Metrology system based on polarization imaging

Abstract

Methods, devices and systems for characterizing polarization components are described. One example method includes illuminating an area of the polarization component with a uniform light beam in a particular polarization state, and receiving, at a pixelated detector, reflected or transmitted light from the polarization component in response to illuminating the area of the polarization component. Each group of pixels of the pixelated detector receives light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image. The method also includes obtaining Stokes parameters of the polarization component based on the received light at the pixelated detector, and determining one or more characteristics of the polarization component for each of the plurality of the spatial regions using the Stokes parameters.

Description

PCT Patent Application 044974.8109.WO00 (UA24-062)   METROLOGY SYSTEM BASED ON POLARIZATION IMAGING CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims priority to the provisional application with serial number 63 / 588,915 titled “METROLOGY SYSTEM FOR WAVEGUIDE DISPLAY, HOLOGRAM AND GRATING USING POLARIZATION IMAGING,” filed October 9, 2023. The entire contents of the above noted provisional application are incorporated by reference as part of the disclosure of this document. TECHNICAL FIELD

[0002] The technology described in this patent document relates to methods, devices and metrology systems to characterize polarization components. BACKGROUND

[0003] Polarization optical components, such as polarization volume holograms (PVHs), surface relief gratings (SRGs), and volume Bragg gratings (VBGs), can be utilized as, for example, waveguides, optical filters, lenses, reflectors, refractors, beam splitters, beam combiners, beam couplers, and compensators for various application such as in a display used in augmented reality (AR), virtual reality (VR) and mixed reality (MR) systems. The fabrication and manufacturing of these polarization optical components are often difficult because of the high uniformity and exact optical requirements necessary for an efficient, high resolution and high contrast AR / VR / MR display. Deviations in thickness, grating angle, grating pitch, uniformity and spatial distribution of the optical components can lead to a large reduction of display quality.

[0004] The existing techniques for measuring the optical characteristics of such polarization components are complex, time consuming and may not be feasible for measuring a large number of components. SUMMARY

[0005] The disclosed embodiments, among other features and benefits, relate to methods, devices and metrology systems to characterize polarization components including, but not limited to, PVHs, SRGs, and VBGs.

[0006] One example method for determining one or more characteristics of a polarization  PCT Patent Application 044974.8109.WO00 (UA24-062)   component includes illuminating an area of the polarization component with a uniform light beam, wherein the uniform light beam is in a particular polarization state, and receiving, at a pixelated detector, reflected or transmitted light from the polarization component in response to illuminating the area of the polarization component; each group of pixels of the pixelated detector receives light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image. The method also includes obtaining Stokes parameters of the polarization component based on the received light at the pixelated detector, and determining one or more characteristics of the polarization component for each of the plurality of the spatial regions using the Stokes parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] FIG.1 illustrates an example waveguide display configuration.

[0008] FIG.2 illustrates an example polarization volume hologram (PVH) that can be used as a waveguide coupler in a waveguide display.

[0009] FIG.3 illustrates diffraction efficiency of an example PVH for circularly polarized light as a function of thickness of the PVH layer.

[0010] FIG.4 illustrates diffraction efficiency of an example PVH for circularly polarized light as a function of wavelength of incident light.

[0011] FIG.5A illustrates three metrology systems in accordance with example embodiments.

[0012] FIG. 5B illustrates a metrology system in accordance with another example embodiment.

[0013] FIG.5C illustrates a pixeled detector configuration that can be used to measure spatial distribution of Stokes parameters of a sample in accordance with an example embodiment.

[0014] FIG. 6 illustrates a set of operations that can be carried out to conduct a metrology measurement process for a sample in accordance with an example embodiment.

[0015] FIG.7 illustrates a set of operations that can be carried out to determine characteristics of a polarization component in accordance with an example embodiment. DETAILED DESCRIPTION

[0016] The existing techniques for measuring the optical characteristics of polarization components typically involves illuminating a section of the polarization component with incident  PCT Patent Application 044974.8109.WO00 (UA24-062)   light, making a measurement, and moving the light source (or the device under test) to measure other locations of the component. This process may need to be repeated at multiple angles of incidence, at multiple wavelengths, and multiple polarization states, which can make the process very complex, and time consuming. Furthermore, in scenarios where a large number of components need to be characterized, the traditional characterization process becomes infeasible.

[0017] The disclosed embodiments, among other features and benefits, measure these deviations in real time. In some embodiments, this is accomplished by imaging the polarization properties of the optical component using a polarization camera and different polarization illuminations. Methods and instruments described herein, among other applications, can be used to facilitate manufacturing process and qualify final product acceptance. In some applications, using the disclosed measurement and detection techniques, defects and non-uniformities in the polarization components can be detected before assembly of those components into finished products, thereby preventing sub-par and lower quality components from being implemented as part of devices. In other examples, quantitative parameters can be measured for process monitoring and development.

[0018] A waveguide display 100, such as that shown in FIG.1, has a small form factor and the ability to overlay transmitted images with digital images, making it suitable for applications in smartglasses and AR / VR / MR systems. Images generated from a microdisplay 101 pass through a lens 102, to a waveguide coupler 103, and into a planar waveguide 104. Light 105 propagates through the waveguide 104 to an output coupler 106 and subsequently to the user’s eye as illustrated by an eyeball 110. In this way, the image generated by the microdisplay 101 is projected onto the retina 111. One application of the disclosed embodiments is to characterize planar waveguide 104 including input coupler 103 and output coupler 106.

[0019] FIG.2 illustrates an example PVH 200 based on self-organized cholesteric liquid crystal (CLC) polymer 204 that can be used as a waveguide coupler in a waveguide display. The PVH layer has a thickness, t, and a tilt angle, ϕ. The orientation of the CLC molecule 204 is spatially varying and is determined by an alignment layer 202. Both the liquid crystal and alignment layers are usually fabricated on a transparent glass substrate 203. A unique and useful property of the CLC is that the individual liquid crystal molecules are self-organized in a periodic structure equal to the Bragg period, Λ^, resulting in a periodic modulation of the  PCT Patent Application 044974.8109.WO00 (UA24-062)   refractive index. The Bragg period can be tuned by adding different concentration of chiral dopant, and a thin film of CLC can act as a Bragg grating with large reflectivity at a predefined wavelength and angle of incidence. The pitches of the PVH in the x and y directions are related to the Bragg period as follows: ΛΛ ൌ ^ Λ^^^, Λ ^௫sin ^௬ ൌcos ^ ^^^.

[0020] The Braggis related to the angle of incidence, ^^, the ordinary refractive index, ^^^, and the extraordinary refractive index, ^^^as shown below: ^^^ൌ 2^^ ^^ଶ^ ^ 2 ^^ଶ^^ / 3Λ^cos ^ ^^^.

[0021] The ordinary andof wavelength can be measured using an ellipsometer. The PVH is highly anisotropic with its reflectance and transmittance being a function of angle of incidence, thickness, wavelength and polarization states. For example, as shown in FIGS.3 and 4, the diffraction efficiency of a PVH for circularly polarized light is a nonlinear function of thickness and wavelength. The optical characteristics of the PVH is determined by a small set of parameters: Λ^, ^^, ^^, ^^ and ^^^,^. In principle, accurate measurements of reflectance and transmittance at different wavelengths, angles and polarization states permit the accurate determination of these parameters.

[0022] The spatial variation of reflectance and transmission of a thin film device can be accurately measured using a calibrated polarization camera which provides the Stokes parameters of the reflected and transmitted light. The Stokes parameters are a set of 4 values that describes the polarization state of light. Examples of a polarization camera which can measure Stokes parameters at different wavelength are described in U.S. Patent Nos. 8,866,997 and 10,254,453, which are incorporated by reference.

[0023] FIGS.5A and 5B illustrate multiple metrology systems in accordance with example embodiments. The systems are designed to have high speed and throughput by rapidly measuring a few images or videos covering a large area. In system 510, the sample of interest comprises a glass wafer 513 with a thin film 514 on top. The glass wafer 513 may include multiple waveguide display devices and is generally spatially varying. An illumination source 511 is used  PCT Patent Application 044974.8109.WO00 (UA24-062)   to illuminate the sample at an angle of incidence, ^^, which can be adjusted depending on the sample. The source illuminates a large area (or all) of the sample to allow a large spatial extent (or all) of the sample to be characterized without moving the illumination source, the detector (e.g., polarization camera 517) or the sample. The source can be a laser, a light emitting diode (LED), a halogen lamp, a tunable light source and / or a combination thereof. The spectrum of the illumination can be broadband, narrowband, and / or can include multiple bands.

[0024] The light passes through an optical filter 512, which can include spectral and / or polarization filters, to illuminate a large area of the sample. The spectrum and polarization state of the light can be tuned, for example by moving, rotating, or otherwise changing the characteristics of the optical filter 512. Reflected light 515 passes through an optical filter 516, which can include spectral and / or polarization filters, to a polarization camera 517, which measures the spatial distribution of Stokes parameters of the sample.

[0025] For example, one implementation can include a pixelated detector 550 as shown in FIG. 5C. The pixelated detector 550 is divided into a plurality of spatial segments, each including a particular number of pixels. In the example configuration of FIG.5C, each segment includes four pixels. In some embodiments, the segment 551 includes pixels A, B, C and D that can be configured similarly or differently (e.g., via unique optical filters) to measure one particular characteristic, such as a particular wavelength (as shown in 552), or a particular Stokes parameter (as shown in 553). For example, the configuration in 553 has four different polarizer and retarder sections (or layers) to convert the received light into four different polarization states, described by Stokes parameters, which are then detected by the detectors. In some examples, the pixelated detector 550 can include a combination of different filters (e.g., spectral and polarization filters), while in other embodiments one or more external filters (as shown in Figure 5A) can be used to effectuate a part (or all) of the filtering.

[0026] Referring back to FIG.5A, the system 510 acquires a polarization image of the sample in a short time. The polarization images contain spatial information about the reflectance and polarization state at multiple wavelengths for different regions of the sample. In some embodiments, multiple images under different illuminations can be acquired. The resulting measurements are compared with reference values (e.g., the desired, optimum and / or ideal values) which can be obtained by performing a simulation (as described later). In this way,  PCT Patent Application 044974.8109.WO00 (UA24-062)   parameters such as Λ^, ^^, and ^^ can be estimated as a function of position (x,y) for the sample. The entire process is designed to be fast, since only a single or a few images are taken.

[0027] In system 520 of FIG.5A, the sample of interest is a glass wafer 523 with thin film 524 on top. The glass wafer 523 may include multiple waveguide display devices and is generally spatially varying. An illumination source 521 is used to illuminate the sample at an angle of incidence, ^^, which can be adjusted depending on the sample. The source can be a laser, a light emitting diode (LED), a halogen lamp, a tunable light source and / or a combination thereof. The spectrum of the illumination can be broadband, narrowband, and / or include multiple bands. The light passes through an optical filter 522, which can be spectral and polarization filters, to illuminate a large area of the sample. The spectrum and polarization state of the light can be tuned, for example by moving, rotating or otherwise altering the filtering characteristics of the optical filter 522. Transmitted light 525 passes through an optical filter 526, which can be a spectral and / or polarization filter, to a polarization camera 527, which measures the spatial distribution of Stokes parameters of the sample. The system 520 acquires a polarization image of the sample in a short time. The polarization images include spatial information about the transmittance and polarization state at multiple wavelengths for different regions of the sample. Multiple images under different illuminations can be acquired. The resulting measurements are compared with the reference (e.g., simulation) results, and parameters such as Λ^, ^^, and ^^ can be estimated as a function of position (x,y) for the sample. The entire process is designed to be fast, since only a single or a few images is taken.

[0028] In system 530 of FIG.5A, the sample of interest is a glass wafer 533 with thin film 534 on top. The glass wafer 533 may include multiple waveguide display devices and is generally spatially varying. The glass wafer 533 may also contain a set of alignment marks, so that images of the wafer taken by multiple cameras can be aligned relative to each other. An illumination source 531 is used to illuminate the sample at an angle of incidence, ^^, which can be adjusted depending on the sample. The source can be a laser, a light emitting diode (LED), a halogen lamp, a tunable light source and / or a combination thereof. The spectrum of the illumination can be broadband, narrowband, and / or include multiple bands. The light passes through an optical filter 532, which can include spectral and / or polarization filters, to illuminate a large area of the sample. The spectrum and polarization state of the light can be tuned, for  PCT Patent Application 044974.8109.WO00 (UA24-062)   example by moving rotating, or otherwise changing the characteristics of the optical filter 532. Reflected light 535 and transmitted light 538 pass through optical filters 536 and 539, respectively, which can be spectral and / or polarization filters, to polarization cameras 537A and 537B, respectively, which measure the spatial distribution of Stokes parameters of the sample. The system 530 acquires at least two polarization images of the sample in a short time. The polarization images include spatial information about the reflectance and transmittance, in addition to polarization state at multiple wavelengths for different regions of the sample. Multiple images under different illuminations can be acquired. The resulting measurements are compared with the reference (simulation) results, and parameters such as Λ^, ^^, and ^^ can be estimated as a function of position (x,y) for the sample. The entire process is designed to be fast, since only a few images is taken.

[0029] In system 540 of FIG.5B, the sample of interest is a glass wafer 543 with thin film 544A on top and thin film 544B on bottom. The glass wafer 543 may include multiple waveguide display devices and is generally spatially varying. The glass wafer 543 may also contain a set of alignment marks, so that images of the wafer taken by multiple cameras can be aligned relative to each other. Two illumination sources 541A and 541B are used to illuminate the top and bottom surfaces of the sample respectively. The angles of incidence, ^^^,ଶ, can be adjusted depending on the sample. The sources can be a laser, a light emitting diode (LED), a halogen lamp, a tunable light source and / or a combination thereof. The spectrum of the illumination can be broadband, narrowband, and / or include multiple bands. The light from the two sources passes through optical filter 542A and 542B, respectively, which can be spectral and / or polarization filters, to illuminate a large area of the sample. The spectrum and polarization state of the light can be tuned, for example by moving, rotating or otherwise altering the characteristics of the optical filters 542A and 542B. Reflected light 545A from source 541A and transmitted light 545B from source 541A pass through optical filters 546A and 546B, respectively, which can be spectral and / or polarization filters. The filtered light is received by polarization cameras 547A and 547B, which measure the spatial distribution of Stokes parameters of the sample. In addition, reflected light 548A from source 541B and transmitted light 548B from source 541B pass through optical filters 546A and 546B, respectively, which can be spectral and / or polarization filters, and then to polarization cameras 547A and 547B,  PCT Patent Application 044974.8109.WO00 (UA24-062)   which measure the spatial distribution of Stokes parameters of the sample.

[0030] The sources 541A and 541B can be turned on and off at different times, so that different set of images can be acquired under different illuminations for front and back surfaces of the sample 543. The system 540 acquires multiple polarization images of the sample in a short time. The polarization images include spatial information about the reflectance and transmittance, in addition to the polarization state at multiple wavelengths for different regions of the sample. More images under different illuminations can be acquired to, for example, improve the confidence or accuracy of the measurements. The resulting measurements are compared with the reference (simulation) results, and parameters such as Λ^, ^^ and ^^ can be estimated as a function of position (x,y) for the sample. The entire process is designed to be fast, since only a few images is taken.

[0031] The polarization state of the light source can be unpolarized, partially polarized, linearly polarized, circularly polarized and elliptically polarized. The polarization state can be chosen differently depending on the sample. For example, a sample with a CLC layer may tend to reflect a large portion of the circularly and elliptically polarized light. For such a sample, the polarization state can be chosen to be circularly or elliptically polarized when a reflective measurement configuration (e.g., system 510 of FIG.5A) is used. In this way, the measured signals have high signal to noise ratios. In another example, a sample with periodic diffraction grating may tend to reflect a linear s-polarized light and a linearly p-polarized light differently. For such a sample, the polarization state can be chosen to be linearly polarized.

[0032] As noted earlier, the disclosed embodiments can be implemented to measure and monitor the quality of polarization components are various stages of processing or product integration. For example, the measurements conducted in accordance with the disclosed embodiments can reveal whether each particular polarization component under test meets the requirements that were specified as part of the design process of the component and / or the larger system that incorporates that component. To facilitate this process, it may be needed to perform a one-time validation / calibration process to ensure the accuracy of the measurements. To this end, the optical properties of PVH, SRG and VBG can be precisely stimulated using, for example, rigorous coupled-wave analysis (RCWA) and / or finite-difference time-domain (FDTD) modeling. The reflectivity and transmission at different wavelengths, angles and polarization  PCT Patent Application 044974.8109.WO00 (UA24-062)   illumination can be calculated for different optical component designs. For example, a waveguide coupler can be made of a PVG using liquid crystal polymer on a glass substrate. The PVG has a predefined thickness, pitch and angle. The optical properties of the waveguide coupler, such as those shown in FIGS.3 and 4, can be calculated, compared and validated using measurements from commercially available (but expensive) polarimeters. Examples of commercial polarimeter which measure the Mueller matrix of the coupler are AxoScan and AxoStep measurement systems made by Axometrics Inc. (Huntsville, Alabama, USA). A Mueller matrix is a 4x4 matrix that describes the linear relationship between input and output polarization states of an optical components. Parameters such as reflectance and transmittance for different polarization states can be extracted from the Mueller matrix.

[0033] A flow diagram of the metrology measurement process is shown in FIG.6. The optical properties of a thin film device are calculated (601) and validated by measurement (602) using a standard. As described in more detail below, the operation at 601 may need to be adjusted based on the validation results obtained at 602. This process may be repeated until the measurements and calculations produce a suitable match within a predefined tolerance. Images of reflectance and transmittance are measured (603) using systems described in, for example, FIGS.5A and 5B. The image data can be compared with tabulated optical properties, and relevant parameters are extracted (604). Alternatively, the reflectance and transmittance can be calculated in real-time using a fast computer, compared and adjusted to fit with measurement data. The relevant parameters such as Λ^^ ^^, ^^^, ^^^ ^^, ^^^, and ^^^ ^^, ^^^ which give the best fit to the measurement data represent the properties of

[0034] To further facilitate the understanding of the described procedure, an example data acquisition and analysis of the metrology system 510 in FIG.5A is described in more detail. In one example implementation, the source 511 is a collimated broadband light source with three LEDs having illumination wavelengths of 470nm (blue), 530nm (green) and 625nm (red). The full-width half-maximum (FHWM) bandwidth of the LEDs is about 30nm. The optical filter 512 is an achromatic circular polarizer. The source 511 illuminates the sample uniformly with circularly polarized light over a circular region of diameter of about 2 inches (50.8mm) on the X- Y plane. The thin film 514 is a PVH similar to that shown in FIG.2. The camera 517 is a division-of-focal plane RGB linear Stokes camera with a Sony IMX264MYR CMOS color  PCT Patent Application 044974.8109.WO00 (UA24-062)   sensor and is sensitive to polarized light having the above-noted three wavelengths. The optical filter 516 is an achromatic quarter wave plate. The camera lens has a magnification of 6X and is focused on the thin film. The square pixel size of the Sony sensor is 3.45 microns. The camera measures a Stokes image of the thin film with spatial resolution of about 6×3.45μm=20.7 μm. The camera is calibrated at the three wavelengths and the reflected Stokes parameters can be calculated from the raw data of each image. The experimental reflected Stokes parameters, ^^^^X, ^^ ^^ ^^, are: ^^^^^0, ^^ ^^ ^^^^^, ^^, 470 ^^ ^^^, ^^^^2, ^^ ^^ ^^^^^, ^^, 470 ^^ ^^^, ^^^^3, ^^ ^^ ^^^^^, ^^, 470 ^^ ^^^^

[0035] TheStokes parameters are measured. The experimental reflected Stokes parameters can be used to calculate the pitch, Λ^, tilt angle, ^^, and thickness, ^^, of the sample.

[0036] First the theoretical reflected Stokes parameters are calculated using the nominal refractive indices ^^^^ ^^^ and ^^^^ ^^^ of the thin film materials: ^ ^^^ோ,௧^^^^௬^Λ^, ^^, ^^ ,470 ^^ ^^^, ^^ଶோ,௧^^^^௬^Λ^, ^^, ^^ ,470 ^^ ^^^, ^^ଷோ,௧^^^^௬^Λ^, ^^, ^^ ,470 ^^ ^^^൧  ^^^^ோ,௧^^^^௬^Λ^ , ^^, ^^ ,530 ^^ ^^^, ^^ଶோ,௧^^^^௬^Λ^ , ^^, ^^ ,530 ^^ ^^^, ^^ଷோ,௧^^^^௬^Λ^ , ^^, ^^ ,530 ^^ ^^^൧ ^ ^^^ோ,௧^^^^௬^Λ^, ^^, ^^ ,625 ^^ ^^^, ^^ଶோ,௧^^^^௬^Λ^, ^^, ^^ ,625 ^^ ^^^, ^^ଷோ,௧^^^^௬^Λ^, ^^, ^^ ,625 ^^ ^^^൧. one example of the operation 601 shown in the diagram 600 in FIG.6. The theoretical Stokes parameters are compared with the measurement results using a calibrated commercial polarimeter, and the values of refractive indices ^^^^ ^^^ and ^^^^ ^^^ can be adjusted in calculations so that the theoretical Stokes parameters match well with the measured values. Note that this process can be carried out once for a given setting (e.g., the entire batch of components produced via the same process, by the same facility, etc.).

[0038] Next, the experimental reflected Stokes parameters are compared with the theoretical  PCT Patent Application 044974.8109.WO00 (UA24-062)   reflected Stokes parameters. A merit function Δ^Λ^, ^^, ^^^ can be defined to quantify the deviation between experiment and theory. An example merit function is: Δ^Λ^, ^^, ^^^ ൌ ^ ห ^^^ோ,௧^^^^௬^ ^^^ െ ^^^ோ,^௫^^ ^^^ห

[0039] Thea standard nonlinear optimization method that minimizes the value of the merit function. The exact form of the metric function is not unique; for example, one can be adjusted by weighting different Stokes parameters to improve the accuracy. The final results are the parametersΛ^^^^, ^^^, ^^^^^, ^^^^^ ^^ ^^ ^^^ ^^, ^^^ of the sample. One example of another merit function is:Δ^Λ , ோ ோ ଶଶ^^^, ^^^ ൌ^^ ห ^^^,௧^^^^௬^ ^^^ െ ^^^,^௫^^ ^^^ห

[0040] As another examplelogy system 530 in FIG.5A is described in more detail using the below example scenario. The source 531 is a collimated broadband light source with one LED of wavelength 530nm (green). The FHWM bandwidth of the LED is about 30nm. The optical filter 532 is an achromatic circular polarizer. The source 531 illuminates the sample uniformly with circularly polarized light over a circular region of diameter of about 2 inches (50.8mm) on the X-Y plane. The thin film 534 is a PVH similar to that shown in FIG.2. The cameras 537A and 537B are division-of-focal plane monochrome linear Stokes camera with a Sony IMX264MZR CMOS monochrome sensor and is sensitive to broadband polarized light. The optical filters 536 and 539 are combination of an achromatic quarter wave plate and a bandpass filter for 530nm light. The camera lenses have a magnification of 6X and are focused on the thin film. The square pixel size of the Sony sensor is 3.45 microns. The camera 537A measures a reflected Stokes image of the thin film from the top. The camera 537B measures a transmitted Stokes image of the thin film from the bottom. The cameras are calibrated at 530nm, and the Stokes parameters can be calculated from the raw data of each image for each camera. The experimental reflected and transmitted Stokes parameters are:  PCT Patent Application 044974.8109.WO00 (UA24-062)   ^^^^^0, ^^ ^^ ^^^^^, ^^, 530 ^^ ^^^, ^^^^2, ^^ ^^ ^^^^^, ^^, 530 ^^ ^^^, ^^^^3, ^^ ^^ ^^^^^, ^^, 530 ^^ ^^^^

[0041] The Λ^, tilt angle, ^^,and thickness, ^^, of the sample.

[0042] First the theoretical reflected Stokes parameters are calculated using the nominal refractive indices ^^^^ ^^^ and ^^^^ ^^^ of the thin film materials: ^^^^^0, ^^ℎ ^^ ^^ ^^ ^^^Λ ^^, ^^, ^^ ,530 ^^ ^^^, ^^^^2, ^^ℎ ^^ ^^ ^^ ^^^Λ ^^, ^^, ^^ ,530 ^^ ^^^, ^^^^3, ^^ℎ ^^ ^^ ^^ ^^^Λ ^^, ^^, ^^ ,530 ^^ ^^^^^is the process 601 shown in the diagram 600 in FIG.6. The theoretical Stokes parameters are compared with the measurement values using a calibrated commercial polarimeter, and the values of refractive indices ^^^^ ^^^ and ^^^^^^^can be adjusted so that the theoretical Stokes parameters match well with the measured values.

[0044] Next, the experimental reflected Stokes parameters are compared with the theoretical reflected Stokes parameters. A merit function Δ^Λ^, ^^, ^^^ can be defined to quantify the deviation between experiment and theory. An example merit function is: Δ^Λ^, ^^, ^^^ ൌ ^ ห ^^^ோ,௧^^^^௬^ ^^^ െ ^^^ோ,^௫^^ ^^^ห ^ ห ^^^்,௧^^^^௬^ ^^^ െ ^^^்,^௫^^ ^^^ห

[0045] , nonlinear optimization method that minimizes the value of the merit function. The exact form of the metric function can be adjusted in some embodiments by weighting different Stokes parameters to improve the accuracy. The final results are the parametersΛ^^^^, ^^^, ^^^^^, ^^^^^ ^^ ^^ ^^^ ^^, ^^^ of the sample.

[0046] As yet another example, the data acquisition and analysis of the metrology system 540 in FIG.5B is described in more detail using the following example scenario. The sources 541A and 541B are collimated broadband light sources with four LEDs of wavelengths 470nm  PCT Patent Application 044974.8109.WO00 (UA24-062)   (blue), 530nm (green), 625nm (red) and 810nm (near infrared). The FHWM bandwidth of the LEDs is about 30nm. The optical filters 542A and 542B are achromatic circular polarizers. The sources 541A and 541B illuminate the sample uniformly with circularly polarized light over a circular region of diameter of about 2 inches (50.8mm) on the X-Y plane. The thin films 544A and 544B are PVHs similar to that shown in FIG.2. The cameras 547A and 547B are division- of-focal plane monochrome linear Stokes cameras with Sony IMX264MZR CMOS monochrome sensors and are sensitive to broadband polarized light. The optical filters 546A and 546B are achromatic quarter wave plates. The cameras 547A and 547B measure reflected and transmitted Stokes images of the top and bottom thin films. The cameras are calibrated at the source wavelengths, and the Stokes parameters can be calculated from the raw data of each image for each camera. The LEDs of the light sources 541A and 541B turn on individually at different times, and both cameras acquire images when each LED is turned on. For example, the 470nm LED of 541A is turned on and all other LEDs are turned off. Camera 547A acquires one image, and camera 547B acquires a second image. Next the 530nm LED of the light source 541A is turned on, and all other LEDs are turned off. Camera 547A acquires a third image, and camera 547B acquires a fourth image. The LEDs are individually turned on and off, and a total of 16 images are acquired. The experimental reflected and transmitted Stokes parameters for camera 547A are: ^ ^^^^0, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^, ^^^^2, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^, ^^^^3, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^^ ^ ^^^ ^^ ^^, ^^ 2, ^^ ^^ ^^, ^^ 3, ^^ ^^ ^^, ^^^  PCT Patent Application 044974.8109.WO00 (UA24-062)

[0047] The experimental reflected and transmitted Stokes parameters for camera 547B are: ^ ^^^^0, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^, ^^^^2, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^, ^^^^3, ^^ ^^ ^^, ^^^ ^^, ^^, 470 ^^ ^^^^ ^ ^ ^^^ ^ ^^

[0048] Λ^, tilt angle, ^^, and thickness, ^^, of the top and bottom thin films.

[0049] First the theoretical reflected Stokes parameters are calculated using the nominal refractive indices ^^^^ ^^^ and ^^^^ ^^^ of the thin film materials: ^ ^^^ோ,௧^^^^௬^Λ^^, ^^^, ^^^,Λ^ଶ, ^^ଶ, ^^ଶ, ^^^, ^^ଶோ,௧^^^^௬^Λ^^, ^^^, ^^^,Λ^ଶ, ^^ଶ, ^^ଶ, ^^^, ^^ଷோ,௧^^^^௬^Λ^^, ^^^, ^^^,Λ^ଶ, ^^ଶ, ^^ଶ, ^^^൧ ^^^angle of top and bottom films. ^^^and ^^ଶdenote the thicknesses of the top and bottom films. The calculation can take into account the finite bandwidth of the LEDs and is the process 601 shown in the diagram 600 in FIG.6. The theoretical Stokes parameters are compared with the measurement values using a calibrated commercial polarimeter, and the values of refractive indices ^^^^ ^^^ and ^^^^ ^^^ can be adjusted so that the theoretical Stokes parameters matches well with the measured values.

[0051] Next, the experimental reflected Stokes parameters are compared with the theoretical reflected Stokes parameters. A merit function Δ^Λ^^, ^^^, ^^^,Λ^ଶ, ^^ଶ, ^^ଶ^ can be defined to  PCT Patent Application 044974.8109.WO00 (UA24-062)   quantify the deviation between experiment and theory. One example merit function is: Δ^Λ^^, ^^^, ^^^,Λ^ଶ, ^^ଶ, ^^ଶ^ ൌ ∑^ୀ^,ଶ,ଷห ^^^ோ,௧^^^^௬,^^ ^^^ െ ^^^ோ,^௫^,^^ ^^^ห ^ ห ^^^்,௧^^^^௬,^^ ^^^ െ ^^^்,^௫^,^^ ^^^ห . ఒ,^ୀ^,^nonlinear optimization method that minimizes the value of the merit function. The exact form ofthe metric function can be by weighting different Stokes parameters to improve the accuracy. The final results are the parametersΛ^^^^^, ^^^, ^^^^^^, ^^^, ^^^^^^, ^^^,Λ^ଶ^^^, ^^^, ^^ଶ^^^, ^^^^^ ^^ ^^ ^^ଶ^^^, ^^^of the sample.out to determine characteristics of a polarization component in accordance with an example embodiment. At 702, an area of the polarization component is illuminated with a uniform light beam, wherein the uniform light beam is in a particular polarization state. At 704, at a pixelated detector, reflected or transmitted light is received from the polarization component in response to illuminating the area of the polarization component; each group of pixels of the pixelated detector receives light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image. At 706, Stokes parameters of the polarization component are obtained based on the received light at the pixelated detector. At 708, one or more characteristics of the polarization component is determined for each of the plurality of the spatial regions using the Stokes parameters.

[0054] In one example embodiment, the polarization component includes a self-organized cholesteric liquid crystal (CLC) polymer thin film. In another example embodiment, the one or more characteristics includes a thickness, an alignment angle or a pitch. In yet another example embodiment, the above noted operations, prior to illuminating the area of the polarization element, include computing reflected Stokes parameters or transmitted Stokes parameters for the polarization component for multiple angles of incidence, wavelengths or input polarizations states, and validating the computed reflected or transmitted Stokes parameters using measurements from a calibrated polarimeter.

[0055] According to another example embodiment, the polarization component includes a thin film, illuminating the polarization component includes illuminating the thin film with at least three different wavelengths, obtaining the Stokes parameters includes obtaining the Stokes parameters  PCT Patent Application 044974.8109.WO00 (UA24-062)   corresponding to each of the at least three wavelengths, and determining the one or more characteristics includes determining a thickness, an alignment angle and a pitch corresponding to the thin film. In one example embodiment, the above noted operations includes computing nominal values of the Stokes parameters, comparing the nominal values of the Stokes parameters to Stokes parameters obtained from a polarimeter, and computing revised nominal values of the Stokes parameters to match the Stokes parameters obtained from the polarimeter. In yet another example embodiment, the above noted operation further include using a merit function to quantify a deviation between the revised nominal values of Stokes parameters, and determining the thickness, the alignment angle and the pitch based on the merit function. In still another example embodiment, computing the nominal values of the Stokes parameter is performed by taking into account a finite bandwidth of a light source used for illuminating the thin film.

[0056] In one example embodiment, the particular polarization state is one of a linear or circular polarization states. In another example embodiment, the particular polarization state is selected to maximize one of the reflection or transmission of the light beam illuminating the area of the polarization component. In still another example embodiment, the above noted operations include receiving, at the pixelated detector, (a) only the reflected light from the polarization component, (b) only the transmitted light from the polarization component, or (c) receiving both the reflected and transmitted light from the polarization component. In yet another example embodiment, the polarization component is one of a polarization volume hologram (PVH), a surface relief grating (SRG), or a volume Bragg grating (VBG).

[0057] In one example embodiment, determining one or more characteristics of the polarization component includes using a predetermined relationship between one or more the characteristics and a measurable property of the polarization component. In another example embodiment, the measurable property is diffraction efficiency, and the one or more characteristics is a thickness of the polarization component. In yet another example embodiment, the measurable property is diffraction efficiency, and the one or more characteristics is Bragg wavelength of the polarization component.

[0058] Another aspect of the disclosed embodiments relates to a system for determining characteristics of a polarization component that includes one or more light sources positioned to illuminate an area of the polarization component with uniform illumination, and one or more filters  PCT Patent Application 044974.8109.WO00 (UA24-062)   positioned in an optical path of the one or more light sources, the one or more filters comprising one or more spectral filters configured to allow light of a particular wavelength or range of wavelengths to pass through, or one or more polarization filters configured to impart a particular polarization state to the light that is directed toward the polarization component. The system also includes one or more pixelated detectors positioned to received light that is reflected from or transmitted through the polarization component, wherein each group of pixels of the pixelated detector is positioned to receive light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image. The system further includes a processor coupled to the one or more pixelated detectors, and a memory coupled to the processor and comprising instructions stored thereon, wherein the instructions upon execution by the processor configure the processor to: obtain Stokes parameters of the polarization component based on signals associated with the received light at the one or more pixelated detectors, and determine one or more characteristics of the polarization component for each of the plurality of the spatial regions based on the Stokes parameters.

[0059] In one example embodiment, the above noted system includes one or more filters positioned in an optical path of the light received by the one or more pixelated detectors, wherein the one or more filters comprise a spectral or a polarization filter. In another example embodiment, the system includes two light sources and two pixelated detectors, where a first of the two light sources is configured to illuminate the polarization component from a first side thereof, a second of the two light sources is configured to illuminate the polarization component from a second side thereof, and each of two pixelated detectors is configured to receive the light that is transmitted through and the light that is reflected from the polarization component.

[0060] In another example embodiment, the system includes one light source and one pixelated detector, where the light source is configured to illuminate the polarization component from a first side thereof, and the pixelated detector is configured to receive the light that is reflected from the first side of the polarization component. In yet another example embodiment, the system includes one light source and one pixelated detector, where the light source is configured to illuminate the polarization component from a first side thereof, and the pixelated detector is configured to receive the light that is transmitted through the polarization component. In still another example embodiment, the system includes one light source and two pixelated detectors, where the light  PCT Patent Application 044974.8109.WO00 (UA24-062)   source is configured to illuminate the polarization component from a first side thereof, a first pixelated detector is configured to receive the light that is reflected from the first side of the polarization component, and a second pixelated detector is configured to receive the light that is transmitted through the polarization component.

[0061] In one example embodiment, each or the one or more light sources is operable at a particular range of wavelengths. In another example embodiment, the one or more pixelated detectors include a polarization camera.

[0062] Various operations disclosed herein can be implemented using a processor / controller is configured to include, or be coupled to, a memory that stores processor executable code that causes the processor / controller carry out various computations and processing of information. The processor / controller can further generate and transmit / receive suitable information to / from the various system components, as well as suitable input / output (IO) capabilities (e.g., wired or wireless) to transmit and receive commands and / or data. The processor / controller may, for example, provide signals to control the operation of various components such as light sources and detectors that are disclosed herein. The processor / controller may be further configured to perform various method steps and computations that are disclosed in this patent document.

[0063] Various information and data processing operations described herein may be implemented in one embodiment by a computer program product, embodied in a computer- readable medium, including computer-executable instructions, such as program code, executed by computers in networked environments. A computer-readable medium may include removable and non-removable storage devices including, but not limited to, Read Only Memory (ROM), Random Access Memory (RAM), compact discs (CDs), digital versatile discs (DVD), etc. Therefore, the computer-readable media that is described in the present application comprises non-transitory storage media. Generally, program modules may include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executable instructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps or processes.  PCT Patent Application 044974.8109.WO00 (UA24-062)

[0064] Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.

Claims

PCT Patent Application 044974.8109.WO00 (UA24-062)   CLAIMS What is claimed is:

1. A method for determining characteristics of a polarization component, the method comprising: illuminating an area of the polarization component with a uniform light beam, wherein the uniform light beam is in a particular polarization state; receiving, at a pixelated detector, reflected or transmitted light from the polarization component in response to illuminating the area of the polarization component, wherein each group of pixels of the pixelated detector receives light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image; obtaining Stokes parameters of the polarization component based on the received light at the pixelated detector; and determining one or more characteristics of the polarization component for each of the plurality of the spatial regions using the Stokes parameters.

2. The method of claim 1, wherein the polarization component includes a self-organized cholesteric liquid crystal (CLC) polymer thin film.

3. The method of claim 1, wherein the one or more characteristics includes a thickness, an alignment angle or a pitch.

4. The method of claim 1, wherein, prior to illuminating the area of the polarization element, computing reflected Stokes parameters or transmitted Stokes parameters for the polarization component for multiple angles of incidence, wavelengths or input polarizations states, and validating the computed reflected or transmitted Stokes parameters using measurements from a calibrated polarimeter.  PCT Patent Application 044974.8109.WO00 (UA24-062)   5. The method of claim 1, wherein: the polarization component includes a thin film, illuminating the polarization component includes illuminating the thin film with at least three different wavelengths, obtaining the Stokes parameters includes obtaining the Stokes parameters corresponding to each of the at least three wavelengths, and determining the one or more characteristics includes determining a thickness, an alignment angle and a pitch corresponding to the thin film.

6. The method of claim 5, comprising: computing nominal values of the Stokes parameters, comparing the nominal values of the Stokes parameters to Stokes parameters obtained from a polarimeter, and computing revised nominal values of the Stokes parameters to match the Stokes parameters obtained from the polarimeter.

7. The method of claim 6, further comprising: using a merit function to quantify a deviation between the revised nominal values of Stokes parameters, and determining the thickness, the alignment angle and the pitch based on the merit function.

8. The method of claim 6, wherein computing the nominal values of the Stokes parameters is performed by taking into account a finite bandwidth of a light source used for illuminating the thin film.

9. The method of claim 1, wherein the particular polarization state is one of a linear or circular polarization states.

10. The method of claim 1, wherein the particular polarization state is selected to maximize one of the reflection or transmission of the light beam illuminating the area of the polarization  PCT Patent Application 044974.8109.WO00 (UA24-062)   component.

11. The method of claim 1, comprising receiving, at the pixelated detector, only the reflected light from the polarization component, only the transmitted light from the polarization component, or receiving both the reflected and transmitted light from the polarization component.

12. The method of claim 1, wherein the polarization component is one of a polarization volume hologram (PVH), a surface relief grating (SRG), or a volume Bragg grating (VBG).

13. The method of claim 1, wherein determining one or more characteristics of the polarization component includes using a predetermined relationship between one or more the characteristics and a measurable property of the polarization component.

14. The method of claim 13, wherein the measurable property is diffraction efficiency and the one or more characteristics is a thickness of the polarization component.

15. The method of claim 13, wherein the measurable property is diffraction efficiency and the one or more characteristics is Bragg wavelength of the polarization component.

16. A system for determining characteristics of a polarization component, comprising: one or more light sources positioned to illuminate an area of the polarization component with uniform illumination; one or more filters positioned in an optical path of the one or more light sources, the one or more filters comprising one or more spectral filters configured to allow light of a particular wavelength or range of wavelengths to pass through, or one or more polarization filters configured to impart a particular polarization state to the light that is directed toward the polarization component; one or more pixelated detectors positioned to received light that is reflected from or transmitted through the polarization component, wherein each group of pixels of the pixelated  PCT Patent Application 044974.8109.WO00 (UA24-062)   detector is positioned to receive light from a corresponding spatial region of the polarization component to allow a plurality of spatial regions of the polarization component to be measured in via a single image; a processor coupled to the one or more pixelated detectors; and a memory coupled to the processor and comprising instructions stored thereon, wherein the instructions upon execution by the processor configure the processor to: obtain Stokes parameters of the polarization component based on signals associated with the received light at the one or more pixelated detectors, and determine one or more characteristics of the polarization component for each of the plurality of the spatial regions based on the Stokes parameters.

17. The system of claim 16, comprising one or more filters positioned in an optical path of the light received by the one or more pixelated detectors, wherein the one or more filters comprise a spectral or a polarization filter.

18. The system of claim 16, including two light sources and two pixelated detectors, wherein: a first of the two light sources is configured to illuminate the polarization component from a first side thereof, a second of the two light sources is configured to illuminate the polarization component from a second side thereof, and each of two pixelated detectors is configured to receive the light that is transmitted through and the light that is reflected from the polarization component.

19. The system of claim 16, including one light source and one pixelated detector, wherein: the light source is configured to illuminate the polarization component from a first side thereof, and the pixelated detector is configured to receive the light that is reflected from the first side of the polarization component.

20. The system of claim 16, including one light source and one pixelated detector, wherein:  PCT Patent Application 044974.8109.WO00 (UA24-062)   the light source is configured to illuminate the polarization component from a first side thereof, and the pixelated detector is configured to receive the light that is transmitted through the polarization component.

21. The system of claim 16, including one light source and two pixelated detectors, wherein: the light source is configured to illuminate the polarization component from a first side thereof, a first pixelated detector is configured to receive the light that is reflected from the first side of the polarization component, and a second pixelated detector is configured to receive the light that is transmitted through the polarization component.

22. The system of claim 16, wherein each or the one or more light sources is operable at a particular range of wavelengths.

23. The system of claim 16, wherein the one or more pixelated detectors include a polarization camera.

24. The system of claim 16, wherein the instructions upon execution by the processor configure the processor to perform the operations in claims 2 to 15.

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