Polarization Interferometer

Abstract

A polarization interferometer is configured to rapidly and accurately characterize a test object, particularly the surface roughness of the test object. The polarization interferometer includes an illumination source that generates light having multiple wavelengths. The light is split into two orthogonally polarized beams, including a reference beam and a test beam, and the test beam is incident on and returned from the test object. The reference beam and the test beam are combined into a combined beam. At least one spectral filter separates the combined beam into two spectral channels with different center wavelengths. Two pixelated polarization phase sensors simultaneously capture images of the two spectral channels and generate a phase map that can be used to measure properties of the test object.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims priority under 35 U.S.C. § 119 to U.S. Provisional Application No. 63 / 435,868, entitled "SURFACE ROUGHNESS INTERFEROMETER," filed December 29, 2022, which is assigned to the assignee of the present application and incorporated herein by reference in its entirety.

[0002] FIELD OF THE INVENTION The subject matter described herein relates to interferometry, and more particularly to polarization interferometry using pixelated polarization phase sensors that capture multiple spectral channels. [Background technology]

[0003] Polarization or phase-shifting interferometry is an established optical method for precise measurement of various physical parameters, including the surface shape and roughness, of optically smooth objects. Optically smooth objects have a local roughness RMS (root mean square) of less than 1 / 30 of the measurement wavelength used for testing, and height variations of less than 1 / 4 of the measurement wavelength within the optical resolution range and between sampling points, which can range from nanometers to microns. In phase-shifting interferometry, multiple data frames, e.g., images, of the object's irradiance are acquired. Each frame is acquired with a different relative phase shift between the interfering reference and test beams, and the data is processed by a computer to determine with high precision the relative path difference between the reference and object surfaces. Unambiguous interferometric measurements require that the object surface has no local steps or discontinuities greater than 1 / 4 of the measurement wavelength used for object testing. Apparent optical smoothness depends not only on the surface characteristics but also on system parameters such as the wavelength of light used for testing and the optical resolution of imaging and illumination. Surfaces with greater roughness must be measured using other methods that extend the vertical range of measurement, such as fringe projection, coherence scanning, or multi-wavelength interferometry. Methods that extend the vertical range of measurement often do not have good vertical resolution or are not instantaneous. A solution that provides an accurate and instantaneous assessment of surface roughness is desirable. Summary of the Invention

[0004] The polarization interferometer uses multiple spectral channels captured simultaneously to characterize a test object, such as the surface roughness of the test object. The polarization interferometer may include an illumination source producing light having multiple wavelengths. The polarization interferometer further includes polarization interferometer optics that split the light into two orthogonally polarized beams, including a reference beam and a test beam, where the test beam is incident on the test object and returned from the test object. The polarization interferometer optics recombine the test beam and the reference beam into a combined beam. At least one spectral filter spectrally filters the combined beam into two spectral channels. The first spectral channel has a first center wavelength, and the second spectral channel has a second center wavelength different from the first center wavelength. The polarization interferometer further includes two pixelated polarization phase sensors configured to simultaneously capture images of the two spectral channels at the two pixelated polarization phase sensors. The two pixelated polarization phase sensors are further configured to generate a phase map corresponding to equivalent wavelengths of the first center wavelength and the second center wavelength. A computer is used to determine the surface roughness based on the phase map, where the variation in surface roughness height is greater than 20 nanometers (nm) root mean square (RMS).

[0005] A polarization interferometric method for characterizing a test object includes generating light having multiple wavelengths using an illumination source. The method further includes splitting the light into two orthogonally polarized beams, including a reference beam and a test beam, using polarization interferometer optics. The test beam is incident on the test object and returned from the test object, and the polarization interferometer optics is used to recombine the test beam and the reference beam into a combined beam. The method includes spectrally filtering the combined beam into two spectral channels using at least one spectral filter. The first spectral channel has a first center wavelength and the second spectral channel has a second center wavelength, the first and second center wavelengths being different. The method further includes simultaneously capturing images of the two spectral channels using two pixelated polarization phase sensors and generating a phase map of the surface of the test object corresponding to equivalent wavelengths of the first and second center wavelengths. The method also includes determining a surface roughness based on the phase map, wherein the variation in height of the surface roughness is greater than 20 nanometers (nm) root mean square (RMS).

[0006] Other objects, features, and advantages of the present disclosure will become apparent to those skilled in the art from a consideration of the following detailed description taken in conjunction with the accompanying drawings and claims. [Brief explanation of the drawings]

[0007] [Figure 1] 1 is a schematic perspective view of a polarization interferometer, particularly showing a measurement device in functional blocks. [Figure 2] The spectral characteristics of the light source and the relative transmittance of the optical filter are shown. [Figure 3] FIG. 1 is a plan view of a pixelated polarizer array illustrating one implementation of a phase sensor that may be used with a polarization interferometer. [Figure 4] FIG. 1 is a schematic diagram of a polarization interferometer configured using a Mirau-type interferometer optical system. [Figure 5] FIG. 1 is a schematic diagram of a polarization interferometer configured using a Linnik-type interferometer optical system. [Figure 6] FIG. 1 is a schematic diagram of an implementation of a splitter and a spectral filter and a dual phase sensor that can be used in a polarization interferometer. [Figure 7A] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 7B] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 7C] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 7D] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 7E] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 7F] 1 illustrates various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer. [Figure 8A] 1 illustrates the sub-pixel alignment of corresponding pixels in a pixelated polarization phase sensor used in a polarization interferometer. [Figure 8B] 1 illustrates the sub-pixel alignment of corresponding pixels in a pixelated polarization phase sensor used in a polarization interferometer. [Figure 9] 1 shows a pixelated polarization phase sensor with an RGB (red, green, blue) Bayer filter. [Figure 10] 1 is an example of data obtained using a measurement system configured in accordance with the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0008] Phase-shifting interferometry can be used for precision measurements of a variety of physical parameters. Unambiguous interferometric measurements require that the surface under test be free of local steps or discontinuities larger than one-quarter of the wavelength used in the interferometric measurement. This severely limits the range of surfaces that can be measured. Techniques exist to extend the measurement range, such as fringe projection, coherence scanning, or multi-wavelength interferometry, but these techniques have traditionally been problematic due to increased measurement acquisition time, loss of precision due to vibration, and inaccuracies due to chromatic dispersion.

[0009] To extend the measurement range, phase shift measurements can be performed at two or more wavelengths and the results combined to obtain a longer "equivalent" wavelength, λ eq This can produce a reduced sensitivity measurement of

number

[0010] where λ1 and λ2 are the two measurement wavelengths. Equivalent wavelengths of several microns to several millimeters can be generated through appropriate selection of the measurement wavelengths. Measuring at more than one wavelength extends the vertical range of surfaces and surface roughness that can be measured, but additional time is typically required to acquire the extra wavelength data in addition to the phase shift data, and it results in high sensitivity to motion and vibration during acquisition. Precision measurements require vibration isolation and / or very tight coupling between the test article and the interferometer.

[0011] Pixelated polarizer arrays can be fabricated so that each pixel element has a different polarizer orientation in a repeating pattern. These micropolarizer arrays can be combined with a polarization interferometer to achieve single-frame phase-shift measurements at a single wavelength. The dual-wavelength technique can be combined with a pixelated polarizer sensor, a microscopic polarization interferometer, and switchable dual-wavelength illumination to achieve surface roughness measurements of surfaces with local roughness depths exceeding one-quarter of an individual wavelength. This method uses at least two frames of data, with the light source switched between exposures. Therefore, this implementation does not offer the significant vibration resistance characteristic of true single-frame measurements. Furthermore, chromatic dispersion has been found to require changing the instrument's focus between measurements, further increasing measurement time.

[0012] Pixelated color filters can be interlaced with pixelated polarizer arrays to achieve single-frame, multi-wavelength measurements. Typically, these are RGB (red, green, blue) color filters. However, the pixels at each wavelength are necessarily displaced from one another due to the interlaced nature of the array. The lateral displacement between different color pixels makes it impossible to measure surfaces with high spatial frequency random phase, such as optically rough surfaces, because different color images do not originate from the same location on the test surface. Furthermore, monolithic interlaced sensors do not allow for independent adjustment to compensate for chromatic dispersion at each wavelength, further reducing their practicality for surface roughness measurements. Therefore, this method is generally limited to measuring optically smooth surfaces.

[0013] As described herein, a polarization interferometer can include a combination of dual spectral channels and dual phase sensors, where both phase sensors simultaneously capture images of the spectral channels. Simultaneous capture of dual spectral channels in a polarization interferometer can be used to generate optical measurements, such as surface roughness, in a single snapshot, thus enabling a vibration-insensitive measurement system that functions over a wide range of surface roughness or discontinuity values. As used herein, simultaneously capturing spectral channels by phase sensors indicates that the phase sensors are exposed to images of each of the spectral channels simultaneously for at least 90% of the exposure time, or that neither phase sensor sees a change in optical path difference of more than a few nanometers relative to the other phase sensor.

[0014] Measurements of surface features where the height variation is (or is) at a high spatial frequency, e.g., the local height variation is greater than λ / 8 or λ / 4 across a single pixel width, where λ is the equivalent wavelength of the measurement light. It should be understood that the polarization interferometers described herein can be used to measure, for example, steps, gratings, or other features, or surfaces that are relatively smooth, e.g., have slowly varying features (varying at a low spatial frequency), or relatively rough, e.g., have rapidly varying features (varying at a high spatial frequency). A smooth surface, such as glass, may have a root-mean-square (RMS) height variation of less than 20 nanometers (nm) from adjacent surfaces. Polarization interferometers can measure smooth surfaces as well as surfaces of objects with RMS values ​​greater than 20 nm, down to several micrometers or microns. In one implementation, the polarization interferometer can quickly and accurately measure RMS values ​​from a few nanometers (e.g., 4 nm RMS) to 10 micrometers RMS. Surface roughness measurements can be 50 nm RMS, 100 nm RMS, 250 nm RMS, 400 nm RMS, or any number between 4 nm RMS and 10 μm RMS. Additionally, interferometers with dual spectral channels and dual phase sensors can be configured to better respond to chromatic dispersion present in the optical path. Many industries, including the semiconductor and medical industries, utilize surface roughness measurements in research and development, quality control, and manufacturing, and therefore, the present disclosure is relevant to a wide variety of applications.

[0015] In some implementations, dual spectral channels can be generated using a non-polarizing beam splitter and a spectral filter in each beam path to generate spectral channels with different center wavelengths. In some implementations, dual spectral channels can be generated using a dichroic beam splitter that splits and spectrally filters light from the polarization interferometer optics to generate channels with different center wavelengths. In some implementations, dual spectral channels can be generated at the camera level, for example, with a sensor that has spectral filtering built directly onto the sensor or associated with the sensor. The dual phase sensor can be a dual pixelated polarization phase sensor that receives light in the first and second channels. The dual phase sensor can be configured to receive two focused channels and laterally aligned to receive the same image with subpixel accuracy. The phase sensors can be physically separated, for example, different phase arrays in different cameras, or different phase arrays in a single camera, for example, mounted on a single monolithic block or different regions of the same sensor phase array in a single camera. The dual-phase sensor can generate a phase map corresponding to the equivalent wavelengths of a first and second central wavelength in a single shot, which can be used to characterize a test object, such as its surface roughness.

[0016] Polarization interferometers provide a useful configuration for quantitatively measuring surface roughness, especially for optically rough surfaces where adjacent height discontinuities are greater than one-quarter of the measurement wavelength. In some implementations, the measurement device may include a combination of a broadband light source filtered for polarization, a microscope-based polarization interferometer that splits the illumination into two orthogonally polarized beams—one containing the phase of the object under test and the other from a high-quality reference surface—a mechanism for further splitting the combined reference and test beams into two separate channels, a means for independently spectrally filtering each channel at a different center wavelength, two pixelated detector regions with a polarizer array subdivided into a plurality of sets of pixels with polarizers, each set adapted to generate a predetermined phase shift between the orthogonally polarized test and reference beams, and a means for focusing and aligning images onto the two detector regions within subpixel accuracy. Thus, each detector region simultaneously generates a pixelated phase-shifted interferogram at a different center wavelength.

[0017] According to some implementations, it is possible to measure the surface roughness of objects with local height discontinuities greater than one-quarter of an optical wavelength and smaller than one-quarter equivalent wavelength in a single snapshot, generated by capturing and processing measurements at two or more wavelengths. The present disclosure offers an improvement over conventional methods using two or more wavelengths because all necessary wavelength and phase-shift information is captured simultaneously, significantly expanding tolerance to vibration and motion. The present invention also offers an improvement over methods using a pixelated RGB color filter array in combination with a pixelated polarizer array detector, which suffers from the drawback of large pixel separation between spectral channels, thereby limiting the practical measurement of rough surfaces. A pixelated polarizer array detector, or pixelated waveplate array, is also called a phase sensor because it enables instantaneous phase measurement between incident orthogonally polarized beams. Such detectors can be purchased with polarizers or waveplates already embedded in the sensor pixels or their arrays, often referred to as a pixelated phase mask, and may be placed on top of a regular sensor array.

[0018] Referring to the drawings, wherein like parts are designated with like numerals and symbols throughout, FIG. 1 schematically illustrates a complete measurement system 50 exhibiting functionality in accordance with the present disclosure. Measurement system 50 is a polarization interferometer and may therefore also be referred to as a polarization interferometer 50. It should be understood that some of the functionality shown in FIG. 1 with two or more separate components may be implemented by a single or fewer elements. Conversely, it should also be understood that some of the functionality shown in FIG. 1 with a single component may be implemented by multiple elements. Various specific implementations of measurement systems are further described below.

[0019] The polarization interferometer 50 enables single-shot measurements with high spatial resolution, e.g., submicron lateral resolution, and a large field of view, e.g., from hundreds of microns to over 1 mm. The system includes an illumination source 1 that generates light 2 having at least two wavelengths. The illumination source 1 may be a broadband illumination source, e.g., a frequency comb laser, laser diode, LED, or other light source that generates light with multiple wavelengths separated by, e.g., 10 nm or more. In some implementations, the illumination source 1 may include two separate light sources, such as two lasers, laser diodes, LEDs, or other light sources, or any combination thereof, that generate light with distinct wavelengths that are combined into a single beam represented by light 2. For example, multiple light sources can be coupled with an optical fiber to actually operate as a single light source with different wavelengths. The illumination source 1 can generate light having a central wavelength λ0. The illumination source 1 can also generate light that is polarized and at least partially spatially and temporally coherent. In some implementations, the illumination source 1 may include a polarizer that polarizes the light. In some implementations, illumination source 1 may include a light source that generates polarized light, such as when illumination source 1 is a laser. In some implementations, at least one polarization control element 3, such as a polarizer, may be used to independently control the polarization of polarized beam 4. In some implementations, polarization control element 3 may be considered part of illumination source 1 or may not be present. The selection of illumination source 1 may be based on a combination of power and spectral bandwidth or wavelength band.

[0020] Polarized beam 4 enters microscope-based polarization interferometer optics 5, which may have a numerical aperture of 0.3 or greater and split the light into orthogonally polarized beams. As shown, polarization interferometer optics 5 includes element 6, which splits polarized beam 4 into reference beam 7 having a predetermined polarization and test beam 8 having a polarization orthogonal to reference beam 7, and beam combiner 9, which recombines test beam 8 so that it is substantially collinear with reference beam 7. Test beam 8 is incident on a test object (not shown) and is returned by the test object. While FIG. 1 functionally illustrates element 6 as splitting polarized beam 4, it should be understood that element 6 may also generate orthogonal polarization states, for example, if element 6 is a polarizing beam splitter. Furthermore, although element 6 and beam combiner 9 are functionally illustrated as separate components in FIG. 1, it should be understood that the functionality may be implemented in a single component.

[0021] The combined beam 11 is split into two spectral channels with different center wavelengths. For example, FIG. 1 shows the combined beam 11 directed to the splitter and spectral filter section 12, where the non-polarizing beam splitter 13 splits the combined beam 11 into two sub-beams 14a and 14b. Sub-beam 14a is filtered by a first spectral filter 15 having a center wavelength of λ1, thereby generating a first spectral channel 18a that is imaged onto a first phase sensor 20. Sub-beam 14b is filtered by a second spectral filter 16 having a center wavelength of λ2, thereby generating a second channel 18b that is imaged onto a second phase sensor 21. However, the spectral channels may be generated in different ways. For example, in some implementations, the spectral channels 18a and 18b may be generated using a dichroic beam splitter 13 that splits the combined beam 11 into separate channels 18a and 18b, thereby eliminating the need for the spectral filters 15 and 16. In some implementations, the functionality of the splitter and spectral filter section 12 may be at least partially implemented in the dual phase sensor section 19. For example, a polarization pixelated camera may include a spectral filter, and thus filtering into two spectral channels may be performed at the camera level. In another implementation, the separate spectral channels 18a and 18b may be generated using a metasurface configured to spectrally separate each point (or pixel) of an image of a test object into spectral channels 18a and 18b received at a corresponding pixel of the phase sensor. The first phase sensor 20 and the second phase sensor 21 of the dual phase sensor section 19 may be aligned with each other, enabling focusing to compensate for any color differences. Alignment of the phase sensor 20 and the phase sensor 21 may be performed mechanically using a positioning stage 22. In some implementations, the phase sensor 20 and the phase sensor 21 may also be digitally aligned.

[0022] First phase sensor 20 and second phase sensor 21 may include a polarization or waveplate array that introduces an effective phase delay between the filtered reference and test beams in each spectral channel 18 a and 18 b, respectively, at each pixel, and subsequently interferes the transmitted light, and a detector array that converts the sensed optical irradiance at each pixel into electrical signals 30 and 31, respectively. Polarization interferometer 50 may also include a digitizing circuit 32 (digitizer) that converts the voltage into a digital bit stream, and a computer 34 that processes the digital bit stream to control operation of polarization interferometer 50, calculate the optical phase difference, and store and / or report the results, for example via a display 36, allowing user interaction in a conventional manner.

[0023] The wavelengths λ1 and λ2 generated by channels 18a and 18b are used to generate the desired equivalent wavelength λeq from Equation 1. As can be seen from Equation 1, the equivalent wavelength is inversely proportional to the difference between wavelengths λ1 and λ2; as the two wavelengths approach each other, the resulting equivalent wavelength increases. However, noise also scales with the equivalent wavelength, e.g., on the order of λ / 50. Therefore, the selection of illumination source 1 and the spectral filters (e.g., filters 15 and 16) generating the spectral channels can be tailored to adjust the equivalent wavelength to be larger than the surface discontinuities being measured to avoid phase ambiguity (2π error), but as small as possible to optimize the signal-to-noise ratio. For example, an equivalent wavelength of approximately four times the maximum surface height may be a good compromise to avoid phase ambiguity, while still keeping the equivalent wavelength as low as possible to minimize noise. In some implementations, two-wavelength measurements can be combined with single-wavelength data to obtain improved vertical resolution when noise is less than one-quarter of a wavelength (again, to avoid phase ambiguity). Thus, in some implementations, the illumination source 1 (and one or more spectral filters) may be selected to produce an equivalent wavelength of about 12 times the fundamental, or about 7 microns, for rough surfaces.

[0024] 2, the spectral output of illumination source 1 is represented by curve 60 having a center wavelength λ0. The response of spectral filter 15 is shown as block 70 having a center wavelength of λ1 and a bandwidth of Δλ1. The response of spectral filter 16 is shown as block 80 having a center wavelength of λ2 and a bandwidth of Δλ2. The responses of spectral filters 15 and 16 may overlap. The center wavelengths λ1 and λ2 and their separation Δλ are used to determine the equivalent wavelength λeq according to Equation 1.

[0025] FIG. 3 shows one implementation of a phase sensor 100 that can be used as one of the phase sensors 20 and 21 in polarization interferometer 50. Other implementations of the phase sensor may be used if desired. As shown in FIG. 3, a pixelated polarizer mask array 106 (e.g., a pixelated wire-grid polarizer array) is bonded or otherwise constructed to be part of a sensor array 108, which may be, for example, of the CCD or CMOS type. Optionally, a quarter-wave plate 104 can be bonded to the pixelated polarizer mask array to form a composite mask 102. The quarter-wave plate 104 may be located elsewhere in the imaging system. Additionally, as mentioned above, in some implementations, spectral filtering can be performed at the phase sensor level using a spectral filter array 103 bonded to the pixelated polarizer mask array 106. As shown, the spectral filter array 103 can have a repeating pattern of spectral filters 103a and 103b of wavelengths λ1 and λ2, respectively, to generate two spectral channels at the camera level. In some implementations, both phase sensors may have different homogeneous spectral filters to generate two spectral channels at the camera level. In some implementations, the spectral filter array 103 may be a metasurface configured to generate two spectral channels.

[0026] The pixelated polarizer mask array 106 is shown schematically in FIG. 3 as a repeating pattern of polarizing elements 301-319. The capital letters A, B, C, and D represent different transfer functions resulting from filtering from the pixelated polarizer mask. Each unit cell 116 is composed of multiple polarization orientations. FIG. 3 shows the unit cell 116 as containing four orientations: 0 degrees (120), 45 degrees (122), 90 degrees (124), and minus 45 degrees (126).

[0027] The signal measured at each sensor pixel is given by its transfer function, the phase difference between the reference and test beams, and the amplitude of each beam. For example, one possible configuration is

number

[0028] where Ir(x,y) and Is(x,y) are the irradiances of the reference wavefront R and the test wavefront T, respectively, at each x,y coordinate in the image, and Δφ(x,y) is the optical phase difference between the reference and test wavefronts, which is linearly proportional to the optical path difference and, in turn, to the object surface being measured as shown in Equations 6 and 7 below.

[0029] The resulting interferogram can be processed by various algorithms known in the art to calculate the phase difference and modulation index.

[0030] For example, a possible implementation for calculating the phase is a simple 4-bucket algorithm, e.g.: Δφn(x,y)=tan -1 {[Cn(x,y)-An(x,y)]}{[Dn(x,y)-Bn(x,y)]} (3)

[0031] where the values ​​A, B, C, and D are taken from nearby neighboring pixels, and n corresponds to either the first wavelength or the second wavelength.

[0032] The phase map corresponding to the equivalent wavelength can be calculated by simply subtracting the phase values ​​of similar pixels between the first phase sensor 20 and the second phase sensor 21. Δφeq=Δφ1-Δφ2 (4)

[0033] However, if there is a 2π discontinuity in either calculation, the resulting phase value will not necessarily accurately account for the discontinuity.

[0034] By using the polarization interferometer 50, an alternative method for calculating the phase difference at each spatial coordinate that is proportional to the equivalent wavelength and avoids the 2π discontinuity problem is given as follows: ΔΦeq(x,y)=tan -1 [X(x,y), Y(x,y)] (5)

[0035] During the ceremony, X(x,y)=[D1(x,y)-B1(x,y)] * [A2(x,y)-C2(x,y)]-[D2(x,y)-B2(x,y)] * [A1(x,y)-C1(x,y)], Y(x,y)=[A1(x,y)-C1(x,y)] * [A2(x,y)-C2(x,y)]+[D1(x,y)-B1(x,y)] * [D2(x,y)-B2(x,y)]. (5a)

[0036] In Equation 5a, A1, B1, C1, and D1 are pixel values ​​from the first phase sensor 20 at wavelength λ1, and A2, B2, C2, and D2 are pixel values ​​captured from the second phase sensor 21 at wavelength λ2.

[0037] The three-dimensional surface shape can be calculated using the equivalent wavelength using the formula:

number

[0038] (In the formula, λ 2 =λ1* λ, and Δλ = |λ − λ|. Noise in the image can be reduced using weighted spatial averaging over neighboring pixels. This can be achieved as follows:

number

[0039] Here, the sum is carried out over the range of nearest neighbors of δ.

[0040] One implementation of a polarization interferometer is shown in Figure 4 and is configured using a Mirow-type interferometer optics system. The system includes a broadband light source 1 with a predetermined lateral size and radiating over a predetermined angle. Light rays emerging from the center of the light source 1 across the entire divergence angle are shown as dotted lines 2a and represent the illumination path. Light rays emerging from the edge of the light source are shown as dark lines 2b and are extensions to the imaging path. The light is captured by a collimation lens 204, and the light source 1 is imaged by a relay lens 206 onto the entrance pupil of an objective lens 210. Other illumination methods, such as critical illumination, may be used in some implementations. The polarization of the light source is controlled by the orientation of a polarizer 3 to control signal contrast. The light is reflected by a first non-polarizing beam splitter 208, which directs the light into the polarization interferometer optics 5, which includes a microscope objective lens arranged in a Mirow configuration. A polarizing thin-film beam splitter 212 reflects one polarization to form a reference beam R and transmits the remaining portion to form a test beam T. Such a polarizing thin-film beam splitter 212 can be constructed, for example, by depositing an array of fine conductive lines on a glass substrate. The reference beam R reflects from a high-quality reflective reference mirror 216 (surface flatness <λ / 10) located within the objective lens (possibly coated on one of the lens elements), then reflects a second time from the polarizing thin-film beam splitter 212, is recollimated by the objective lens 210, and is transmitted back through the first non-polarizing beam splitter 208. The test beam T reflects from the test object 214, transmits through the polarizing thin-film beam splitter 212, is recollimated by the objective lens 210, and is transmitted back through the first non-polarizing beam splitter 208 to form an orthogonally polarized reference and test beam combination beam 11. The test beam T and reference beam R have orthogonal polarizations, which can be linear or circular, for example, if different polarization splitting methods are used. Imaging lens 220 is positioned to form images of the test surface onto first phase sensor 20 and second phase sensor 21, respectively. Splitter / filter section 12 includes a second non-polarizing beam splitter 222 that directs the beam into two paths. The first path travels through first spectral filter 15 to produce first channel 18a.First channel 18a optionally passes through a quarter-wave plate 224 and is incident on first phase sensor 20. A second path travels through second spectral filter 16 to produce second channel 18a. Second channel 18b optionally passes through a second quarter-wave plate 226 and is incident on second phase sensor 21. Phase sensor module 19 includes first phase sensor 20 and second phase sensor 21 mechanically bonded together using a low-expansion thermal material such as Invar, and further includes a precision adjuster 22 for setting the relative position of first phase sensor 20 with respect to second phase sensor 21 so that the image is focused. Precision adjuster 22 need not be a permanent component of the final system, as it can be removed after the sensors are bonded in place. For example, a nanopositioning stage can be used to align the second phase sensor 21 to the first phase sensor 20, e.g., to position the x, y, and z axes in the same plane before cementing the sensors in place. For example, the system can generate a focused image on the first phase sensor 20 across the entire field of view, and then use the nanopositioning stage of the precision adjuster 22 to generate a focused image on the second phase sensor 21 across the entire field of view, and then pixel-match, e.g., so that the same portion of the sample is imaged onto the pixels of the first phase sensor 20 and the second phase sensor 21, which are aligned with sub-pixel accuracy. Mechanical alignment and temperature control can be used to increase stability over time, e.g., to prevent or compensate for thermal drift. In some implementations, the phase sensors 20 and 21 can be digitally aligned pixel-by-pixel to further improve mechanical alignment, correct for differences in field aberrations, and provide stability over time, e.g., if the phase sensors 20 and 21 drift relative to each other over time due to a normal working environment. For example, digital alignment can be performed by periodically measuring mismatches using a calibration surface, e.g., a flat surface with high visual contrast, including various inherent features such as scratches and divots in semi-abrasive materials, which can be corrected during measurement to maintain mutual alignment.

[0041] Figure 5 shows a polarization interferometer according to the present disclosure, constructed using a modified Linnik-type interferometer. The system includes a broadband light source 1 with a predetermined lateral size and radiating over a predetermined angle. The light beam emerging from the center of the light source over the entire divergence angle is shown as dotted line 2a and represents the illumination path. The light beam emerging from the edge of the light source is shown as dark line 2b and is an extension to the imaging path. The light is captured by a collimation lens 204, and the broadband light source 1 is imaged by a relay lens 206 onto the entrance pupil of an objective lens 211. Other illumination methods, such as critical illumination, may be used in some implementations. The polarization of the light source is controlled by the orientation of a polarizer 3 to control the signal contrast. A first non-polarizing beam splitter 208 directs the light into the polarization interferometer optics 5, which is a so-called Linnik-type system and includes two microscope objective lenses 211 and 213 aligned conjugately to each other. Polarizing beam splitter 215 reflects one polarization component of the beam to form test beam T and transmits the remaining portion to form reference beam R.

[0042] Reference beam R reflects from a high-quality reflective reference mirror 216 (surface flatness < λ / 10) located in the focal plane of objective lens 211, then is recollimated by objective lens 211 and transmitted back through polarizing beam splitter 215. Test beam T reflects from test object 214, is recollimated by objective lens 213, and is reflected back through polarizing beam splitter 215 to form combined reference and test beam 11. Test beam T and reference beam R have orthogonal linear polarizations and are further transmitted through first non-polarizing beam splitter 208. Imaging lens 220 is positioned to form images of the test surface on first phase sensor 20 and second phase sensor 21, respectively. Splitter / filter section 12 includes a non-polarizing beam splitter 222 that directs the beams into two paths. The first path travels through first spectral filter 15 to generate first channel 18a. First channel 18a optionally passes through a quarter-wave plate 224 and is incident on first phase sensor 20. A second path travels through second spectral filter 16 to produce second channel 18a. Second channel 18b optionally passes through a second quarter-wave plate 226 and is incident on second phase sensor 21. Phase sensor module 19 includes first phase sensor 20 and second phase sensor 21 mechanically bonded together using a low-expansion thermal material such as Invar, and further includes precision adjusters 22 for setting the focus and lateral position of first phase sensor 20 relative to second phase sensor 21 to within sub-pixel accuracy. Precision adjusters 22 need not be a permanent component of the final system, as they can be removed after the sensors are bonded in place.

[0043] Figure 6 shows another implementation of a splitter / spectral filter and dual polarization phase sensor that can be used with the polarization interferometers shown in Figures 1, 4, and 5. Combined beam 11 enters non-polarizing beam splitter 13, is partially reflected to form first sub-beam 14a, and is partially transmitted to form second sub-beam 14b. First sub-beam 14a reflects from mirror 400, passes through first spectral filter 15 to form a first spectral channel, reflects from mirrors 401 and 402, and enters first sensor 20. Second sub-beam 14b is reflected from mirror 404, passes through second spectral filter 16 to form a second spectral channel, and then reflects from mirrors 405, 406, and 407. In some implementations, the beam splitter 13 may be a dichroic beam splitter for generating the first and second spectral channels, thereby eliminating the need for the first and second spectral filters 15 and 16. The dual polarization phase sensor module is formed from the first and second phase sensors 20 and 21, which may be mounted coplanarly on a single monolithic block 440 as part of a single camera. For example, mounting the phase sensors 20 and 21 on a single monolithic block 440 eliminates differential thermal drift that may occur if the sensors were mounted further apart. Furthermore, as part of a single camera, the first and second phase sensors 20 and 21 may be driven by the same controller and have the same settings, shutters, gains, etc., such that the sensors are synchronized to simultaneously capture the first and second channels. Using a single camera with the first and second phase sensors 20 and 21 advantageously facilitates synchronization, control, alignment, and allows for a single cable output. Additionally, the first and second phase sensors may be different regions of a single sensor array, thus further reducing any mounting or thermal drift.The splitter and spectral filter 12 further includes a focus adjuster 22a that ensures that the focal points of the sub-beams 14a and 14b are identical and compensates for any color differences, and an angle adjuster 22b that ensures that the detector areas are spatially co-aligned within the sub-pixels.

[0044] 7A-7F show various configurations of dual spectral channel and dual phase sensors that can be used with a polarization interferometer.

[0045] 7A illustrates the use of a beam splitter 702 that receives combined light 700 from polarization interferometer optics 5 and splits the light into sub-beams 14a and 14b, which are filtered by spectral filters 15 and 16 to produce two spectral channels 18a and 18b. The two spectral channels 18a and 18b are simultaneously imaged by phase sensors 704 and 706 (images 18a and 18b, respectively). 画像 and 18b 画像 )). Phase sensors 704 and 706 may comprise pixelated polarizer mask arrays bonded or otherwise configured to be part of a sensor array, e.g., a CCD or CMOS, as described in FIG. 3. Phase sensors 704 and 706 may be sensor arrays in separate cameras or in a single camera (but not bonded on a single substrate, as shown in FIG. 7D below), with the sensors driven synchronously to simultaneously capture two spectral channels 18a and 18b and controlled to have the same settings, shutters, gains, etc. Additionally, the relative positions of phase sensors 704 and 706 may be adjusted, for example, mechanically or mechanically and digitally, so that the image 18a is captured accurately. 画像 and image 18b 画像 are laterally aligned within sub-pixel accuracy.

[0046] FIG. 7B is similar to FIG. 7A, but accepts combined light 700 from polarization interferometer optics 5 and splits the light into two spectral channels 18a and 18b that are simultaneously imaged by phase sensors 704 and 706 (images 18a and 18b, respectively). 画像 and 18b 画像 7 illustrates the use of a dichroic beam splitter 712 (as indicated by

[0047] FIG. 7C illustrates the use of a beam splitter 702 that receives combined light 700 from polarization interferometer optics 5 and splits the light into sub-beams 14a and 14b. FIG. 7C is similar to FIG. 7A, but illustrates spectral filters bonded or otherwise coupled to phase sensors 724 and 726 to generate two separate spectral channels, as described in FIG. 3. For example, as shown, the spectral filter array bonded to phase sensors 724 and 726 may have a repeating pattern to generate two spectral channels for each unit cell 725 and 727, respectively. Thus, as shown, each phase sensor 724 and 726 can image both spectral channels, but the phase sensors 724 and 726 are aligned such that corresponding unit cells image different spectral channels. Thus, the two spectral channels are imaged simultaneously by phase sensors 724 and 726 (respectively, images 18a and 18b). 画像 and 18b 画像 7C). It should be understood that the pattern or combination of polarization orientations and spectral channels may differ from that shown in FIG. 7C. In some implementations, a single spectral filter, i.e., a homogeneous spectral filter, may be bonded to each phase sensor 724 and 726, which is similar to the implementation shown in FIG. 7A, but with the spectral filters bonded to the phase sensors.

[0048] 7D illustrates the use of a beam splitter 732 that receives combined light 700 from polarization interferometer optics 5 and splits the light into sub-beams 14a and 14b, which are filtered by spectral filters 15 and 16 to generate two spectral channels 18a and 18b, for example, as shown in FIG. 6. In some implementations, a dichroic beam splitter can be used to generate the two spectral channels 18a and 18b, thereby eliminating the need for spectral filters 15 and 16. The two spectral channels 18a and 18b are simultaneously imaged by phase sensors 734 and 736 (respectively, images 18a and 18b). 画像 and 18b 画像 (denoted by ). Each of the phase sensors 734 and 736 may be a pixelated polarizer mask array bonded or otherwise constructed to be part of a sensor array, e.g., CCD or CMOS, as described in FIG. 3, mounted together on the same block 738 in a single camera. The phase sensors 734 and 736 may be synchronized to capture the two spectral channels 18a and 18b simultaneously and driven by the same controller to have the same settings, shutter, gain, etc. Additionally, the relative positions of the phase sensors 734 and 736 may be fixed, e.g., mechanically, or mechanically and digitally calibrated, so that the image 18a 画像 and 18b 画像 are laterally aligned within sub-pixel accuracy.

[0049] FIG. 7E illustrates the use of a beam splitter 732 that receives combined light 700 from polarization interferometer optics 5 and splits the light into sub-beams 14a and 14b, which are filtered by spectral filters 15 and 16 to generate two spectral channels 18a and 18b, for example, as shown in FIG. 6. In some implementations, a dichroic beam splitter can be used to generate the two spectral channels 18a and 18b, thereby eliminating the need for spectral filters 15 and 16. FIG. 7E is similar to FIG. 7D, but illustrates that the two spectral channels 18a and 18b are simultaneously imaged by phase sensors 744 and 746, which are two separate regions of a single phase sensor array 748 (images 18a and 18b, respectively). 画像 and 18b 画像 ) as described in FIG. 3 . Phase sensor array 748 may be a pixelated polarizer mask array bonded or otherwise constructed to be part of a sensor array, e.g., a CCD or CMOS, which is split into two regions, as indicated by dotted line 749, to produce two phase sensors 744 and 746. Because phase sensors 744 and 746 are different regions of a single phase sensor array 748, phase sensors 744 and 746 are synchronized to simultaneously capture two spectral channels 18 a and 18 b and have the same settings, shutters, gains, etc. Additionally, the relative positions of phase sensors 734 and 736 may be fixed, e.g., mechanically or mechanically and digitally calibrated, so that image 18 a is captured. 画像 and 18b 画像 are laterally aligned within sub-pixel accuracy.

[0050] 7F illustrates the use of a metasurface 752 configured to receive coupled light 700 from polarization interferometer optics 5 and split the light into two spectral channels 18a and 18b. The metasurface 752 may be bonded or otherwise coupled to a phase sensor array 758 (e.g., as shown in FIG. 3), but is shown separated in FIG. 7F for illustrative purposes. The metasurface 752 may be configured such that each point (e.g., each pixel on the metasurface) is split into two spectral channels 18a and 18b that are directed to be incident on two separate unit cells of the phase sensor array 758. The two unit cells of the phase sensor array 758 thus split the light into two spectral channels 18a and 18b. 画像 The metasurface 752 and the phase sensor array 758 capture two spectral channels 18a and 18b from the same location within the image sensor. Thus, the metasurface 752 and the phase sensor array 758 function as two interlaced phase sensors configured to simultaneously capture two distinct spectral channels. Other configurations of the metasurface 752 and the phase sensor array 758 are possible. Different sensors with co-aligned color images exist, and the pixelated polarization mask of the phase sensor can be combined with a sensor made from vertically stacked color photodiodes, each with a different spectral sensitivity. The spectral splitting occurs in the vertical stack of photodiodes, and the two spectral channels are captured by two co-aligned vertically stacked pixel arrays.

[0051] 8A and 8B illustrate, by way of example, sub-pixel alignment of corresponding pixels in pixelated polarization phase sensors. Figure 8A illustrates a first pixelated polarization phase sensor 802 capturing a first image 804 of a test object in a first spectral channel and a second pixelated polarization phase sensor 812 capturing a second image 814 of the test object in a second spectral channel. It should be understood that the first image 804 and the second image 814 are the same image of the test object, generated, for example, by splitting the combined beam 11 (as shown in FIG. 1 ). The first pixelated polarization phase sensor 802 and the second pixelated polarization phase sensor 812 may be aligned with sub-pixel precision, for example, in lateral, rotational, skew, magnification, field aberrations, etc. (indicated by arrow 815), so that the same location on the test object, indicated by crosshairs 800, is imaged into corresponding pixels 806 and 816 in the first pixelated polarization phase sensor 802 and the second pixelated polarization phase sensor 812. FIG. 8B illustrates the sub-pixel alignment of the first pixelated polarization phase sensor 802 and the second pixelated polarization phase sensor 812 by showing the second pixelated polarization phase sensor 812 (in dotted lines) overlapping the first pixelated polarization phase sensor 802. As can be seen in FIG. 8B, the same location on the test object, indicated by crosshairs 800, is imaged into corresponding pixels in the first pixelated polarization phase sensor 802 and the second pixelated polarization phase sensor 812.

[0052] FIG. 9 shows a pixelated polarization phase sensor 902 overlaid with RGB Bayer filters (shown in different shading) to collect three spectral (RGB) channels. FIG. 9 also shows an image 904 of a test object collected by the pixelated polarization phase sensor 902 with three spectral channels. As can be seen, due to the multiple spectral channels, the unit cell 903 of the pixelated polarization phase sensor 902 is four pixels in height and width. While the pixelated polarization phase sensor 902 can capture an image 904 in all three spectral channels in a single shot, the corresponding pixels of each spectral channel image different locations on the test object. For example, pixels 906R, 906G, and 906B corresponding to the red, green, and blue spectral channels are adjacent pixels in the array (i.e., they are a full pixel apart) and therefore image different locations on the test object. While pixelated polarization phase sensor 902 may be suitable for measuring relatively smooth surfaces, e.g., surfaces with little or no local height variation between pixels, it is not suitable for measuring surface roughness as contemplated herein, e.g., surface roughness having local heights greater than an individual λ or λ, λ / 8, or λ / 4 (or more) between the measured pixels. In addition, pixelated polarization phase sensor 902 without subpixel alignment is larger to accommodate the spectral channels; i.e., unit cell 903 is significantly larger than unit cells 803 and 813 of respective pixelated polarization phase sensors 802 and 812; therefore, the high-frequency components of roughness that can be resolved by pixelated polarization phase sensor 902 are significantly reduced, e.g., reduced by half.

[0053] Alignment of the phase sensors may be performed mechanically, as described above. In some implementations, it may be desirable to additionally or alternatively align the phase sensors digitally to further refine the alignment and correct for possible field aberrations, residual relative camera / image tilt effects, temperature effects, etc. Digital alignment of the phase sensors may be performed through a calibration process. By applying a digital calibration process partially to an image captured by one phase sensor, or partially to both images captured by both phase sensors, each newly generated image is aligned with sub-pixel accuracy to within a small fraction of a pixel's width, e.g., less than 20%, 10%, or 5% of the pixel's width.

[0054] A suitable software application may be utilized by computer 32 (see FIG. 1 ) for data acquisition and processing for each of the aforementioned implementations of a measurement system according to the present disclosure. The software application preferably causes computer 34 to acquire, process, analyze, and display data on display 36. Data acquisition may be accomplished, for example, by recording a single interferogram from each phase sensor 20 and 21. A wrapped phase map at the equivalent wavelength is then calculated using an algorithm such as Equation 5. The result is unwrapped to yield a map of the phase difference between the reference and object wavefronts at the equivalent wavelength. As is well understood in the art, “unwrapping” refers to a procedure used to remove the modulo 2π ambiguity that is characteristic of interferometric data.

[0055] Figure 10 illustrates the performance of a measurement system according to the present disclosure. In particular, the image shown in Figure 10 was acquired using a Linnik-type interferometer system similar to that shown in Figure 5, equipped with a light source generating a central wavelength λ of 567 nm with a full width of 100 nm, a first spectral filter with a central wavelength λ of 535 nm, and a second spectral filter with a central wavelength λ of 560 nm. A high-quality flat mirror was used as the reference mirror 216, and a polished cylinder was used as the test object 214. The measurement showed a structure with vertical features with a height of 6 microns, much larger than the wavelength of light (567 nm), demonstrating that single-shot surface roughness measurements of optically non-smooth surfaces can be achieved with high vertical resolution, submicron lateral resolution, and a large field of view, e.g., 754 μm.

[0056] The above description is intended to be illustrative and not limiting. For example, the above examples (or one or more aspects thereof) may be used in combination with each other. Other implementations may be used, for example, by one of ordinary skill in the art, upon reviewing the above description. Also, various features may be grouped together, and fewer than all features of a particular disclosed implementation may be used. For example, although the present disclosure has been described throughout using primarily linearly polarized test and reference beams directed at pixelated phase masks, circularly polarized beams will function similarly in all of the disclosed systems, as long as they are orthogonally polarized. Accordingly, the following aspects are hereby incorporated into the above description as examples or implementations, and it is contemplated that each aspect stands on its own as a separate implementation, and that such implementations can be combined with each other in various combinations or permutations. Therefore, the spirit and scope of the appended claims should not be limited to the foregoing description.

Claims

1. 1. A polarization interferometer for determining the surface roughness of a test object, comprising: an illumination source producing light having a plurality of wavelengths; polarization interferometer optics that split the light into two orthogonally polarized beams, including a reference beam and a test beam, the test beam incident on the test object and returned from the test object, the polarization interferometer optics recombining the test beam and the reference beam into a combined beam; at least one spectral filter that spectrally filters the combined beam into two spectral channels, a first spectral channel having a first center wavelength and a second spectral channel having a second center wavelength, the first center wavelength and the second center wavelength being different; two pixelated polarization phase sensors configured to simultaneously capture images of the two spectral channels, the two pixelated polarization phase sensors configured to generate a phase map of the surface of the test object corresponding to equivalent wavelengths of the first central wavelength and the second central wavelength; a computer configured to determine the surface roughness of the test object based on the phase map, wherein the surface roughness of adjacent height variations is greater than a root mean square (RMS) of 20 nanometers (nm).

2. The polarization interferometer of claim 1 , wherein the illumination source comprises a polarizer that controls the polarization state and orientation of the light received by the polarization interferometer optics.

3. The polarization interferometer of claim 1 , wherein the illumination source includes a light source that produces polarized light.

4. 10. The polarization interferometer of claim 1, wherein the surface roughness of the test object is between 50 nm and 10 micrometers.

5. The polarization interferometer of claim 1 , wherein the illumination source comprises one of a single broadband light source, a single light source producing multiple wavelengths, or multiple light sources.

6. a beam splitter that splits the combined beam into a first sub-beam and a second sub-beam; The at least one spectral filter comprises: a first spectral filter receiving the first sub-beam and filtering the first sub-beam to generate the first spectral channel having the first center wavelength; a second spectral filter that receives the second sub-beam and filters the second sub-beam to produce the second spectral channel having the second center wavelength.

7. 10. The polarization interferometer of claim 1, wherein the at least one spectral filter comprises a dichroic beam splitter that splits the combined beam into the first spectral channel having the first center wavelength and the second spectral channel having the second center wavelength.

8. The polarization interferometer of claim 1 , wherein the at least one spectral filter comprises a pixelated wavelength filter on the two pixelated polarization phase sensors.

9. 2. The polarization interferometer of claim 1, wherein the first and second central wavelengths differ by at least 10 nm.

10. 10. The polarization interferometer of claim 1, wherein the surface roughness has adjacent height variations greater than 1 / 8 of an individual measurement wavelength across a single pixel width but less than 1 / 4 of an equivalent wavelength.

11. 10. The polarization interferometer of claim 1, wherein the two pixelated polarization phase sensors are one of separate sensor arrays in different cameras, separate sensor arrays in a single camera, or different regions of a single sensor array.

12. The polarization interferometer of claim 1 , further comprising a computer configured to digitally align the two pixelated polarization phase sensors based on calibration data.

13. 1. A polarization interferometry method for determining surface roughness of a test object, comprising: generating light having a plurality of wavelengths using an illumination source; splitting the light into two orthogonally polarized beams, including a reference beam and a test beam, using polarization interferometer optics, where the test beam is incident on the test object and returned from the test object; and recombining the test beam and the reference beam into a combined beam using the polarization interferometer optics; spectrally filtering the combined beam with at least one spectral filter into two spectral channels, a first spectral channel having a first center wavelength and a second spectral channel having a second center wavelength, the first center wavelength and the second center wavelength being different; simultaneously capturing images of the two spectral channels using two pixelated polarization phase sensors; generating a phase map of the surface of the test object corresponding to equivalent wavelengths of the first central wavelength and the second central wavelength; determining the surface roughness of the test object based on the phase map, wherein the surface roughness of adjacent height variations is greater than a root mean square (RMS) of 20 nanometers (nm).

14. 14. The method of claim 13, further comprising using a polarizer to control the polarization state and polarization orientation of the light received by the polarization interferometer optics.

15. The method of claim 13 , further comprising polarizing the light using a light source of the illumination source.

16. The method of claim 13, wherein the surface roughness of the test object is between 50 nm and 10 micrometers.

17. further comprising splitting the combined beam into a first sub-beam and a second sub-beam using a beam splitter; Spectrally filtering the combined beam into the two spectral channels with the at least one spectral filter includes: filtering the first sub-beam with a first spectral filter that receives the first sub-beam and generates the first spectral channel having the first center wavelength; and filtering the second sub-beam with a second spectral filter that receives the second sub-beam and produces the second spectral channel having the second center wavelength.

18. 14. The method of claim 13, wherein spectrally filtering the combined beam into the two spectral channels using at least one spectral filter comprises splitting the combined beam into the first spectral channel having the first center wavelength and the second spectral channel having the second center wavelength using a dichroic beam splitter.

19. The method of claim 13 , wherein the at least one spectral filter comprises a pixelated wavelength filter on the two pixelated polarization phase sensors.

20. 14. The method of claim 13, wherein the first central wavelength and the second central wavelength differ by at least 10 nm.

21. 14. The method of claim 13, wherein the surface roughness has adjacent height variations greater than 1 / 8 of a measurement wavelength across a single pixel width.

22. 14. The method of claim 13, wherein the two pixelated polarization phase sensors are one of separate sensor arrays in different cameras, separate sensor arrays in a single camera, or different regions of a single sensor array.

Images