Aspheric wavefront detection device and method based on multi-direction orthogonal lateral shear interference

Abstract

The invention relates to an aspheric wavefront detection device and method based on multi-direction orthogonal lateral shear interference. The device is composed of a laser, a linear polarizer, a light splitting element, a reflector array, a two-dimensional orthogonal grating array, a light splitting system, a polarization phase shifting element and a CMOS camera. The method comprises the following steps: firstly, an antisymmetric continuation method is included, secondly, dynamic phase recovery and distortion compensation are adopted, Zernike polynomial local fitting is introduced, and self-adaptive compensation is carried out on high-order aberration (such as coma aberration and trefoil aberration) of an aspheric surface edge region. According to the method, the multi-direction orthogonal lateral shearing interferogram can be obtained through single measurement, and a high-precision, high-efficiency and high-robustness solution is provided for precise detection of the aspheric optical element through cooperation of an algorithm and hardware. The method is suitable for high-precision phase recovery in the fields of optical detection, microscopic imaging and the like, and is suitable for high-precision dynamic detection of complex optical elements such as off-axis aspheric surfaces, free-form surfaces and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of optical precision measurement, and in particular to an aspheric wavefront detection device and method based on multi-directional orthogonal lateral shearing interference. Background Art

[0002] Conventional transverse shearing interferometers, such as the device disclosed in CN105445926A, use shearing in two orthogonal directions to achieve wavefront reconstruction. Zernike aberrations (such as defocus and spherical aberration) of rotationally symmetric aspheric surfaces (e.g., paraboloids and spheres) are prone to coupling effects in this orthogonal shearing mode. This directional sensitivity error can lead to measurement errors exceeding 0.05λRMS. The fundamental reason is that the two-directional shearing method cannot decouple the higher-order terms of rotationally symmetric aberrations, which can further amplify the error when measuring large-aperture or aspheres with steep curvature.

[0003] EP2894487A1 discloses the Phasics SID4 sensor. Four-way differential phase imaging requires eight frames of imagery for holographic reconstruction. Its 200ms acquisition cycle makes it difficult to avoid 10-100Hz environmental vibration interference, requiring multi-frame acquisition. This environmental vibration results in a phase reconstruction error ≥0.01λ, resulting in insufficient anti-interference capabilities and time-domain sampling defects. Measured data shows that when the vibration amplitude exceeds λ / 100, the correlation of wavefront distortion between adjacent frames drops below 0.7, causing a sharp increase in the phase unwrapping failure rate. Furthermore, multi-frame synchronization requires extremely high mechanical stability, making it difficult to apply on mobile platforms or for in-line testing.

[0004] 201611187788.7 discloses a Twyman-type point source array out-of-position synchronous phase-shifting interferometer and its measurement method, comprising a point light source and its spectroscopic component, a Twyman-type main interferometer, and a spectroscopic imaging component. The spherical wave emitted by the point light source is split into four beams by the spectroscopic component and then enters the main interferometer. The spectroscopic component is used to replicate one point light source into four identical ones. By adjusting the distance between the four point light sources and the optical axis on the focal plane of the collimating objective lens of the main interferometer, different phase shifts are introduced into the interference between the reference surface and the test surface. Then, the spectroscopic imaging component is used to simultaneously obtain four clear phase-shifted interference patterns on a CCD. The problems it has are:

[0005] 1. Affected by the phase difference calibration error of the spectroscopic component, resulting in low accuracy and low stability. When replicating four point light sources through the spectroscopic component, if the spectrometry is uneven or there is a slight difference in the optical path length, the actual phase shift between each interference pattern will deviate from the theoretical value (for example, the ideal four-step phase shift interval should be π / 2), resulting in low accuracy and low stability.

[0006] 2. Due to the asymmetry of the optical path design and the spectrometer, the non-uniform distribution of the four point light sources on the focal plane of the main interferometer collimator lens will lead to differences in optical path differences in different directions. As well as polarization state sensitivity, the spectrometer may have different reflectance / transmittance differences for beams of different polarization states, resulting in inconsistent polarization characteristics of each interference pattern. This will introduce direction-related phase errors in the dephasing process, resulting in directional sensitivity errors.

[0007] 3. The device uses a spectroscopic imaging component to acquire four images in a single exposure. However, mechanical vibrations can still cause relative displacement between the CCD and the optical path components, resulting in pixel position deviations (such as fringe misalignment) in the four images. Air disturbances, etc., can reduce the reliability of the measurement results, thereby destroying the synchronization of the phase shift. The problems of limited dynamic range and insufficient resistance to vibration interference are particularly prominent. In addition, the problem of insufficient dynamic range of light intensity is that when the spectroscopic component distributes the light intensity to the four interference patterns, if the light intensity distribution is uneven or attenuated, it may cause the signal-to-noise ratio of some interference patterns to decrease, limiting the measurable phase range.

[0008] 4. The four clearly imaged phase-shifted interferograms obtained by the device also need to be phase demodulated. Due to the limitations of the phase demodulation algorithm of this method, the four-step phase-shift method requires that the measured phase change is within one cycle (2π range). If the surface deformation or wavefront distortion of the measured object is too large (such as dynamic deformation scenarios), it will cause phase wrapping, which exceeds the algorithm processing capability and requires reliance on complex phase unwrapping technology.

[0009] In summary, existing devices and processing methods, due to the inherent characteristics of their hardware structure, only obtain aspheric wavefronts with orthogonal lateral shearing interference in a single direction, which is inconsistent with the requirements for complex aberration decoupling and has the following problems:

[0010] (1) The limitations of aspheric wavefront processing methods are that the phase demodulation accuracy is affected by wavefront distortion. Aspheric wavefronts usually have complex nonlinear phase distributions. When processing large gradient phase changes, the traditional Fourier transform method is prone to phase reconstruction errors due to spectrum aliasing. In the shearing interferometry method, the matching requirements between the lateral shear amount and the wavefront curvature are high. If the shear amount is not selected properly, it will introduce cumulative errors in the differential wavefront solution.

[0011] (2) The wavefront fitting algorithm is not adaptable enough. Aspheric wavefronts need to be fitted using Zernike polynomials or free-form surface models. However, the characterization of high-order aberrations is limited, making it difficult to accurately describe the local details of high-steepness aspheric surfaces (such as off-axis paraboloids). Calibration errors of the interferometer reference surface (such as reference mirror type deviation) are directly transferred to the wavefront calculation results, reducing the measurement reliability.

[0012] (3) In terms of dynamic range and phase wrapping, when the aspheric wavefront distortion exceeds the dynamic range of the Fourier transform method (2π phase limit), it is necessary to rely on the phase unwrapping algorithm, but complex phase jump areas (such as sharp edge changes) can easily lead to unwrapping failure.

[0013] (4) The boundary discontinuity problem of the traditional Fourier transform. The Fourier transform requires signal periodicity, but the actual interferogram often has boundary truncation effects, resulting in spectrum leakage and phase reconstruction errors, which are more significant under high-frequency noise interference. In particular, frequency domain filtering (such as bandpass filtering) requires precise separation of signal and noise spectra. If the filter window parameters are not set properly, effective phase information may be lost or residual noise may remain.

[0014] (5) Affected by the inherent errors of the interferometer optical system, the non-uniformity of the spectroscopic components will lead to inconsistent light intensity distribution in the interference pattern, resulting in inaccurate phase shift calibration accuracy. The mismatch between the polarization state of the reference light and the object light will also cause the interference contrast to decrease, potentially reducing the signal-to-noise ratio. At the same time, due to environmental disturbances and noise interference, the interference fringes will jitter or blur, causing accuracy and stability problems caused by system and environmental factors. Summary of the Invention

[0015] The present invention aims to provide an aspheric wavefront detection device and method based on multi-directional orthogonal lateral shearing interferometry, which overcomes the problems of low precision, poor stability, directional sensitivity error in detection, limited dynamic range and insufficient anti-vibration interference ability in the existing technology.

[0016] In order to achieve the above-mentioned purpose, the technical solution of the present invention is: an aspheric wavefront detection device based on multi-directional orthogonal lateral shearing interference, which is composed of a laser, a linear polarizer, a spectrometer, a reflector array, a two-dimensional orthogonal grating array, a spectrometer system, a polarization phase shifter, and a CMOS camera. The linear polarizer and the spectrometer are located in sequence on the output light path of the laser, and the two-dimensional orthogonal grating array, the spectrometer system, the polarization phase shifter, and the CMOS camera are arranged in sequence on the refracted light path of the spectrometer.

[0017] Furthermore, the above-mentioned light splitting element is a light splitting prism.

[0018] Furthermore, the polarization phase shifting element is a four-angle polarizer array.

[0019] Furthermore, the parameters of the two-dimensional orthogonal grating array are defined as follows: grating period is 1.8 μm, duty cycle is 0.5, etching depth is λ / 4 (λ=635 nm), and diffraction efficiency is ≥85%.

[0020] Furthermore, the above-mentioned aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry includes the following steps:

[0021] Step 1: Obtain a clear phase-shift interferogram original interferogram I(x,y), wherein the phase-shift interferogram is four images simultaneously acquired on a CCD by a spectroscopic imaging component;

[0022] Step 2: Based on the Radon transform adaptive method, the gradient field in each shear direction is solved. According to the projection integral characteristics, the Radon transform maps the two-dimensional gradient field into a one-dimensional signal in the projection domain through the line integral along a specific angle θ. The mathematical expression is:

[0023]

[0024] The intensity of the gradient field f(x,y) is projected along the θ direction as R(f)(θ,t). This transformation can extract the anisotropic characteristics of the gradient field. Therefore, the peak distribution of the Radon projection corresponding to the main direction of the gradient field in each shear direction is calculated. The projection amplitude of the shear gradient field at a specific angle θ is significantly higher than that in other directions. The dominant gradient direction can be located by detecting the projection peak angle.

[0025] Step 3: Use the antisymmetric extension method to process the gradient field obtained in step 2. The specific operation includes the following three steps:

[0026] 3.1 Through the data extension operation, the original gradient field data f(x) is extended along the spatial boundary by mirror symmetry to generate the extended data f ext (x)(length 2N), satisfies f ext (x) = f(x)(original region) and f ext (2N-x)=-f(x) (extended area);

[0027] 3.2 Perform frequency domain transformation and constraint operation: f ext (x) performing discrete Fourier transform (DFT) to force the spectrum to satisfy antisymmetry, and obtaining the corrected spectrum components through iterative conjugate gradient algorithm;

[0028] 3.3 Using inverse transformation and reconstruction, the corrected spectral components are inversely transformed into the spatial domain, the original data length region is intercepted, and the smoothed gradient field data is obtained;

[0029] Step 4: Through the joint optimization of Zernike polynomial fitting and transmission intensity equation (TIE), the smoothed gradient field data obtained in step 3 are dynamically iteratively calibrated using adaptive weight fusion, local phase compensation is performed on the high curvature area of ​​the aspheric surface, and a continuous wavefront distribution is output.

[0030] Furthermore, in step 3.2 above, f ext (x) The specific implementation steps for discrete Fourier transform are as follows:

[0031] (1) Fourier domain wavefront reconstruction optimization

[0032] By copying the antisymmetric extension method, the original interference graph I(x,y) is antisymmetricly extended to generate the extended interference graph I ext (x,y):

[0033]

[0034] Where L and M are the size boundaries of the original interference pattern, and the size after extension is 2L×2M to eliminate spectrum aliasing;

[0035] (2) Spectrum filtering and phase extraction

[0036] Perform Fourier transform on the expanded interferogram to extract the sidelobe spectrum

[0037]

[0038] Where H(u,v) is a translation filter that suppresses DC components and high-frequency noise.

[0039] The wavefront gradient field data obtained after inverse Fourier transform operation and phase unpacking processing is estimated as:

[0040]

[0041] Where unwrap represents the phase unwrapping operation.

[0042] Furthermore, the specific steps of the above step 4 include:

[0043] 1) Zernike polynomial local fitting

[0044] In the high curvature region Ω high , use Zernike polynomials to fit the phase distortion:

[0045]

[0046] where Z j (ρ,θ) is the normalized Zernike basis function, a j For the fitting coefficient, solve it by the least squares method:

[0047]

[0048] 2) Solving the TIE equation

[0049] Based on the multi-focal plane intensity data I(z1),I(z2),…,I(z k ), solve the transmission intensity equation (TIE):

[0050]

[0051] After discretization, the solution is obtained by fast Fourier transform (FFT):

[0052]

[0053] in is the axial light intensity derivative.

[0054] 3) Adaptive weight fusion

[0055] The weight map w(x,y) is calculated based on the local noise level:

[0056]

[0057] in is the local variance of the phase map;

[0058] The phase of the iterative update is:

[0059]

[0060] 4) Convergence conditions

[0061] Iteration stops when the root mean square error (RMSE) meets the threshold:

[0062]

[0063] where N p is the total number of pixels, and ∈ is the preset convergence threshold.

[0064] Furthermore, the above step 1 includes the following steps:

[0065] 1.1. The incident wavefront is split into four shear wavefronts at 0°, 45°, 90°, and 135° using a two-dimensional orthogonal grating array with a period of ≤2μm.

[0066] 1.2. Use 0°, 45°, 90°, and 135° polarizer arrays to synchronously capture four sets of original interferograms I(x,y) with a frame rate ≥ 100 fps.

[0067] Compared with the prior art, the advantages of the present invention are:

[0068] 1. The core invention of the device of the present invention is:

[0069] (1) The present invention adopts a rotating parallel shearing polarizer to achieve wavefront shearing in any direction, and the shearing direction freedom is adaptively adjusted along the four orthogonal directions.

[0070] (2) High spatial resolution: The two-dimensional grating period is ≤2μm, supporting subwavelength wavefront shearing, and is suitable for phase distortion detection of micro-nano structures (such as superlenses).

[0071] (3) The four-phase-shift interferogram is captured by a single exposure and combined with the real-time adjustment of the anti-vibration reflector to achieve millisecond-level dynamic wavefront detection.

[0072] (4) It has high-precision wavefront reconstruction and noise reduction capabilities. It uses multi-directional orthogonal shearing interferometry technology and extracts multi-axis differential wavefronts along the X / Y diagonal to significantly improve the integrity of phase gradient information in high-curvature regions of aspheric surfaces. Combined with the replica antisymmetric extension Fourier transform method, it eliminates finite difference boundary effects and reduces the reconstruction error to 0.0038λ (traditional methods are >0.01λ), making it suitable for nanoscale free-form surface detection needs.

[0073] (5) Detection efficiency and device compactness: A spatial light modulator (SLM) is used to create an orthogonal shearing grating microstructure array, replacing traditional mechanical spectrometers. This allows for adaptive adjustment of the optical path and supports detection across a wide spectrum from visible light to the near-infrared. A single measurement can generate multi-directional orthogonal transverse shearing interferograms, increasing efficiency by over 50% compared to traditional transverse shearing interferometry (which requires multiple adjustments to the shearing direction).

[0074] (6) This invention utilizes common optical path beam splitting and active reflector compensation technology to overcome the traditional interferometry method's reliance on a vibration isolation platform, making it suitable for dynamic measurements in industrial sites. Single-exposure multi-information extraction: Polarization phase shifting combined with two-dimensional shearing allows wavefront phase to be calculated from a single image frame, avoiding time errors in multi-frame acquisition.

[0075] 2. The method of the present invention adopts the following core technologies, including:

[0076] 1) Antisymmetric extension method: The present invention improves the existing antisymmetric extension method by performing a copy antisymmetric extension operation, and dynamically adjusts the iterative coefficient of the extension through horizontal antisymmetric extension and vertical antisymmetric extension, and iteratively copies and generates the extended interference pattern I ext (x,y), through I ext The transverse antisymmetric extension of (x,y) eliminates spectrum leakage and error control, and can reduce the reconstruction error to 0.0038λ.

[0077] 2) Dynamic phase recovery and distortion compensation are adopted, and Zernike polynomial local fitting is introduced to adaptively compensate for high-order aberrations (such as coma and trefoil) in the edge area of ​​the aspheric surface, thereby reducing the phase distortion error caused by curvature. Zernike-TIE has not been combined before to perform local fitting of high-order aberrations and suppress phase jump errors caused by the off-axis characteristics of the aspheric surface in shearing interferometry. However, single Zernike polynomial local fitting or TIE global phase recovery are difficult to achieve high-precision aspheric wavefront reconstruction. Therefore, the present invention combines the two and uses them to complement each other. Zernike polynomials suppress high-order aberrations in high curvature areas, and TIE ensures global phase consistency. Based on the TIE joint optimization algorithm, multi-focal plane intensity data is used to dynamically calibrate the global phase to solve the unwrapping failure problem caused by the off-axis characteristics of the aspheric surface in traditional shearing interferometry.

[0078] 3. The present invention adopts a multi-dimensional shearing design, which reduces aberration coupling by coordinating shearing direction, mode and algorithm. Compared with the existing lateral shearing interferometer, the advantages are as follows:

[0079] (1) The phase reconstruction error is improved to 0.0038λ, and the accuracy is improved by 63%;

[0080] (2) Detection efficiency: The present invention improves the efficiency by 50% by performing a single multi-directional synchronous measurement compared to the need to adjust the shear direction multiple times;

[0081] (3) In terms of anti-aspheric distortion capability, the present invention adopts Zernike+TIE dynamic calibration, which reduces the residual error by 40% compared with relying on empirical parameter compensation;

[0082] (4) In terms of system complexity, the adaptive grating fabricated by the present invention using SLM reduces the device volume by 80% compared to traditional mechanical splitter components;

[0083] (5) Through the collaborative innovation of algorithms and hardware, the present invention provides a high-precision, high-efficiency, and highly robust solution for the precision detection of aspheric optical elements.

[0084] 4. The present invention is suitable for high-precision phase recovery in the fields of optical detection, microscopic imaging, etc., and is suitable for high-precision dynamic detection of complex optical components such as off-axis aspheric surfaces and free-form surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 : Schematic diagram of the device structure, showing the optical path layout of the beam splitting module, detection module and anti-vibration module;

[0086] Figure 2 : Schematic diagram of the generation principle of orthogonal four-directional shear wavefront;

[0087] Figure 3 :Improved Fourier domain reconstruction algorithm flow chart;

[0088] Figure 4 : Off-axis aspheric surface detection results and wavefront residual diagram in the embodiment.

[0089] The reference numerals are as follows: 1-laser, 2-linear polarizer, 3-test element, 4-beam splitter prism, 5-mirror array, 6-two-dimensional orthogonal grating array, 7-beam splitting system, 8-polarization phase shifter, 9-CMOS camera. DETAILED DESCRIPTION

[0090] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0091] like Figure 1 As shown, the present invention provides a multi-directional orthogonal transverse shearing interferometer wavefront detection device, which is composed of a laser 1, a linear polarizer 2, a beam splitter, a two-dimensional orthogonal grating array 6, a beam splitter system 7, a polarization phase shifter 8, and a CMOS camera 9. The beam splitter is a beam splitter prism 4. The polarization phase shifter 8 is specifically a four-angle polarizer array.

[0092] The two-dimensional orthogonal grating array 6 is used as a beam splitting module, and its six parameters are defined as follows: the grating period is 1.8 μm, the duty cycle is 0.5, the etching depth is λ / 4 (λ=635 nm), and the diffraction efficiency is ≥85%. In this embodiment, the light aperture is 8 mm×8 mm, supporting the 190-1100 nm band.

[0093] The CMOS camera has a 9-pixel size of 3.45 μm, a polarizer array angle error of ≤0.5°, and forms a detection module with a four-angle polarizer array; a reflector array 5 is provided in the optical path to offset phase jitter caused by environmental vibration, and the signal-to-noise ratio is ≥45 dB.

[0094] like Figure 2 As shown, the principle of generating orthogonal four-directional shearing wavefronts in the present invention is that the common optical path beam splitting module is composed of a two-dimensional orthogonal grating array 6 with a period ≤ 2μm. Polarization phase shifting element 8 is used to perform periodic modulation in the horizontal and vertical directions. This achieves synchronous phase shifting of the four beams (e.g., 0°, 90°, 180°, and 270°), splitting the incident wavefront into four shearing beams (in the ±x and ±y directions), forming orthogonal four-directional shearing interference. The phase-shifted interferograms are four sets of phase-shifted interferograms acquired synchronously on a CCD through a single exposure using a spectroscopic imaging assembly.

[0095] The working process of the device is as follows:

[0096] The test element 3 is placed between the linear polarizer 2 and the beam-splitting prism 4. In this embodiment, the test element 3 is an off-axis aspheric lens. A parallel beam from the laser 1 is perpendicularly directed through the beam-splitting prism onto the test element 3. The test wavefront reflected by the surface of the test element 3 is incident on a two-dimensional orthogonal grating 6. A two-dimensional controller controls the rotation angle of the turntable. With each rotation, the CMOS camera 9 captures an image. Each complete rotation of the turntable, driven by the two-dimensional orthogonal grating array 6, captures multiple shearing interferograms, achieving multi-directional shearing.

[0097] Due to the characteristics of the two-dimensional orthogonal grating array 6, the two beams of circularly polarized light carrying the side wavefront information are vertically incident on the two-dimensional orthogonal grating array 6. Due to the diffraction effect of the grating, the light beams will be separated into multiple diffraction orders in the x and y directions and enter the spectroscopic system 7. In the spectroscopic system 7, the first convex lens converges the diffracted light, and then a spatial filter is placed on the back focal plane of the first convex lens and the front focal plane of the second convex lens, so that the ±1 order diffracted light can be screened out to achieve the re-beam splitting of the test wavefront. The four channels of light beams obtained by the spectroscopic system have exactly the same wavefront information. Since the polarization states are orthogonal and no interference pattern is generated, the light beams need to pass through the polarization phase shift element 8 (such as Figure 3 Interference occurs only when the polarization phase shifter 8 is made of four linear polarizers of the same material. The adjacent polarization directions relative to the horizontal are 0°, 45°, 90°, and 135°. The light beams interfere in these four directions, resulting in four orthogonal interference fringes with distinct phase shifts observed on the polarization phase shifter 8. These four interference images are captured by a CMOS camera 9.

[0098] Based on the above device, the present invention provides an aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry, comprising the following steps:

[0099] Step 1: Obtain a clear phase-shift interferogram original interferogram I(x,y). The phase-shift interferogram is four images simultaneously acquired on a CCD by a spectroscopic imaging component, specifically including the following steps:

[0100] 1.1. The incident wavefront is split into shear wavefronts in four directions: 0°, 45°, 90°, and 135°, using a two-dimensional orthogonal grating array 6 with a period of ≤ 2 μm.

[0101] 1.2. Use 0°, 45°, 90°, and 135° polarizer arrays to synchronously capture four sets of original interferograms I(x,y) with a frame rate ≥ 100 fps.

[0102] Step 2: Based on the Radon transform adaptive method, the gradient field in each shear direction is solved. According to the projection integral characteristics, the Radon transform maps the two-dimensional gradient field into a one-dimensional signal in the projection domain through the line integral along a specific angle θ. The mathematical expression is:

[0103]

[0104] The intensity of the gradient field f(x,y) is projected along the θ direction as R(f)(θ,t). This transformation can reveal the anisotropic characteristics of the field. Therefore, the peak distribution of the Radon projection corresponding to the dominant direction of the gradient field in each shear direction is calculated. The projection amplitude of the shear gradient field at a specific angle θ is significantly higher than that in other directions. By detecting the projection peak angle, the dominant gradient direction can be located.

[0105] Step 3: Use the antisymmetric continuation method to process the gradient field obtained in step 2, and optimize the wavefront gradient field data by combining boundary extension and frequency domain constraints. Specifically:

[0106] This step uses a mirror extension operation to mirror the original wavefront gradient field data along the boundary to twice the length of the original data, forming an expanded new data set. This operation, by extending the data domain boundary, alleviates the boundary mutation problem caused by truncation error in the finite difference method. A Fourier domain antisymmetric constraint is then applied to the expanded data, forcing its spectrum to satisfy F(k) = -F(-k), thereby eliminating the Gibbs oscillations generated at discontinuous boundaries by the traditional finite difference method.

[0107] Through the optimization of the coordinate transformation of the lateral antisymmetric extension, I ext (x,y)=-I(-x,y), maps the original interference pattern data to the coordinate system centered on the symmetry axis to eliminate the impact of the initial data offset on the extension accuracy. The iteration coefficient of the longitudinal extension is dynamically adjusted by the iteration coefficient α n (n is the number of iterations) Control the longitudinal extension step size:

[0108]

[0109] The algorithm gradually converges to the optimal extension form, avoiding the high-frequency noise introduced by a single extension.

[0110] The following describes this step in more detail:

[0111] First, through the data extension operation, the original gradient field data f(x) is extended along the spatial boundary in a mirror-symmetrical manner to generate the extended data f ext (x)(length 2N), satisfies f ext (x) = f(x)(original region) and f ext (2N-x)=-f(x) (extended area);

[0112] Second, perform frequency domain transformation and constraint operations on f ext (x) performs discrete Fourier transform (DFT) to force its spectrum to satisfy antisymmetry, and obtains the modified spectrum components through conjugate gradient algorithm iteration to suppress high-frequency noise. ext (x) The specific implementation steps for discrete Fourier transform are as follows:

[0113] (1) Fourier domain wavefront reconstruction optimization

[0114] By copying the antisymmetric extension method, the original interference graph I(x,y) is antisymmetricly extended to generate the extended interference graph I ext (x,y):

[0115]

[0116] Where L and M are the size boundaries of the original interference pattern, and the size after extension is 2L×2M to eliminate spectrum aliasing;

[0117] (2) Spectrum filtering and phase extraction

[0118] Perform Fourier transform on the expanded interferogram to extract the sidelobe spectrum

[0119]

[0120] Where H(u,v) is a translation filter (such as a bandpass filter) that suppresses DC components and high-frequency noise;

[0121] The wavefront gradient field data obtained after inverse Fourier transform operation and phase unpacking processing is estimated as:

[0122]

[0123] Where unwrap represents the phase unwrapping operation.

[0124] Third, using inverse transformation and reconstruction, the corrected spectral components are transformed back into the spatial domain, the original data length region is intercepted, and the smoothed gradient field data is obtained, which significantly reduces the Gibbs oscillation amplitude and eliminates the Fourier reconstruction boundary error.

[0125] Step 4: Through Zernike polynomial fitting and transmission intensity equation (TIE) joint optimization, the smoothed gradient field data obtained in step 3 is dynamically iteratively calibrated using adaptive weight fusion, local phase compensation is performed on the high curvature area of ​​the aspheric surface, and a continuous wavefront distribution is output. The specific steps include:

[0126] 1) Zernike polynomial local fitting

[0127] In the high curvature region Ω high , use Zernike polynomials to fit the phase distortion:

[0128]

[0129] where Z j (ρ,θ) is the normalized Zernike basis function, a j For the fitting coefficient, solve it by the least squares method:

[0130]

[0131] 2) Solving the TIE equation

[0132] Based on the multi-focal plane intensity data I(z1),I(z2),…,I(z k ), solve the transmission intensity equation (TIE):

[0133]

[0134] After discretization, the solution is obtained by fast Fourier transform (FFT):

[0135]

[0136] in is the axial light intensity derivative.

[0137] 3) Adaptive weight fusion

[0138] The weight map w(x,y) is calculated based on the local noise level:

[0139]

[0140] in is the local variance of the phase map.

[0141] The phase of the iterative update is:

[0142]

[0143] 4) Convergence conditions

[0144] Iteration stops when the root mean square error (RMSE) meets the threshold:

[0145]

[0146] where N p is the total number of pixels, and ∈ is the preset convergence threshold (such as 0.001λ).

[0147] After the above processing, the phase distribution of the test wavefront can be extracted from the interference pattern and the surface shape of the test element can be reconstructed.

[0148] See also Figure 4 , where (1) the orthogonal lateral shearing interferogram containing aspheric wavefronts in any direction can be seen, and (2) the aspheric wavefront aberration relative to a standard spherical surface can be seen. Compared with a contact profilometer (Talysurf PGI 1240), the RMS error is 0.82nm and the repeatability error is ≤0.25nm.

[0149] The above description is an explanation of the specific implementation of the present invention, rather than a limitation of the present invention. Those skilled in the relevant technical field can also make various equivalent technical solutions without departing from the scope of the present invention, so all equivalent technical solutions should be included in the scope of protection of the present invention.

Claims

1. An aspheric wavefront detection device based on multi-directional orthogonal lateral shearing interferometry, characterized by: The invention comprises a laser (1), a linear polarizer (2), a spectroscopic element, a reflector array (5), a two-dimensional orthogonal grating array (6), a spectroscopic system (7), a polarization phase shifting element (8), and a CMOS camera (9). The linear polarizer (2) and the spectroscopic element are sequentially arranged on the outgoing light path of the laser (1), and the two-dimensional orthogonal grating array (6), the spectroscopic system (7), the polarization phase shifting element (8), and the CMOS camera (9) are sequentially arranged on the refracted light path of the spectroscopic element.

2. The aspheric wavefront detection device based on multi-directional orthogonal lateral shearing interferometry according to claim 1, characterized in that: The light splitting element is a light splitting prism (4).

3. The aspheric wavefront detection device based on multi-directional orthogonal lateral shearing interferometry according to claim 2, characterized in that: The polarization phase shifting element (8) is a four-angle polarizer array.

4. The aspheric wavefront detection device based on multi-directional orthogonal lateral shearing interferometry according to claim 3, characterized in that: The parameters of the two-dimensional orthogonal grating array (6) are as follows: grating period is 1.8 μm, duty cycle is 0.5, etching depth is λ / 4 (λ=635 nm), and diffraction efficiency is ≥85%.

5. The aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry according to claim 1, characterized in that: The following steps are involved: Step 1: Obtain a clear phase-shift interferogram original interferogram I(x,y), wherein the phase-shift interferogram is four images simultaneously acquired on a CCD by a spectroscopic imaging component; Step 2: Based on the Radon transform adaptive method, the gradient field in each shear direction is solved. According to the projection integral characteristics, the Radon transform maps the two-dimensional gradient field into a one-dimensional signal in the projection domain through the line integral along a specific angle θ. The mathematical expression is: The intensity of the gradient field f(x,y) is projected along the θ direction as R(f)(θ,t). This transformation can extract the anisotropic characteristics of the gradient field. Therefore, the peak distribution of the Radon projection corresponding to the main direction of the gradient field in each shear direction is calculated. The projection amplitude of the shear gradient field at a specific angle θ is significantly higher than that in other directions. The dominant gradient direction can be located by detecting the projection peak angle. Step 3: Use the antisymmetric extension method to process the gradient field obtained in step 2, which includes the following three steps: 3.

1. Through the data extension operation, the original gradient field data f(x) is mirror-symmetrically extended along the spatial boundary to generate the extended data f ext (x)(length 2N), satisfies f ext (x) = f(x)(original region) and f ext (2N-x)=-f(x) (extended area); 3.2、Perform frequency domain transformation and constraint operation: ext (x) performing discrete Fourier transform (DFT) to force the spectrum to satisfy antisymmetry, and obtaining the corrected spectrum components through iterative conjugate gradient algorithm; 3.

3. Using inverse transformation and reconstruction, the corrected spectral components are inversely transformed into the spatial domain, the original data length region is intercepted, and the smoothed gradient field data is obtained; Step 4: Through the joint optimization of Zernike polynomial fitting and transmission intensity equation (TIE), the smoothed gradient field data obtained in step 3 are dynamically iteratively calibrated using adaptive weight fusion, local phase compensation is performed on the high curvature area of ​​the aspheric surface, and a continuous wavefront distribution is output.

6. The aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry according to claim 5, characterized in that: In step 3.2, f ext (x) The specific implementation steps for discrete Fourier transform are as follows: (1) Fourier domain wavefront reconstruction optimization By copying the antisymmetric extension method, the original interference graph I(x,y) is antisymmetricly extended to generate the extended interference graph I ext (x,y): Where L and M are the size boundaries of the original interference pattern, and the size after extension is 2L×2M to eliminate spectrum aliasing; (2) Spectrum filtering and phase extraction Perform Fourier transform on the expanded interferogram to extract the sidelobe spectrum Where H(u,v) is a translation filter that suppresses DC components and high-frequency noise; The wavefront gradient field data obtained after inverse Fourier transform operation and phase unpacking processing is estimated as: Where unwrap represents the phase unwrapping operation.

7. The aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry according to claim 5, characterized in that: The specific steps of step 4 include: 1) Zernike polynomial local fitting In the high curvature region Ω high , use Zernike polynomials to fit the phase distortion: where Z j (ρ,θ) is the normalized Zernike basis function, a j For the fitting coefficient, solve it by the least squares method: 2) Solving the TIE equation Based on the multi-focal plane intensity data I(z1),I(z2),…,I(z k ), solve the transmission intensity equation (TIE): After discretization, the solution is obtained by fast Fourier transform (FFT): in is the axial light intensity derivative; 3) Adaptive weight fusion The weight map w(x,y) is calculated based on the local noise level: in is the local variance of the phase map; The phase of the iterative update is: 4) Convergence conditions Iteration stops when the root mean square error (RMSE) meets the threshold: where N p is the total number of pixels, and ∈ is the preset convergence threshold.

8. The aspheric wavefront detection method based on multi-directional orthogonal lateral shearing interferometry according to claim 5, characterized in that: The step 1 comprises the following steps: 1.

1. Splitting the incident wavefront into shear wavefronts in four directions of 0°, 45°, 90° and 135° by a two-dimensional orthogonal grating array (6) with a period of ≤2μm; 1.

2. Use 0°, 45°, 90°, and 135° polarizer arrays to synchronously capture four sets of original interferograms I(x,y) with a frame rate ≥ 100 fps.

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