 112.

[0094] Detector 112 may comprise any sensor or combination of sensors located at an imaging plane suitable for capturing light associated with frequency comb 104. In some embodiments, detector 112 is a temporal detector suitable for capturing temporal signals in one or more pixels. For example, detector 112 may comprise (but is not limited to) a photodiode or an array of photodiodes. This configuration may be suitable for generating spatially resolved transfer matrix data. In some embodiments, detector 112 is a single-pixel sensor, such as (but not limited to) a photodetector. This configuration may generate transfer matrix data associated with a location on a sample (e.g., defined by the resolution of imaging subsystem 110 combined with the size of detector 112), but may advantageously provide a faster measurement speed than two-dimensional sensors. In this way, any reference herein to an image generated by detector 112 may refer to a single-pixel or multi-pixel image.

[0095] Figure 2 A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure.

[0096] exist Figure 2 In the measurement system 100, two phase-locked frequency comb sources 102 are provided with two frequency combs 104 having different frequencies, wherein the relative frequencies can be fixed. It may be programmable. The frequency comb source 102 may contain any combination of components suitable for generating the frequency comb 104 using any technology. In addition, the frequency comb source 102 may be provided as a separate component coupled to the phase-locked loop 202 or as a single component.

[0097] exist Figure 2 In this embodiment, the measurement system 100 includes a beam splitter 204 to align and overlap two frequency combs 104 along a collinear optical path. In this way, the two frequency comb sources 102 can be guided as a single beam to the sample 108. However, this is for illustrative purposes only and not a requirement.

[0098] The illumination subsystem 106 and imaging subsystem 110 may include any combination of optical elements suitable for guiding one or more frequency combs 104 to the sample 108 and imaging the sample 108 based on the frequency combs 104. For example, Figure 2 The configuration is depicted in which the illumination subsystem 106 includes a pair of illumination lenses 206 to focus the frequency comb 104 onto the sample 108 and the imaging subsystem 110 includes a pair of collection lenses 208 to image the sample 108 onto the detector 112 (e.g., located at a field plane conjugate to the sample 108). It should be noted that, although... Figure 2 The measurement system 100 is depicted as a reflection system (e.g., where the imaging subsystem 110 images the light reflected from the sample 108, but this is merely illustrative). In some embodiments, the measurement system 100 is a transmission system, where the imaging subsystem 110 images the light transmitted through the sample. Furthermore, Figure 2 The drawing lens 210 manipulates the frequency comb 104 before and after the sample 108 to provide the desired angle of incidence and angle of collection. Any angle of incidence and angle of collection can be provided, such as (but not limited to) 65 degrees. The focal lengths of the illumination lens 206 and the collection lens 208 can be selected to provide any desired illumination spot size and / or imaging field of view. In some cases, the illumination lens 206 and the collection lens 208 are selected to be equal (e.g., F1 = F2 = F3 = F4). In some cases, the focal lengths of the illumination lens 206 and the collection lens 208 are selected to be complementary (e.g., F1 = F4; F2 = F3). In some cases, depending on the application requirements, the focal lengths of the illumination lens 206 and the collection lens 208 are selected to have different values.

[0099] also, Figure 2 A configuration with a two-dimensional detector 112 (e.g., a detector 112 with a multi-pixel sensor) is depicted. Therefore, Figure 2 This is suitable for providing an image sequence as a three-dimensional dataset, where each image provides spatial data (e.g., data in the x and y dimensions) and the image sequence provides temporal data (e.g., t). In summary, this dataset can be represented as (x, y, t).

[0100] According to one or more embodiments of this disclosure, various aspects of the temporal and spatial encoding of data associated with the elements of the transition matrix are now described in more detail.

[0101] In some embodiments, the coding optics 114 includes a generator 212 in the illumination subsystem 106 and an analyzer 214 in the imaging subsystem 110, wherein the generator 212 and the analyzer 214 are formed by polarizing manipulation optics suitable for coding the input and output Stokes vectors in the spatial frequency channels in Fourier space (e.g., spatial frequency space). In this configuration, the transition matrix elements (or combinations thereof) associated with sample 108 can be inferred from these channels after an inverse Fourier transform or other suitable spatial frequency analysis technique.

[0102] Generator 212 and analyzer 214 may include any component or combination of components suitable for writing the input and output Stokes vectors in the spatial frequency channels in Fourier space. For example, generator 212 and / or analyzer 214 may be formed of polarizing manipulation components (e.g., but not limited to, waveplates, BSPs, or BSAs).

[0103] Figure 3A A schematic diagram illustrating a BSP 302 according to one or more embodiments of the present disclosure.

[0104] In some embodiments, the BSP 302 includes a half-wave plate (HWP) 304 located between a first shear plate 306 and a second shear plate 308. For example, the first shear plate 306 and the second shear plate 308 may be formed as birefringent plates having optical axes 310 that rotate relative to each other to provide two spatially separated beams 312. As an illustration, Figure 3A A non-limiting configuration is depicted, wherein the optical axis of the first shear plate 306 is oriented at 45 degrees relative to the incident angle of the frequency comb 104 and at 90 degrees relative to the optical axis of the second shear plate 308 in a common plane. Furthermore, the HWP 304 is oriented at a 45-degree angle to the polarized light from the frequency comb 104 to provide a 90-degree polarization rotation between the first shear plate 306 and the second shear plate 308. In this configuration, the beam shearing distance D is:

[0105] (2)

[0106] Where d is the thickness of the first shear plate 306 and the second shear plate 308, n o It is the general refractive index of the first shear plate 306 and the second shear plate 308, and It is the refractive index of the first shear plate 306 and the second shear plate 308.

[0107] This paper, after careful consideration, suggests the selection of both the first shear plate 306 and the second shear plate 308 to provide achromatic performance. For example, the chromaticity change due to lateral shift can be reduced by orders of magnitude across a broadband spectrum. Additionally, as... Figure 3A The shearing distance (D) of the BSP 302 described herein can be greater than that of an alternative beam shearing plate design (e.g., a Savart plate). times).

[0108] Figure 3B The illustration shows a schematic diagram of a BSA 314 according to one or more embodiments of the present disclosure. In some embodiments, the BSA 314 consists of two BSPs 302 (e.g., Figure 3A HWP316 is formed between the two examples of BSP 302 depicted in the text. Specifically, Figure 3B A non-limiting configuration is depicted including a first BSP 302a and a second BSP 302b rotated by 90 degrees, wherein the HWP 316 is oriented with its optical axis at a 22.5-degree angle relative to the polarized light from the frequency comb source 102 and the first BSP 302a to provide a 45-degree polarization rotation. In this configuration, the BSA 314 provides four shear beams 318 separated by a shear distance D, as shown in illustration 320.

[0109] Figure 4 This describes an optical chain of a measurement system 100 according to one or more embodiments of the present disclosure, having a generator 212 preceding sample 108 and an analyzer 214 following sample 108, wherein both the generator 212 and the analyzer 214 are configured to have, as Figure 3B The HWP 316 described in the document. Specifically, Figure 4 The configuration is depicted in which generator 212 includes a polarizer 322 oriented at 45 degrees relative to the shear direction of the first BSP 302 in BSA 314a (e.g., configured to provide four shear beams 318 from BSA 314a with equal intensity). Additionally, analyzer 214 includes a polarizer 324 rotated at 45 degrees after the second BSA 314b.

[0110] In this configuration, analyzer 214 generates output using illumination lens 206 (e.g., Figure 4 The F2) is focused on a common point on sample 108 and then diverges into four shear beams 318 after interaction with the sample, wherein the beams are straightened by collecting lens 208 and guided to BSA 314b. It should be noted that, although... Figure 4 The shear beam 318 is depicted as propagating through sample 108, but this is merely illustrative. The shear beam 318 can be reflected by sample 108, as... Figure 2 As shown in the image.

[0111] Next, analyzer 214 can shear each of the shear beams 318 into four additional beams, resulting in sixteen shear beams 402. To avoid overlap of the shear beams 402, the thickness of the BSP 302 in analyzer 214 can be different from that in generator 212 (e.g., thicker). Figure 4 The configuration is depicted in which the BSP 302 in analyzer 214 comprises a thickness twice that of the BSP 302 in generator 212 (e.g., comprising a birefringent plate that is twice as thick). In this configuration, sixteen shear beams 402 form a uniform grid emanating from analyzer 214.

[0112] Next, the collection lens 208 (e.g., Figure 4 The shear beam 402 (F4) can be refocused onto the detector 112. As previously described herein, the imaging subsystem 110 can image the sample 108 onto the detector 112 using various shear beams 402, wherein the image produced by the detector 112 corresponds to an interferogram associated with the combination of shear beams 402. Furthermore, the collection lens 208 in the imaging subsystem 110 can form a spatial frequency plane located at a focal length away from the two collection lenses 208. For example, the collection lenses 208 can form a 4-F imaging system, wherein the sample 108 is located at a focal length away from the first collection lens 208 (F1), the detector 112 is located at a focal length away from the second collection lens 208 (F2), and the spatial frequency plane is located between the two collection lenses 208 and a focal length away from each other. In this configuration, each of the shear beams 402 is located at a different position in the spatial frequency plane and can therefore correspond to a spatial frequency channel in the image of the sample 108 produced by the detector 112.

[0113] In this configuration, the input Stokes vector associated with the frequency comb 104 before generator 212 can be written as

[0114] (3)

[0115] in This is the total incident power. Next, the output Stokes vector of the light distribution at detector 112 after analyzer 214 can be written as:

[0116] (4)

[0117] BSP1 and BSP2 are birefringent plates in the first BSP 302a, BSP3 and BSP4 are birefringent plates in the second BSP 302b, P1 is the first polarizer 322, P2 is the second polarizer 324, and MM(x,y) represents the Mueller matrix data (e.g., transfer matrix data) associated with sample 108.

[0118] This document takes into careful consideration that the various shear beams 402 have different polarization states and each can provide information associated with one or more Mueller matrix elements related to sample 108. For example, each of the various shear beams 402 can resemble a polarization configuration that can be produced by a conventional single-beam elliptic polarimeter. However, the systems and methods disclosed herein provide such configurations simultaneously rather than sequentially.

[0119] This paper further carefully considers that the Mueller matrix elements associated with sample 108 can be encoded into various spatial frequency channels within the image of sample 108 generated using metric system 100. For example, by Figure 4 The image generated by detector 112 may contain 33 channels in the spatial frequency domain (e.g., the Fourier domain), where each channel corresponds to the sum of certain Mueller matrix elements. Spatial frequency filtering can then be used to recover the Mueller matrix element data in any particular channel to isolate the spatial frequencies within the image associated with the location of a specific entity in the channel in the spatial frequency plane. For example, processor 118 of controller 116 may perform a spatial Fourier transform of the image from detector 112, isolating the spatial frequencies associated with a specific entity in the channel, and perform a second spatial Fourier transform of the resulting signal to produce a channel image. In this way, the spatially filtered channel image can provide spatially resolved elliptic polarization measurements for a specific polarization configuration, which in turn provides spatially resolved data (e.g., transfer matrix data) associated with the associated Mueller matrix data.

[0120] Figure 5 A simplified diagram illustrating various channels in the spatial frequency plane of an image according to one or more embodiments of the present disclosure. Table 1 depicts the Mueller matrix data in each of the channels according to one or more embodiments of the present disclosure.

[0121]

[0122] Table 2 depicts various Mueller matrix elements (mm) based on one or more channel images. ij The restoration of ).

[0123] From the calibrated Fourier domain channel c n Recovering Mueller matrix element m ij

[0124]

[0125] In Table 2, I sn and I rn CH corresponding to the sample and reference n And S rnThe sum of the Mueller matrix elements corresponding to the nth channel of the reference light.

[0126] Will Figure 5 Together with Tables 1 and 2, spatially resolved measurements of any particular Mueller matrix element associated with sample 108 can be generated by using detector 112 to capture an image of sample 108, generating one or more channel images based on spatial frequency filtering of the image from detector 112, and recovering the values ​​of a particular Mueller matrix element based on a combination of channel images. (e.g., as depicted in Table 2).

[0127] For reference Figure 6 The above steps can be repeated for a series of images (e.g., a time series of images generated at different times) to produce spectrally resolved Mueller matrix data. Figure 6 This describes different sampling states using the dual-frequency comb 104 according to one or more embodiments of the present disclosure. In some embodiments, the frequency comb 104 is a fixed offset frequency comb (FOFC), which depends on the repetition rate of the relative combs and their difference. Control to be in -1 / (2f r ) to +1 / (2f r The relative pulse delay (T) RPD ) Above △T RPD Continuous, uniformly spaced incremental sampling, where f r The frequency of the reference frequency comb 104 is (e.g., illustrated in illustration 602). The resulting heterodyne RF signal is broadband and can be mapped to a frequency domain spectral response. In this configuration, there are trade-offs between measurement speed, sensitivity, resolution, and the like. In some embodiments, the frequency comb 104 is a time-programmable frequency comb (TPFC). The TPFC method transcends optics by replacing the reference FOFC with a relative comb pulse delay (T0). RPD Digital dynamic control. In this configuration, which has the ability to control the relative pulse timing, we can program arbitrary sampling patterns in the region of interest (e.g., apodized acquisition as illustrated in Figure 604), scaled sample reduction (e.g., compressed acquisition as illustrated in Figure 606), or fixed time offset (e.g., cyclic acquisition as illustrated in Figure 608).

[0128] Figure 7 This describes a series of steps for generating spatially and spectrally resolved Mueller matrix data according to one or more embodiments of the present disclosure.

[0129] In some embodiments, method 700 includes step 702 of generating one or more channel images based on spatial frequency filtering techniques applied to the images of sample 108. In some embodiments, method 700 includes step 704 of generating one or more Mueller matrix element datasets (e.g., transfer matrix element datasets) based on the one or more channel images, wherein the Mueller matrix dataset (e.g., transfer matrix dataset) contains one or more Mueller array element datasets.

[0130] For example, Figure 7 Depicting the spatial Fourier transform of the image 706 (e.g., an interferogram image) generated by detector 112, using bandpass filter operation (708) to isolate data in one or more spatial frequency channels, and performing additional spatial Fourier transform (710) to produce channel images ( Figure 7 (Not explicitly shown in the text). As mentioned above, compared to... Figure 5 As described in Tables 1 and 2, spectrally resolved Mueller matrix element data (e.g., Mueller matrix element images) can be generated based on a combination of one or more channel images. This process can be repeated to generate spatially resolved Mueller matrix data with any number of Mueller matrix elements. This process can be further repeated on image sequences from detector 112 to generate Mueller matrix element image sequences.

[0131] In some embodiments, method 700 includes step 712 of extracting spectrally resolved Mueller matrix element data for at least some pixels in an image sequence using spectral frequency analysis techniques. For example, Figure 7 A time-frequency analysis (e.g., time-Fourier transform) is performed on the temporal data associated with common pixels in the image sequence (714) to generate amplitude and phase spectral data (716). Specifically, the RF beat frequency voltage signal at the frequency comb repetition rate f r The time-fourth transform of the image yields the amplitude and phase spectra at each pixel, providing spectral-resolved data. When combined with an image of Mueller matrix elements, it produces a complete set of spectral and spatially resolved Mueller matrix data 718.

[0132] Next, the Mueller matrix data 718 can be used to generate one or more measurements 720 of sample 108 (e.g., in...). Figure 1B (In step 128 of method 122 described herein). For example... Figure 7 Depicts mappings (e.g., real-time measurement mappings) associated with spatially resolved measurements (e.g., superposition, CD, or the like) generated based on Mueller matrix data 718.

[0133] For reference Figures 8 to 16 , Figures 8 to 16 Non-limiting variations of the measurement system 100 according to one or more embodiments of the present disclosure are described.

[0134] Figure 8 A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure is provided. (Except for...) Figure 8 Further including a spectral shifter 802 to shift and / or broaden the spectrum of at least one of the bandwidth combs 104, Figure 8 Generally similar to Figure 2 So that the above Figure 2 The description can be extended to Figure 8 As an illustration, one or both of the frequency combs 104 generated by the frequency comb source 102 may have wavelengths in the visible or near-infrared range, wherein the spectral shifter 802 can shift the spectrum of at least one of the frequency combs 104 to a higher wavelength (e.g., 2 to 12 μm) and / or a lower wavelength (e.g., wavelengths in the visible or ultraviolet spectral range). In this way, the spectral range of the Mueller matrix data can be extended.

[0135] The spectral shifter 802 may include any type of element suitable for shifting and / or broadening the spectrum of at least one of the frequency combs 104. For example, the spectral shifter 802 may include (but is not limited to) a nonlinear crystal, a photonic crystal fiber, or the like.

[0136] In some embodiments, electro-optic sampling (EOS) can be used to shift the detection wavelength relative to the wavelength of the frequency comb 104. For example, detectors suitable for mid-infrared wavelengths may have various disadvantages compared to detectors suitable for mid-infrared, near-infrared, or visible wavelengths, such as (but not limited to) relatively slow readout times, high noise, low resolution, high cost, or the requirement for cryogenic cooling. Therefore, EOS sampling (e.g., using EOS detector 112) allows for measurements within the desired wavelength range.

[0137] Figures 9A to 12 Describe the Mueller matrix data (e.g., transfer matrix data) generated based on spectral frequency coding. Figure 9A A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure.

[0138] In some embodiments, the code-writing optics 114 includes a series of spectrally dependent phase retarders. For example, Figure 9A The configuration is described, wherein the coding optics 114 includes a generator 902 in the illumination subsystem 106 and an analyzer 904 in the imaging subsystem 110, wherein the generator 902 and the analyzer 904 include spectral dependent phase retarders with different thicknesses and therefore different delay values.

[0139] Figure 9B Description of one or more embodiments according to this disclosure Figure 9AThe optical chain of the measurement system 100. In this non-limiting configuration, the generator 902 includes a first polarizer 906 at 0-degree orientation, followed by a phase delay at 45-degree rotation. The first delayer 908 (e.g., thickness d) and the same phase delay in 0-degree orientation. The second delayer 910. Next, the analyzer 904 includes a phase delay of 5 times at 0-degree orientation. A third retarder 912 (e.g., 5d thick) has the same phase delay of 5d when oriented at 45 degrees. The fourth retarder 914 and the second polarizer 916 oriented at 90 degrees. In this case, the combination of (1,1,5,5) cascaded phase retarders results in 13 channels of spectral frequency modulation. It has been carefully considered that any number of channels can be determined by the choice of retarder thickness. For example, if each retarder has a different delay, then the maximum number of independently modulated channels is 49. Furthermore, the higher the number of channels, the lower the spectral resolution. It has been further carefully considered that choosing third and fourth retarders 912 and 914 with a thickness five times that of the first and second retarders 908 and 910 can advantageously prevent harmonic overlap. However, any retarder thickness and any number of channels are within the spirit and scope of this disclosure.

[0140] In this configuration, the output Stokes vector can be written as:

[0141] (5)

[0142] in, .

[0143] According to one or more embodiments of this disclosure, Table 3 lists the recovery of Mueller matrix elements based on different modulation channels for this configuration.

[0144] Table 3

[0145]

[0146] Figure 10 This describes a series of steps, according to one or more embodiments of the present disclosure, for generating spatially and spectrally resolved Mueller matrix data based on spectral coding. Figure 10 In this image, the image generated by detector 112 corresponds to the real image 1002 of sample 108 (e.g., as shown in the image). Figure 4(Compared to the interferogram based on the interference of shear beam 402 depicted in the image). Additionally, temporal data associated with each pixel is extracted (1004), and time-frequency analysis (1006) (e.g., time Fourier transform) is performed on the temporal data associated with common pixels in the image sequence to generate amplitude and phase spectral data (1008). Furthermore, various polarization channels (1010) can be analyzed to generate Mueller matrix data 718 (e.g., transfer matrix data) for each pixel. Then, as depicted in step 128 of method 122, the Mueller matrix data 718 can be used as the basis for generating measurement data (e.g., measurement data, test data, or the like).

[0147] Figure 11 This illustration shows a measurement system 100 according to one or more embodiments of the present disclosure. Except that detector 112 is a single-pixel sensor (e.g., a photodetector), Figure 11 Generally similar to Figure 9A This configuration is suitable for measurements of a single point on sample 108 (e.g., Mueller matrix data 718 is not spatially resolved).

[0148] Figure 12 A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure. Figure 12 Generally similar to Figure 11 The addition of a spectral shifter 802 allows it to function similarly to... Figure 8 The configuration described herein modifies the spectral content of at least one of the frequency combs 104. In this way, it is possible to... Figure 8 The description is extended Figure 12 For example, EOS detection can be performed in... Figure 12 The use of China makes Figure 12 The detector 112 can be selected to operate in a desired wavelength range that is different from the wavelength range provided by the frequency comb 104.

[0149] Figures 13A to 16 This describes the Mueller matrix data generated based on time-polarized optical coding. Figure 13A A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure.

[0150] In some embodiments, the coding optics 114 includes one or more rotating elements in the illumination subsystem 106 and the imaging subsystem 110 to provide time coding of Mueller matrix data (e.g., transfer matrix data). For example, the coding optics 114 may include a rotating quarter-wave plate and / or a polarizer.

[0151] As an explanation, Figure 13B Description of one or more embodiments according to this disclosure Figure 13A The optical chain of the measurement system 100 depicted in the figure. Figure 13B In a specific configuration, the generator 1302 in the illumination subsystem 106 includes a first polarizer 1304 and a first rotating quarter-wave plate 1306 having a thickness d, which can operate at a first angular frequency. Rotation. Next, the analyzer 1308 in the imaging subsystem 110 may include a second rotating quarter-wave plate 1310 and a second polarizer 1312. This second rotating quarter-wave plate may have the same thickness d, but may rotate at a different angular frequency (e.g., 5ω) than the first rotating quarter-wave plate 1306. In this configuration, the output Stokes vector can be written as:

[0152] (6)

[0153] Furthermore, this configuration allows Mueller matrix elements to be encoded in 25 channels of the Fourier dilation coefficients associated with the intensity signal measured by detector 112. Table 4 describes the recovery of the Mueller matrix elements encoded in the Fourier dilation coefficients of the intensity signal measured by detector 112. Similarly, this paper carefully considers any combination of angular frequencies that can be utilized, and different choices of angular frequencies can provide different numbers of channels. However, some configurations can advantageously prevent harmonic overlap and / or provide relatively more efficient coding.

[0154] Table 4

[0155]

[0156] However, it should be understood that Figure 13B The description of the rotating quarter-wave plate is for illustrative purposes only and should not be construed as limiting the scope of this disclosure. Rather, the coding optics 114 may comprise any type or combination of rotating elements suitable for coding the transfer matrix data into an image generated by the detector 112.

[0157] Figure 14 This describes a series of steps, according to one or more embodiments of the present disclosure, for generating spatially and spectrally resolved Mueller matrix data based on time-polarized coding. Figure 14 In the image generated by detector 112, similar to Figure 10 The manner corresponds to the real image 1402 of sample 108. Additionally, temporal data associated with each pixel is extracted (1404), and time-frequency analysis (e.g., time Fourier transform) is performed on the temporal data associated with common pixels in the image sequence to generate amplitude and phase spectral data (1406). Furthermore, time multiplexing (1408) can be applied to generate Mueller matrix data 718 (e.g., transfer matrix data) for each pixel. Then, as described in step 128 of method 122, the Mueller matrix data 718 can be used as the basis for generating measurement data (e.g., measurement data, test data, or the like).

[0158] Figure 15 This illustration shows a measurement system 100 according to one or more embodiments of the present disclosure. Except that detector 112 is a single-pixel sensor (e.g., a photodetector), Figure 15 Generally similar to Figure 13A This configuration is suitable for measurements of a single point on sample 108 (e.g., Mueller matrix data 718 is not spatially resolved).

[0159] Figure 16 A schematic diagram illustrating a measurement system 100 according to one or more embodiments of the present disclosure. Figure 16 Generally similar to Figure 15 The addition of a spectral shifter 802 allows it to function similarly to... Figure 8 The configuration described herein modifies the spectral content of at least one of the frequency combs 104. In this way, it is possible to... Figure 8 The description is extended Figure 16 For example, EOS detection can be performed in... Figure 16 The use of China makes Figure 16 The detector 112 can be selected to operate in a desired wavelength range different from the wavelength range provided by the frequency comb 104.

[0160] Normal reference Figures 2 to 16 It should be understood that this information is provided for illustrative purposes only. Figures 2 to 16 And should not be construed as limiting the scope of this disclosure. For example, Figure 2 , 9A And 13A describes the configuration of the measurement system 100, wherein one or more frequency combs 104 are provided at an angle of incidence on the sample 108 in a manner similar to a conventional elliptical polarization system. However, this is not required. Figures 17 to 19 This paper describes the variation of a measurement system 100 that provides both illumination and imaging at a normal incident angle. It is carefully considered that imaging at a normal incident angle is easier to implement and, in some cases, provides fewer aberrations than imaging at an oblique angle. Figure 17 Description of one or more embodiments according to this disclosure Figure 2 A schematic diagram of the changes in the measurement system 100 depicted in the figure. Figure 18 Description of one or more embodiments according to this disclosure Figure 9A A schematic diagram of the changes in the measurement system 100 depicted in the figure. Figure 19 Description of one or more embodiments according to this disclosure Figure 13A A schematic diagram illustrating the changes in the measurement system 100 depicted in the diagram. Figures 17 to 19In this configuration, a first collecting lens 208 (e.g., F3) may be provided as an objective lens. Furthermore, the measurement system 100 in these embodiments may include a beam splitter 1702 such that one or more frequency combs 104 incident on the sample 108 may also be guided through the objective lens. In this configuration, the objective lens may also be part of an illumination subsystem 106.

[0161] In addition, Figures 17 to 19 In this configuration, detector 112 can be a multi-pixel detector or a single-pixel detector. In this manner, Figures 17 to 19 Suitable for use Figures 2 to 16 Any party to the technology described herein provides Mueller matrix data 718.

[0162] The objects described herein sometimes refer to different components contained within or connected to other components. It should be understood that such depicted architectures are merely illustrative, and many other architectures can in fact be implemented to achieve the same functionality. Conceptually, any arrangement of components that achieve the same functionality is effectively “associated” to achieve the desired functionality. Therefore, any two components combined herein to achieve a particular functionality can be considered “associated” with each other to achieve the desired functionality, regardless of the architecture or intermediate components. Similarly, any two such associated components can also be considered “connected” or “coupled” to each other to achieve the desired functionality, and any two components that can be suchly associated can also be considered “coupled” to each other to achieve the desired functionality. Specific examples of “coupleable” include (but are not limited to) physically interactive and / or physically interactive components and / or wirelessly interactive and / or logically interactive components.

[0163] It is believed that this disclosure and its many accompanying advantages will be understood from the foregoing description, and it should be understood that various changes can be made to the form, construction, and arrangement of the components without departing from this disclosure or sacrificing all its material advantages. The forms described are for illustrative purposes only, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A measurement system comprising: The first frequency comb source is configured to generate the first frequency comb; A second frequency comb source is configured to generate a second frequency comb with a different repetition rate than the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources. An illumination subsystem comprising one or more illumination lenses to direct an illumination beam containing at least one of the first frequency comb or the second frequency comb toward a sample; An imaging subsystem comprising one or more imaging lenses and a detector configured to generate an image sequence of the sample based on the first frequency comb and the second frequency comb; One or more coding optical elements, comprising at least one of one or more optical retarders or one or more polarizers, wherein at least one of the one or more coding optical elements is located in the illumination subsystem, wherein at least one of the one or more coding optical elements is located in the imaging subsystem, wherein the one or more coding optical elements encode data associated with one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial domain, spectral domain, or temporal domain of the image sequence; and A controller comprising one or more processors configured to execute program instructions that cause the one or more processors to: A transfer matrix dataset is generated based on at least one of spatial, spectral, or temporal analyses of the image sequence, comprising measurements of at least one of the one or more transfer matrix elements associated with the sample, wherein the transfer matrix dataset is at least one of spatial, spectral, or temporal resolution. and One or more measurements of the sample are generated based on the transition matrix dataset.

2. The measurement system of claim 1, wherein generating the transfer matrix dataset containing at least one of the measurements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence comprises: Decoding at least one of the one or more transition matrix elements from the image sequence based on at least one of spatial, spectral, or frequency analyses of the image sequence.

3. The measurement system according to claim 1, wherein the one or more transfer matrix elements comprise: Muller matrix elements.

4. The measurement system according to claim 1, wherein the one or more transfer matrix elements comprise: Jones matrix elements.

5. The measurement system according to claim 1, wherein the illumination subsystem further comprises: A beam combiner configured to combine the first frequency comb and the second frequency comb into a single illumination beam, wherein the one or more imaging lenses of the illumination subsystem guide the single illumination beam to the sample.

6. The measurement system of claim 1, wherein the image sequence corresponds to a multi-pixel image of the sample, wherein the transfer matrix dataset includes the measurement of at least one of the one or more transfer matrix elements as a function of wavelength and spatial location on the sample.

7. The measurement system of claim 1, wherein the image sequence corresponds to a single-pixel image of the sample, wherein the transfer matrix dataset contains the measurement of at least one of the one or more transfer matrix elements as a function of the wavelength at a single spatial location on the sample.

8. The measurement system according to claim 1, wherein the one or more coding optical elements comprise: The generator in the illumination subsystem includes one or more beam shears to generate two or more sheared beams with different polarization states, wherein the one or more illumination lenses of the illumination subsystem guide the two or more sheared beams to a common point on the sample. and The analyzer in the imaging subsystem includes one or more additional beam shears to cut the two or more sheared beams into additional sheared beams with different polarization states, wherein the one or more imaging lenses of the imaging subsystem interfere with the additional sheared beams on the detector.

9. The measurement system of claim 8, wherein generating the transfer matrix dataset containing at least one of the one or more transfer matrix elements associated with the sample based on at least one of spectral or spatial frequency analysis of the image sequence comprises: One or more channel images are generated for specific images in the image sequence based on spatial frequency filtering technology; and One or more transfer matrix element datasets are generated based on the one or more channel images, wherein the transfer matrix datasets contain the one or more transfer matrix element datasets.

10. The measurement system of claim 9, wherein the image sequence comprises multi-pixel images, and wherein the one or more transfer matrix element datasets comprises a sequence of spatially resolved transfer matrix element images; The transfer matrix dataset, which generates the measurement containing at least one of the one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence, further includes: The time-frequency analysis technique is used to extract spectrally resolved transfer matrix element data for at least some pixels in the image sequence, wherein the transfer matrix dataset contains the spectrally resolved transfer matrix element data.

11. The measurement system of claim 1, wherein the one or more coding optical elements comprise: A series of cascaded spectral dependent phase delayers for encoding the data associated with the one or more transfer matrix elements into the spectral domain of a series of images.

12. The measurement system of claim 11, wherein the measurement of at least one of the one or more transition matrix elements at each location on the sample is decoded by spectral analysis of the image sequence.

13. The measurement system of claim 1, wherein the one or more coding optical elements comprise: One or more rotating optical elements in at least one of the illumination subsystem or the imaging subsystem.

14. The measurement system of claim 13, wherein the one or more rotating optical elements comprise: The first rotating quarter-wave plate in the illumination subsystem; and The second rotating quarter-wave plate in the imaging subsystem, wherein the first rotating quarter-wave plate and the second rotating quarter-wave plate rotate at different speeds, wherein the data associated with the one or more transfer matrix elements is encoded into the time domain of the image sequence.

15. The measurement system of claim 13, wherein the measurement of at least one of the one or more transition matrix elements at each location on the sample is decoded by time-frequency analysis of the image sequence.

16. The measurement system of claim 1, wherein the imaging subsystem provides the image sequence via electro-optic sampling.

17. The measurement system of claim 1, wherein the one or more measurements include: One or more measurements.

18. The measurement system of claim 1, wherein the one or more measurements include: One or more inspection measurements.

19. A measurement system comprising: A controller comprising one or more processors configured to execute program instructions that cause the one or more processors to: A transfer matrix dataset is generated based on at least one of spatial, spectral, or temporal analysis of an image sequence, comprising measurements containing one or more transfer matrix elements associated with a sample, wherein the transfer matrix dataset is at least one of spatial resolution or spectral resolution, and wherein the image sequence is generated by a measurement subsystem comprising: The first frequency comb source is configured to generate the first frequency comb; A second frequency comb source is configured to generate a second frequency comb with a different repetition rate than the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources. An illumination subsystem comprising one or more illumination lenses to direct an illumination beam containing at least one of the first frequency comb or the second frequency comb toward the sample; An imaging subsystem comprising one or more imaging lenses and a detector configured to generate the image sequence of the sample based on the first frequency comb and the second frequency comb; and One or more coding optical elements, each comprising one or more optical retarders, wherein the one or more coding optical elements encode data associated with the one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial, spectral, or temporal domains of the image sequence; and One or more measurements of the sample are generated based on the transition matrix dataset.

20. The measurement system of claim 19, wherein generating the transfer matrix dataset containing the one or more transfer matrix elements associated with the sample based on at least one of spatial, spectral, or temporal analysis of the image sequence comprises: The one or more transition matrix elements are decoded from the image sequence based on at least one of spatial, spectral, or frequency analysis of the image sequence.

21. The measurement system of claim 19, wherein the one or more transfer matrix elements comprise: Muller matrix elements.

22. The measurement system of claim 19, wherein the one or more transfer matrix elements comprise: Jones matrix elements.

23. The measurement system of claim 19, wherein the illumination subsystem further comprises: A beam combiner configured to combine the first frequency comb and the second frequency comb into a single illumination beam, wherein the one or more imaging lenses of the illumination subsystem guide the single illumination beam to the sample.

24. The measurement system of claim 19, wherein the image sequence corresponds to a multi-pixel image of the sample, wherein the transfer matrix dataset contains the measurements of the one or more transfer matrix elements as a function of wavelength and spatial location on the sample.

25. The measurement system of claim 19, wherein the image sequence corresponds to a single-pixel image of the sample, wherein the transfer matrix dataset contains the measurements of the one or more transfer matrix elements as a function of the wavelength at a single spatial location on the sample.

26. The measurement system of claim 19, wherein the one or more coding optical elements comprise: The generator in the illumination subsystem includes one or more beam shears to generate two or more sheared beams with different polarization states, wherein the one or more illumination lenses of the illumination subsystem guide the two or more sheared beams to a common point on the sample. and The analyzer in the imaging subsystem includes one or more additional beam shears to cut the two or more sheared beams into additional sheared beams with different polarization states, wherein the one or more imaging lenses of the imaging subsystem interfere with the additional sheared beams on the detector.

27. The measurement system of claim 26, wherein generating the transfer matrix dataset containing the one or more transfer matrix elements associated with the sample based on at least one of spectral or spatial frequency analysis of the image sequence comprises: One or more channel images are generated for specific images in the image sequence based on spatial frequency filtering technology; and One or more transfer matrix element datasets are generated based on the one or more channel images, wherein the transfer matrix datasets contain the one or more transfer matrix element datasets.

28. The measurement system of claim 27, wherein the image sequence comprises multi-pixel images, and wherein the one or more transfer matrix element datasets comprises a sequence of spatially resolved transfer matrix element images; The transfer matrix dataset, which generates the measurements containing the one or more transfer matrix elements associated with the samples based on at least one of spatial, spectral, or temporal analysis of the image sequence, further includes: The time-frequency analysis technique is used to extract spectrally resolved transfer matrix element data for at least some pixels in the image sequence, wherein the transfer matrix dataset contains the spectrally resolved transfer matrix element data.

29. The measurement system of claim 19, wherein the one or more coding optical elements comprise: A series of cascaded spectral dependent phase delayers for encoding the data associated with the one or more transfer matrix elements into the spectral domain of a series of images.

30. The measurement system of claim 29, wherein the one or more transition matrix elements at each location on the sample are decoded by spectral analysis of the image sequence.

31. The measurement system of claim 19, wherein the one or more coding optical elements comprise: One or more rotating optical elements in at least one of the illumination subsystem or the imaging subsystem.

32. The measurement system of claim 31, wherein the one or more rotating optical elements comprise: The first rotating quarter-wave plate in the illumination subsystem; and The second rotating quarter-wave plate in the imaging subsystem, wherein the first rotating quarter-wave plate and the second rotating quarter-wave plate rotate at different speeds, wherein the data associated with the one or more transfer matrix elements is encoded into the time domain of the image sequence.

33. The measurement system of claim 31, wherein the one or more transition matrix elements at each location on the sample are decoded by time-frequency analysis of the image sequence.

34. The measurement system of claim 19, wherein the imaging subsystem provides the image sequence via electro-optic sampling.

35. The measurement system of claim 19, wherein the one or more measurements include: One or more measurements.

36. The measurement system of claim 19, wherein the one or more measurements include: One or more inspection measurements.

37. A measurement method comprising: A transfer matrix dataset is generated based on at least one of spatial, spectral, or temporal analysis of an image sequence of a sample, comprising measurements containing one or more transfer matrix elements associated with the sample, wherein the transfer matrix dataset is at least one of spatial, spectral, or temporal resolution, and wherein the image sequence is generated by a measurement subsystem comprising: The first frequency comb source is configured to generate the first frequency comb; A second frequency comb source is configured to generate a second frequency comb with a different repetition rate than the first frequency comb, wherein the second frequency comb source is frequency-locked or phase-locked to at least one of the first frequency comb sources. An illumination subsystem comprising one or more illumination lenses to direct an illumination beam containing at least one of the first frequency comb or the second frequency comb toward the sample; An imaging subsystem comprising one or more imaging lenses and a detector configured to generate the image sequence of the sample based on the first frequency comb and the second frequency comb; and One or more coding optical elements, each comprising one or more optical retarders, wherein the one or more coding optical elements encode data associated with the one or more transfer matrix elements into the image sequence of the sample, wherein the data associated with the one or more transfer matrix elements is encoded into at least one of the spatial, spectral, or temporal domains of the image sequence; and One or more measurements of the sample are generated based on the transition matrix dataset.

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