A free-form surface adaptive measurement device and method based on fourier spot analysis

Abstract

The application discloses a free-form surface adaptive measurement device and method based on Fourier spot analysis, in particular to a free-form surface adaptive zero-position interferometer device for large surface shape deviation, and belongs to the field of optical detection. The device comprises a light source system, an adaptive compensation system, an interference system and a surface to be measured. The liquid crystal spatial light modulator is used for guiding aberration compensation of the adaptive element through analysis of Fourier transform spots of the system, and the dependence on an interference pattern is broken, so that the measurement range of the traditional adaptive interferometer is greatly expanded, and destructive modification of a traditional interferometer light path is not needed.

Description

Technical Field

[0001] This invention belongs to the field of optical detection technology, specifically relating to an adaptive measurement device and method for freeform surfaces based on Fourier spot analysis, which is particularly suitable for null-point interferometry measurement of freeform surfaces with large surface deviations. Background Technology

[0002] Freeform surfaces, due to their non-rotational symmetry and the resulting multiple degrees of design freedom, are widely used in ultraviolet lithography systems, synchrotron radiation systems, large telescope systems, and remote sensing systems. The surface accuracy of freeform surfaces directly impacts the performance of optical systems. To accurately detect surface errors in optical components and further guide manufacturing, high-precision and high-resolution wavefront interferometry is typically used. For components under test with significant surface deviations, compensators with inherent aberration corrections, such as Offner compensators, Dall compensators, and computer holograms (CGH), are commonly employed. However, due to limited compensation capabilities and the one-to-one relationship between the compensator and the surface under test, fixed compensators are almost exclusively used for final testing, making them extremely expensive. In recent years, adaptive wavefront interferometry (AWI), which incorporates dynamic optical elements such as spatial light modulators (SLMs) and deformable mirrors (DMs) into interferometers, has expanded the measurement range of traditional interferometers. However, existing control algorithms for adaptive interferometers largely rely on the identification, reconstruction, and sparsification of interference fringe patterns. When facing freeform surfaces with extremely large deviations in shape (such as during the rough polishing stage), interference fringes are often difficult to form or completely indistinguishable, leading to algorithm failure and the inability to perform measurements.

[0003] Therefore, there is an urgent need to develop an adaptive interferometry method that does not rely on interference fringe patterns in order to overcome the limitations of current technology in detecting large deviations from freeform surfaces. Summary of the Invention

[0004] The purpose of this invention is to overcome the measurement failure problem caused by the reliance on interference fringe patterns when dealing with large-area deviations from freeform surfaces in existing adaptive interferometry techniques. This invention proposes an adaptive measurement device and method for freeform surfaces based on Fourier spot analysis. By analyzing the characteristics of the Fourier spot distribution, zero-point testing of the freeform surface is achieved. Theoretically, regardless of the surface error, a spot pattern will appear on the Fourier surface, thus greatly expanding the measurement range of adaptive interferometry. A population-based non-metaphorical metaheuristic algorithm is used to effectively explore the target region within the search space and ensure optimal convergence. A liquid crystal spatial light modulator is used as a dynamic compensation element.

[0005] The technical solution of the present invention is as follows:

[0006] An adaptive measurement device for freeform surfaces based on Fourier spot analysis is characterized by comprising a light source system, an adaptive compensation analysis system, an interferometric system, and a computer.

[0007] The light source system includes a laser, a first polarizer and beam expander, and a first λ / 4 waveplate and polarization beam splitter arranged sequentially along the optical path;

[0008] The adaptive compensation system includes a second λ / 4 waveplate, a second polarizer, and a liquid crystal spatial light modulator arranged sequentially along the beam propagation direction on the transmission side of the polarization beam splitter; a third λ / 4 waveplate, a partial null compensation mirror, and a station for placing the component under test arranged sequentially along the beam propagation direction on the reflection side of the polarization beam splitter; and a third polarizer, a first lens, a beam splitter, and a first image sensor arranged sequentially along the beam propagation direction on the optical path opposite to the reflected light of the polarization beam splitter. The liquid crystal spatial light modulator is connected to the computer for loading a dynamically compensated wavefront according to computer instructions, and the first image sensor is connected to the computer for acquiring Fourier surface spot images and transmitting them to the computer.

[0009] The interference system includes a pinhole aperture, a second lens, and a second image sensor arranged sequentially along the beam propagation direction, and the second image sensor is connected to the computer for acquiring interference images and transmitting them to the computer.

[0010] The computer is configured to: in the optimization phase, control the third polarizer to minimize the intensity of the reference beam, calculate the evaluation function value based on the Fourier surface spot image acquired by the first image sensor, and use an optimization algorithm to iteratively generate a compensation wavefront loaded onto the liquid crystal spatial light modulator with the goal of optimizing the evaluation function value, until the Fourier surface spot reaches the system diffraction limit; in the measurement phase, control the third polarizer to match the intensity of the reference beam with the intensity of the test beam, obtain the residual wave aberration based on the interferogram acquired by the second image sensor, and reconstruct the surface shape error of the surface under test by combining the compensation wavefront obtained in the optimization phase.

[0011] Furthermore, the operating wavelength of the laser is consistent with the operating wavelength of the liquid crystal spatial light modulator, and the optical axis direction of the second polarizer is consistent with the response polarization state of the liquid crystal spatial light modulator.

[0012] Furthermore, the polarization beam splitter is used to split the incident circularly polarized light into a transmitted P-polarized light component and a reflected S-polarized light component, and to provide a common or split propagation path for the reference light and the test light; the intensity of the reference light is adjusted by rotating the third polarizer.

[0013] Furthermore, the first lens, the pinhole aperture, and the second lens constitute a Kepler telescope system for spatial filtering and imaging of the Fourier surface.

[0014] Furthermore, the partial null compensation mirror is a spherical lens, an aspherical lens, or a computational hologram, used to provide basic aberration compensation; the liquid crystal spatial light modulator is a reflective spatial light modulator or a deformable mirror, used to provide dynamically programmable higher-order aberration compensation.

[0015] On the other hand, the present invention provides an adaptive measurement method for freeform surfaces based on Fourier spot analysis, employing the aforementioned device, characterized by comprising the following steps:

[0016] Step 1. Turn on the light source system to generate a collimated beam with a polarized state, which is then split into a reference beam and a measurement beam for illuminating the surface under test by a polarization beam splitter;

[0017] Step 2. Adjust the polarization element in the adaptive compensation system to match the polarization state of the beam incident on the liquid crystal spatial light modulator with its response polarization state. The modulated beam carries the compensation wave before and after forming the test beam, which is then combined with the reference beam.

[0018] Step 3. Rotate the third polarizer to minimize the intensity of the reference light, acquire the initial Fourier surface light spot image through the first image sensor and transmit it to the computer; the computer calculates the evaluation function value of the light spot image, and uses an optimization algorithm to iteratively optimize the compensation wavefront loaded onto the liquid crystal spatial light modulator with the goal of optimizing the evaluation function value, until the Fourier surface light spot reaches the system diffraction limit, at which point the zero-position detection condition is met;

[0019] Step 4: Rotate the third polarizer to match the intensity of the reference light with the intensity of the test light, acquire the interferogram through the interferometer system, and calculate the residual wave aberration of the system from the interferogram;

[0020] Step 5: Establish a ray tracing model for the entire system. Substitute the compensated wavefront obtained from Step 3 and the residual wave aberration measured in Step 4 into the model to calculate the actual surface shape of the surface to be measured. Subtract the actual surface shape from the theoretical surface shape to obtain the surface shape error distribution of the surface to be measured.

[0021] Furthermore, the compensation wavefront described in step 3 is characterized using a Zernike fringe polynomial, and the dynamic adjustment of the compensation wavefront is achieved by optimizing the coefficients of the polynomial.

[0022] Furthermore, the evaluation function mentioned in step 3 is an index used to quantify the energy concentration of the light spot, including Strell ratio, circumferential energy, or average radius; the optimization objective is to maximize the Strell ratio or circumferential energy, or minimize the average radius, so that the light spot approaches the diffraction limit.

[0023] Furthermore, the optimization algorithm described in step 3 is a population-based metaheuristic optimization algorithm. Its search process is based on the fourth-order Jung-Kutta algorithm for gradient estimation and includes a solution quality enhancement mechanism. The specific steps include:

[0024] Step 3.1: Initialization, randomly generate N sets of Zernike polynomial coefficients as the initial population;

[0025] Step 3.2: Calculate the gradient direction of population evolution based on the fourth-order Jung-Kutta algorithm, and determine the current optimal and worst solutions by combining the individual evaluation function values;

[0026] Step 3.3: Adopt an adaptive search strategy to determine whether individuals in the population should conduct global exploration or local development based on random numbers in order to generate new Zernike polynomial coefficients;

[0027] Step 3.4: Introduce a solution quality enhancement mechanism, which generates potential better solutions by combining information from multiple excellent individuals, and compares and selects between these solutions and the current solutions;

[0028] Step 3.5: Determine whether the preset termination condition has been met. If so, stop the optimization and output the optimal compensation wavefront; otherwise, return to sub-step 3.2.

[0029] This invention utilizes an optimizer to optimize the phase compensation of a spatial light modulator, using the mean radius (MR) as the evaluation function and the system diffraction limit as the final optimization objective. The overall idea is to optimize the initially generated subgroup, using the fourth-order Jung-Kutta algorithm to calculate the gradient, and employing enhanced solution quality (ESQ) to generate the Zernike fringe polynomial coefficients at the end of each iteration. After several iterations, the interference fringes are sparsified to a few fringes. Then, using a ray tracing model of the entire system, the surface shape error distribution of the measured surface is output.

[0030] Compared with the prior art, the technical effects of the present invention are as follows:

[0031] 1) The biggest difference from traditional adaptive interferometry is that adaptive interferometry based on Fourier surface spot analysis does not rely on the reconstruction, sparsification, identification, and unwrapping of interferograms. By analyzing the Fourier surface spot to guide the iterative optimization principle, it can theoretically test all freeform surfaces, because regardless of the size of the surface deviation of the freeform surface, there will inevitably be a spot pattern on the Fourier surface.

[0032] 2) The method of this invention has a fast measurement speed and can compensate for freeform wavefronts with peak-to-valley (PV) values ​​of tens to hundreds of wavelengths and root-mean-square (RMS) values ​​of tens of wavelengths within dozens of iterations. The RUN optimizer is superior to the SPGD algorithm in terms of convergence speed, convergence ability, and avoidance of getting trapped in local optima.

[0033] 3) By combining λ / 4 waveplates and polarizers, independent control of the reference and test beams on the Fourier and interference surfaces was achieved, providing an optical path foundation for Fourier spot analysis and interferometric measurements. Employing a metaheuristic optimizer based on the fourth-order Jung-Kutta algorithm, combined with a solution quality enhancement strategy, rapid convergence of large-area deviations from the wavefront can be achieved within dozens of iterations, demonstrating both global search and local refinement capabilities.

[0034] 4) The device and method of the present invention are applicable to various surface shapes such as plane, sphere, aspherical and freeform surface, and are compatible with various interference structures such as Fizeau type, Tyman-Green type, and Michelson type, and have good scalability and versatility. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the overall structure of the freeform surface adaptive measurement device based on Fourier surface spot analysis of the present invention.

[0036] Figure 2 This is a schematic diagram of the polarization optical path of the adaptive compensation system in this invention;

[0037] Figure 3 This is a simulation diagram of the changes in Fourier spot and corresponding interferogram during the detection optimization process in this invention. (a) Fourier spot diagram in the initial state; (b) Interferogram in the initial state; (c) Fourier spot diagram after optimization, at which point the spot is close to the system diffraction limit; (d) Interferogram after optimization, at which point the zero-position detection condition has been reached and the interference fringes have become sparse to the zero-fringe state.

[0038] Figure 4 This is a graph showing the change of the evaluation function value of the Fourier spot detection in this invention with the number of iterations;

[0039] Figure 5 This is a comparison diagram of the detection results of the present invention and the detection results of the Zygo commercial interferometer, wherein (a) is the surface shape error distribution diagram obtained by the method of the present invention; (b) is the surface shape error distribution diagram obtained by the Zygo interferometer; and (c) is the surface shape error distribution diagram after point-to-point subtraction between the detection results of the present invention and the Zygo detection results. Detailed Implementation

[0040] The technical solution of the present invention will be described in detail and completely below with reference to the accompanying drawings and embodiments. However, the examples described herein are not all embodiments and should not be used to limit the scope of protection of the present invention.

[0041] like Figure 1 As shown, this embodiment provides a freeform surface adaptive interferometer device based on Fourier surface spot analysis, including: a light source system S1, an adaptive compensation system S2, and an interferometer system S3;

[0042] The light source system S1 includes a laser L1, a first polarizer L2 and a beam expander L3, a first λ / 4 waveplate L4, and a polarizing beam splitter L5, all placed horizontally in sequence. The beam emitted from the laser L1 is converted into linearly polarized light by the first polarizer L2, then expanded into a collimated beam by the beam expander L3, and finally converted into circularly polarized light by the first λ / 4 waveplate L4 before entering the polarizing beam splitter L5.

[0043] The adaptive compensation system S2 includes a second λ / 4 waveplate L6, a second polarizer L7, and a liquid crystal spatial light modulator L8 arranged horizontally in sequence on the transmission side of the polarization beam splitter L5; a third λ / 4 waveplate L9, a partial null compensation mirror L10, and a test surface S4 arranged in sequence along the optical path on the reflection side of the polarization beam splitter L5; and a third polarizer L11, a first lens L12, a beam splitter L13, and a first image sensor L14 arranged in sequence in the reverse optical path of the polarization beam splitter L5.

[0044] The interference system S3 includes a pinhole aperture L15, a second lens L16, and a second image sensor L17, which are arranged horizontally in sequence on the reflection of the beam splitter L13.

[0045] The liquid crystal spatial light modulator L8, the first image sensor L14, and the second image sensor L17 are respectively connected to the computer L18 to realize closed-loop control and data processing.

[0046] In this embodiment, the operating wavelength of the laser L1 is the same as that of the liquid crystal spatial light modulator L8, and the optical axis direction of the second polarizer L7 is the same as the operating polarization state of the liquid crystal spatial light modulator L8; the third polarizer L11 is used to adjust the intensity of the reference light; the first lens L12, the pinhole aperture L15, and the second lens L16 constitute a Kepler telescope system for imaging the Fourier surface.

[0047] Polarizing beam splitter L5 splits the incident light into two beams, wherein the transmission side is the P-polarized light component and the reflection side is the S-polarized light component; the reference light intensity of the interference system S3 is adjusted by rotating the third polarizer L11; beam splitter L13 splits the incident light into two beams, with the transmission side and the reflection side having the same polarization state.

[0048] The adaptive measurement method for freeform surfaces based on Fourier leaf surface spot analysis includes the following steps:

[0049] Step 1) Optical path setup and initialization:

[0050] according to Figure 1 The measurement optical path is set up as shown. Laser L1 is started, and all optical components are adjusted to be coaxial. The optimizer parameters are initialized on computer L18, setting the number of terms in the Zernike fringe polynomial (e.g., the first 36 terms or more, depending on the surface complexity), and N initial subgroups are randomly generated, each subgroup representing a set of Zernike coefficient vectors Z=[c1,c2,...,c...]. n ].

[0051] Step 2: Beam separation and polarization control:

[0052] The laser beam emitted from laser L1 is converted into linearly polarized light by the first polarizer L2, then expanded and collimated by beam expander L3, and finally converted into circularly polarized light by the first λ / 4 waveplate L4. The circularly polarized light is then split into two parts by polarizing beam splitter L5:

[0053] Test optical path: The P-polarized component of the circularly polarized light enters the adaptive compensation system S2 through the polarization beam splitter L5. After passing through the second λ / 4 waveplate L6, it becomes circularly polarized again. After the stray polarization state is filtered out by the second polarizer L7, it becomes linearly polarized light with the response direction consistent with the liquid crystal spatial light modulator L8. This linearly polarized light is reflected by the liquid crystal spatial light modulator L8, and after phase compensation, it returns along the same path, passing through the second polarizer L7 and the second λ / 4 waveplate L6 again to become circularly polarized. At this time, the S-polarized component of the circularly polarized light is reflected by the polarization beam splitter L5, passes through the third λ / 4 waveplate L9 and the partial zero-position compensation mirror L10, and illuminates the test surface S4. After being reflected by the test surface S4, the beam returns along the same path, passing through the partial zero-position compensation mirror L10 and the third λ / 4 waveplate L9 again. Because it passes through the λ / 4 waveplate twice, its polarization state rotates by 90°, changing from S-polarized light to P-polarized light. It then passes through the polarization beam splitter L5 and the third polarizer L11 to form a test beam.

[0054] Reference beam: The S-polarized component of circularly polarized light is reflected by polarization beam splitter L5 and passes through the third polarizer L11 into interference system S3, serving as the reference beam. By rotating the third polarizer L11, the intensity of the reference beam can be adjusted to control the presence or absence of the reference beam in adaptive compensation system S2 and the fringe contrast in interference system S3.

[0055] In this optimization process, the third polarizer L11 is rotated to minimize the intensity of the reference light (close to extinction) in order to avoid the reference light interfering with the light spot morphology analysis on the Fourier surface.

[0056] Step 3: Fourier Leaf Spot Acquisition and Initial Evaluation:

[0057] After the test beam and the reference beam are combined, they pass through the first lens L12 and are split into two parts by the beam splitter L13. The transmitted beam is focused onto the target surface of the first image sensor L14, which is the Fourier transform surface (spectral surface) of the system.

[0058] Computer L18 controls the first image sensor L14 to acquire the current Fourier surface light spot image, and records its gray-level distribution matrix as I0, which is then input into computer L18.

[0059] Define an evaluation function J to measure the quality of the light spot, as shown in the following formula:

[0060] (2)

[0061] In the formula, (x,y) are pixel coordinates, and (x',y') are the centroid coordinates of the light spot.

[0062] Step 4: Optimize control and zero-point detection

[0063] The L18 computer runs the optimizer to iteratively optimize the Zernike coefficients loaded on the L8 of the liquid crystal spatial light modulator. The compensation wavefront is represented by a Zernike fringe polynomial, and the optimization objective is to make the Fourier surface spot approach the system's diffraction limit. The specific process is as follows:

[0064] 4.1 Initialization: All learning parameters are initialized. N (N≥20) initial subgroups are randomly generated based on the boundary conditions. Each subgroup represents a set of Zernike fringe polynomial coefficients, as shown in the following formula:

[0065]

[0066] In the formula, rand represents a random number within the interval [0,1], and L l and U l The l-th parameter of the n-th subgroup The upper and lower boundaries.

[0067] 4.2 Optimal Solution Search Process: The optimal solution search mechanism is based on the fourth-order Jung-Kutta algorithm, and the formula is as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] in, and These are the optimal and worst solutions, determined by the magnitude of the evaluation function values, respectively. For displacement increment, For optimizer step size, For regulator, The average of all solutions. and These represent the current iteration number and the maximum iteration number, respectively. `round` is the rounding operation, and the evaluation function is the average radius, as shown in the following formula:

[0076]

[0077] Where: (x, y) are the pixel coordinates in the spot image I0, and (x`, y`) are the centroid coordinates of the spot image I0;

[0078] The other three weighting coefficients , and The formula is as follows:

[0079]

[0080]

[0081]

[0082] 4.3 Position Update: Generate the initial striped Zernikal polynomial coefficients for the next iteration If the generated random number is less than 0.5, a global search is used, as shown in the following formula:

[0083]

[0084] Otherwise, use a local search, as shown in the following formula:

[0085]

[0086] Where SF is the adaptive factor, and the formula is as follows:

[0087]

[0088]

[0089]

[0090] Where a and b are integers used to balance the global search and the local search, r is used to determine whether to search for the optimal solution in the direction of the maximum or minimum of the evaluation function, and is 1 or -1, g is a random number in the interval [0, 2], and randn is a random number that follows a normal distribution.

[0091] x s and x s’ It can be represented as

[0092]

[0093]

[0094] In the formula,

[0095]

[0096]

[0097] in, A random number within the interval (0,1). This is the best solution to date. This is the optimal solution for each iteration.

[0098] 4.4 Solution Quality Enhancement: Using the average of three randomly selected solutions Generate a better solution from the optimal solution. ,if If the value is less than 1, the formula is as follows:

[0099]

[0100] Otherwise, the formula is as follows:

[0101]

[0102] in, It is a random number. It is a combined solution, and the formula is as follows:

[0103]

[0104]

[0105] in, is a random number within the interval [0, 1], and c is a random number within the interval [0, 5].

[0106] if The evaluation function value is greater than the current solution. Then use the following formula to generate :

[0107]

[0108] In the formula,

[0109]

[0110] Based on the evaluation function value, the optimal solution after each iteration is determined as follows: , or .

[0111] 4.5 After one iteration, update the global optimal solution and record the evaluation function value;

[0112] 4.6 Repeat the iteration until the Fourier surface spot approaches the diffraction limit, that is, the evaluation function value converges to the minimum value. At this point, the zero-position detection condition is met, and the optimization stops.

[0113] Step 5: Residual Wave Aberration Measurement

[0114] After optimization, the third polarizer L15 is rotated to match the intensity of the reference beam with that of the test beam. The reference beam and the test beam enter the interferometer system S3 via the reflection section of the beam splitter L13, then pass sequentially through the pinhole aperture L15 and the second lens L16, reaching the second image sensor L17. The residual wave aberration of the system is measured using the interferometer system S3.

[0115] Step 6: Calculation of surface shape error

[0116] Based on the optical path arrangement of the adaptive compensation system S2 and the interference system S3, a ray tracing model is established using optical software such as Zemax. The compensation wavefront formed by the optimized liquid crystal spatial light modulator L8 and the residual wave aberration measured in step 5 are substituted into the model.

[0117] The wavefront data of the surface of the test surface S4 was calculated using optical software such as Zemax and Matlab and data analysis software. The wavefront data was then subtracted point-to-point from the theoretical surface shape of the test surface S4 to obtain the surface shape error distribution of the test surface S4.

[0118] This embodiment uses the above method to perform simulation and experimental testing on freeform surfaces with large surface deviations. The surface shape to be tested in the simulation testing consists of the first 15 Zernike polynomials, with each coefficient ranging from [-30λ, 30λ] (λ=633nm). The resolution of the spot pattern and the interferogram is the same, both being 1024x1024, and the number of subgroups N=20. The other settings remain unchanged. The parameter settings for the experimental testing and the simulation testing are the same.

[0119] like Figure 3 The image shown is a simulation testing example. Figure 3 (a) is the Fourier pattern of the light spot in the initial state. Figure 3 (b) shows the corresponding interferogram. It can be seen that the fringes in most areas of the initial interferogram are indistinguishable, indicating that the surface under test has a large surface shape deviation. Figure 3 (c) is the Fourier spot pattern after optimization, which is close to the diffraction limit of the system; Figure 3 (d) shows the corresponding interferogram, which has formed sparse fringes, achieving the zero-fringe detection condition. It can be seen that by using the method of this patented invention to adaptively compensate the freeform surface wavefront, even if most pixels in the initial interferogram are unrecognizable, this method can still guide the modulation of the compensated wavefront through the principle of Fourier spot analysis, ultimately optimizing it to the diffraction limit, achieving zero-fringe detection, and forming a zero-fringe interferogram.

[0120] like Figure 4 The diagram shows an experimental detection example. In the initial interferogram, the indistinguishable region exceeded 90%, indicating that the surface under test, S4, is a freeform surface with a large deviation in shape. Neither traditional interferometers nor adaptive interferometers based on interferogram analysis can effectively detect this. The experiment demonstrates that an adaptive interferometer for freeform surfaces based on Fourier surface spot analysis can be optimized within dozens of iterations, resulting in an interferogram with only a few fringes. Using a commercial interferometer and optical software for ray tracing, it can detect freeform surfaces with large deviations, and is particularly suitable for detecting freeform surfaces in the rough polishing stage. Figure 5 This paper presents the detection results of this invention and compares them with those of the Zygo commercial interferometer. Figure 5 (a) shows the surface shape error distribution detected by the method of the present invention. Figure 5 (b) shows the detection results from the Zygo commercial interferometer. Figure 5 (c) shows the residual distribution after point-to-point subtraction of the two. The results show that the method of the present invention is highly consistent with the detection results of commercial interferometers, verifying the measurement accuracy of the present invention.

[0121] As a variant embodiment of the present invention, the structure of the interferometric system S3 can be a Fizeau-type, Thyman-Green-type, or Michelson-type interferometric optical path. The partial null compensation mirror L10 can be an optical element capable of generating specific aberration compensation, such as a spherical lens, an aspherical lens, or a computational hologram. The liquid crystal spatial light modulator can employ an optical element capable of modulating the wavefront, such as a deformable mirror. The evaluation function can use Strell ratio, sharpness function, or circumferential energy instead of the average radius. The surface to be measured S4 can be a plane, a sphere, an aspherical surface, or a freeform surface.

[0122] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A freeform surface adaptive measurement device based on Fourier spot analysis, characterized in that: Includes a light source system, an adaptive compensation analysis system, an interferometric system, and a computer: The light source system includes a laser, a first polarizer and beam expander, and a first λ / 4 waveplate and polarization beam splitter arranged sequentially along the optical path; The adaptive compensation system includes a second λ / 4 waveplate, a second polarizer, and a liquid crystal spatial light modulator arranged sequentially along the beam propagation direction on the transmission side of the polarization beam splitter; a third λ / 4 waveplate, a partial null compensation mirror, and a station for placing the component under test arranged sequentially along the beam propagation direction on the reflection side of the polarization beam splitter; and a third polarizer, a first lens, a beam splitter, and a first image sensor arranged sequentially along the beam propagation direction on the optical path opposite to the reflected light of the polarization beam splitter. The liquid crystal spatial light modulator is connected to the computer for loading a dynamically compensated wavefront according to computer instructions, and the first image sensor is connected to the computer for acquiring Fourier surface spot images and transmitting them to the computer. The interference system includes a pinhole aperture, a second lens, and a second image sensor arranged sequentially along the beam propagation direction, and the second image sensor is connected to the computer for acquiring interference images and transmitting them to the computer. The computer is configured to: in the optimization phase, control the third polarizer to minimize the intensity of the reference beam, calculate the evaluation function value based on the Fourier surface spot image acquired by the first image sensor, and use an optimization algorithm to iteratively generate a compensation wavefront loaded onto the liquid crystal spatial light modulator with the goal of optimizing the evaluation function value, until the Fourier surface spot reaches the system diffraction limit; in the measurement phase, control the third polarizer to match the intensity of the reference beam with the intensity of the test beam, obtain the residual wave aberration based on the interferogram acquired by the second image sensor, and reconstruct the surface shape error of the surface under test by combining the compensation wavefront obtained in the optimization phase.

2. The adaptive measurement device for freeform surfaces based on Fourier spot analysis according to claim 1, characterized in that: The operating wavelength of the laser is the same as the operating wavelength of the liquid crystal spatial light modulator, and the optical axis direction of the second polarizer is the same as the response polarization state of the liquid crystal spatial light modulator.

3. The adaptive measurement device for freeform surfaces based on Fourier spot analysis according to claim 1, characterized in that: The polarization beam splitter is used to split the incident circularly polarized light into a transmitted P-polarized light component and a reflected S-polarized light component, and to provide a common or split propagation path for the reference light and the test light; the intensity of the reference light is adjusted by rotating the third polarizer.

4. The adaptive measurement device for freeform surfaces based on Fourier spot analysis according to claim 1, characterized in that: The first lens, the pinhole aperture, and the second lens constitute a Kepler telescope system, used for spatial filtering and imaging of the Fourier surface.

5. The adaptive measurement device for freeform surfaces based on Fourier spot analysis according to claim 1, characterized in that: The zero-position compensation mirror is a spherical lens, an aspherical lens, or a computational hologram, used to provide basic aberration compensation; the liquid crystal spatial light modulator is a reflective spatial light modulator or a deformable mirror, used to provide dynamically programmable higher-order aberration compensation.

6. A freeform surface adaptive measurement method based on Fourier spot analysis, employing the apparatus described in any one of claims 1-5, characterized in that, Includes the following steps: Step 1. Turn on the light source system to generate a collimated beam with a polarized state, which is then split into a reference beam and a measurement beam for illuminating the surface under test by a polarization beam splitter; Step 2. Adjust the polarization element in the adaptive compensation system to match the polarization state of the beam incident on the liquid crystal spatial light modulator with its response polarization state. The modulated beam carries the compensation wave before and after forming the test beam, which is then combined with the reference beam. Step 3. Rotate the third polarizer to minimize the intensity of the reference light, acquire the initial Fourier surface light spot image through the first image sensor and transmit it to the computer; the computer calculates the evaluation function value of the light spot image, and uses an optimization algorithm to iteratively optimize the compensation wavefront loaded onto the liquid crystal spatial light modulator with the goal of optimizing the evaluation function value, until the Fourier surface light spot reaches the system diffraction limit, at which point the zero-position detection condition is met; Step 4: Rotate the third polarizer to match the intensity of the reference light with the intensity of the test light, acquire the interferogram through the interferometer system, and calculate the residual wave aberration of the system from the interferogram; Step 5: Establish a ray tracing model for the entire system. Substitute the compensated wavefront obtained from Step 3 and the residual wave aberration measured in Step 4 into the model to calculate the actual surface shape of the surface to be measured. Subtract the actual surface shape from the theoretical surface shape to obtain the surface shape error distribution of the surface to be measured.

7. The adaptive measurement method for freeform surfaces based on Fourier spot analysis according to claim 6, characterized in that, The compensation wavefront described in step 3 is characterized by a Zernike fringe polynomial, and the dynamic adjustment of the compensation wavefront is achieved by optimizing the coefficients of the polynomial.

8. The adaptive measurement method for freeform surfaces based on Fourier spot analysis according to claim 6, characterized in that, The evaluation function mentioned in step 3 is an index used to quantify the energy concentration of the light spot, including Strell ratio, circumferential energy, or average radius; the optimization objective is to maximize the Strell ratio or circumferential energy, or minimize the average radius, so that the light spot approaches the diffraction limit.

9. The adaptive measurement method for freeform surfaces based on Fourier spot analysis according to claim 6, characterized in that, The optimization algorithm described in step 3 is a population-based metaheuristic optimization algorithm. Its search process is based on the fourth-order Jung-Kutta algorithm for gradient estimation and includes a solution quality enhancement mechanism. The specific steps include: Step 3.1: Initialization, randomly generate N sets of Zernike polynomial coefficients as the initial population; Step 3.2: Calculate the gradient direction of population evolution based on the fourth-order Jung-Kutta algorithm, and determine the current optimal and worst solutions by combining the individual evaluation function values; Step 3.3: Adopt an adaptive search strategy to determine whether individuals in the population should conduct global exploration or local development based on random numbers in order to generate new Zernike polynomial coefficients; Step 3.4: Introduce a solution quality enhancement mechanism, which generates potential better solutions by combining information from multiple excellent individuals, and compares and selects between these solutions and the current solutions; Step 3.5: Determine whether the preset termination condition has been met. If so, stop the optimization and output the optimal compensation wavefront; otherwise, return to sub-step 3.2.

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