A Nonlinear Optimization Wavefront Reconstruction Method for Shearing Interferometry Systems

Abstract

The present invention discloses a non-linear optimization wavefront reconstruction method for a shearing interferometry system, comprising the following steps: building a shearing interferometry system, where the incoherent light emitted by an incoherent light source sequentially passes through an object-side Ronchi grating, a lens to be measured, and an image-side checkerboard grating, and is received by an image sensor; performing a rough extraction of the wavefront phase by using a two-step phase-shifting phase extraction method; constructing an error function with the interference light intensity as the target, calculating the numerical gradient of the Zernike coefficients representing the wavefront, and using the gradient descent algorithm to optimize the roughly extracted wavefront phase to obtain a reconstructed wavefront. The present invention overcomes the influence of high-order interference on phase detection, thereby realizing high-precision reconstruction of the wavefront phase. The wavefront can be accurately reconstructed with only two interference patterns, having high reconstruction accuracy and high robustness.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement and wavefront detection, and in particular to a non-linear optimized wavefront reconstruction method for a shearing interference measurement system. Background Art

[0002] The lithography process is an ultra-precision machining process and plays a great role in chip production. Today in the 21st century, its development can even directly reflect the development level of the semiconductor industry. The projection objective lens is the core component of the lithography machine, and its wave aberration affects the lithography resolution and overlay accuracy. Therefore, high-precision detection of the wavefront aberration of the lithography projection objective lens is of great significance. The methods for wavefront detection of lithography objective lenses include the point diffraction method, the Shack-Hartmann method, and the Ronchi shearing interference method used by ASML. It extracts the differential wavefront phase in two orthogonal shearing directions. After wavefront reconstruction, the measured wave aberration can be obtained. The advantage of Ronchi shearing interference is that it does not need to use a small hole to generate a reference wavefront, can better utilize the illumination system of the lithography machine, is more suitable for in-situ detection, and it belongs to common-path interference, with high system stability and measurement accuracy, so it is widely used.

[0003] For Ronchi shearing interference, the biggest challenge is the phase reconstruction process. According to the van Cittert-Zernike theorem, the spatial coherence of the light field is equal to the normalized Fourier transform of the light source intensity distribution. Therefore, after the 0th order and other odd-order diffracted lights interfere, an interference image is formed on the detector plane, and there is no interference between other diffraction orders. So when the shearing rate is small, on the detector plane, in addition to the interference between the ±1st order and the 0th order to obtain the required interference fringes, higher-order terms will also interfere with the 0th order light, seriously affecting the accuracy of phase extraction. The interference light intensity can be expressed as:

[0004]

[0005] where (x, y) are the coordinates of the interference plane, I i (x, y) is the i-th interference pattern recorded, I'(x, y) is the background light intensity, that is, the slowly varying part, n is the interference order, k is a natural number, τ |n| is the interference amplitude coefficient, and its value is equal to sinc(n / 2) 2 , is the phase of the wavefront to be measured, S is the normalized shearing amount, and δ is the phase shift amount.

[0006] Eliminating the influence of multi-level parasitic interference on the phase extraction accuracy is a prerequisite for the Ronchi shearing interferometer to achieve high-precision wavefront aberration detection. This is mainly achieved by increasing the number of phase steps. Therefore, based on the traditional four-step phase-shifting method, methods such as eight-step, ten-step, thirteen-step, and 3N+1 step phase-shifting methods have been studied. The quality of a phase-shifting method is mainly judged by the peak-to-valley value (PV) and root mean square (RMS) of the error wavefront. In addition, if the number of phase steps required is too large, the requirements for the phase shifter are very high, and the process time is long, which is likely to introduce errors such as vibration error and phase-shift error, reducing the measurement accuracy and increasing the complexity of the experimental setup. Among the existing methods, the accuracy of the first four methods of four-step, eight-step, ten-step, and thirteen-step is relatively low, only reaching the order of 0.01 wavelength, while the 3N+1 method is accurate, but requires more than 20 precisely phase-shifted interferograms. Therefore, there is an urgent need for a new phase-shifting method that can ensure both a relatively small PV value and RMS value and only requires a small number of phase steps. Summary of the Invention

[0007] Aiming at the deficiencies of the existing technology, the present invention proposes a non-linear optimized wavefront reconstruction method for a shearing interference measurement system, which can not only ensure that the PV value and RMS value of the error wavefront are relatively small, only about 1% of the mainstream ten-step and thirteen-step methods, improving the wavefront phase reconstruction accuracy, but also only requires two-step phase-shifting to capture the interferogram, simplifying the experimental process and reducing the introduction of noise during the phase-shifting process.

[0008] The specific technical solution is as follows:

[0009] A non-linear optimized wavefront reconstruction method for a shearing interference measurement system includes the following steps:

[0010] S1: Fix the lens to be measured on the optical platform to be measured of the shearing interference measurement system. The incoherent light emitted by the incoherent light source passes through the object-side Ronchi grating, the lens to be measured, and the image-side checkerboard grating in sequence and is received by the image sensor; the object-side Ronchi grating is two groups of one-dimensional grating lines with mutually perpendicular directions; the optical axis direction is the z-axis. According to the right-hand rule, the two directions perpendicular to the z-axis are the x-axis and y-axis respectively; the two diagonals of the image-side checkerboard grating are perpendicular to the x-axis and y-axis directions respectively; the magnification is equal to the ratio of the grating constant of the image-side checkerboard grating to that of the object-side Ronchi grating.

[0011] S2: Move the object-side Ronchi grating to make the light pass through the one-dimensional grating line perpendicular to the x direction, and move the image-side checkerboard grating along the y direction to obtain the interferogram in the x direction; move the image-side checkerboard grating to make the light pass through the one-dimensional grating line perpendicular to the y direction, and move the object-side Ronchi grating along the x direction to obtain the interferogram in the y direction.

[0012] S3: Process the spectrum of the light intensity using a filter to remove the slow-varying part, obtaining the light intensities before and after phase shift after filtering, thereby obtaining the roughly extracted wavefront phase;

[0013] S4: Use the image sensor to obtain the actual measurement value of the light intensity, generate an estimated value of the light intensity through the roughly extracted wavefront phase, and construct an error function based on the actual measurement value and the estimated value of the light intensity;

[0014] S5: Represent the roughly extracted wavefront phase using Zernike polynomials and perform non-linear iterative optimization on the Zernike coefficients. Specifically: perform linear fitting on the Zernike coefficients and then optimize using the gradient descent algorithm. For the error function after each optimization, judge its relationship with the optimization judgment threshold. If the optimized error function is greater than or equal to the optimization judgment threshold, then judge the relationship between the number of optimizations and the total number of optimizations. If the number of optimizations is less than the total number of optimizations, then perform the next optimization, repeating step S5; otherwise, end the optimization and output the accurate Zernike coefficients of the wavefront; if the optimized error function is less than the optimization judgment threshold, then end the optimization and output the accurate Zernike coefficients of the wavefront;

[0015] S6: Reconstruct the wavefront to be measured according to the accurate Zernike coefficients of the wavefront obtained in step S5.

[0016] Further, if only considering ±1 order interference in step S2, the expressions of the light intensities before and after phase shift are

[0017]

[0018] where (x, y) are the coordinates on the interference plane, is the light intensity of the interference pattern before phase shift, is the light intensity of the interference pattern after phase shift, I'(x, y) is the background light intensity, i.e., the slow-varying part, I”(x, y) is the light intensity coefficient varying with the phase, is the phase of the wavefront to be measured, and δ is the phase shift amount.

[0019] Further, in step S3, the expressions for the light intensities before and after phase shift after filtering are as follows:

[0020]

[0021] where (x, y) are the coordinates on the interference plane, I1(x, y) is the light intensity of the interference pattern before phase shift after filtering, I2(x, y) is the light intensity of the interference pattern after phase shift after filtering, I”(x, y) is the light intensity coefficient varying with the phase, is the phase of the wavefront to be measured, and δ is the phase shift amount;

[0022] The roughly extracted wavefront phase is obtained from the above formula The expression is as follows:

[0023]

[0024] Furthermore, the expression of the error function in step S4 is as follows:

[0025]

[0026] where x and y are the position coordinates of the interference spot on the interference plane, n is the interference order, k is a natural number; τ |n| is the interference amplitude coefficient, and its value is equal to sinc(n / 2) 2 ; is the wavefront phase of the rough extraction; S is the shear rate.

[0027] Furthermore, the rough-extracted wavefront phase is represented by Zernike polynomials in step S5 and the expression is as follows:

[0028]

[0029] a = [a1, a2,..., a j

[0030] where (ρ, θ) are the polar coordinates within the unit circle, a j are the Zernike coefficients, Z j (ρ, θ) are the Zernike polynomials, and a is the vector composed of all Zernike coefficients.

[0031] Furthermore, the non-linear iterative optimization algorithm in step S5 is implemented through the following sub-steps:

[0032] (5.1) Linear fitting; multiply the initial values of all calculated Zernike coefficients by the same constant k, i.e., a = ka, to minimize the value of the error function E;

[0033] (5.2) Optimize the Zernike coefficients using the gradient descent algorithm, and the numerical gradient is defined as:

[0034]

[0035] g = [g1, g2,..., g j

[0036] where E is the error function, h is a positive number; g is the vector composed of all numerical gradients;

[0037] (5.3) The series of expressions for updating the Zernike coefficients after gradient descent are as follows:

[0038] m t = β1·m t-1 ​​+(1 - β1)·g t

[0039]

[0040] Where t is the number of optimization times, m t is the first moment of g t and v t is the second moment of g t . Both β1 and β2 are moment decay coefficients, is the bias correction of m t ; is the bias correction of v t ; a t is the Zernike coefficient after the t-th optimization, α is the learning rate, and ε is a constant added to maintain numerical stability;

[0041] (5.4) According to the Zernike coefficient a t after the t-th optimization, the error function E t after the t-th optimization is obtained, and the relationship between the error function E t and the optimization judgment threshold TH is judged. If E t ≥TH, then the relationship between the optimization times t and the total number of optimizations N is judged. If t < N, the next optimization is performed, that is, t = t + 1, and steps (5.2) to (5.4) are repeated; if t ≥ N, the optimization ends and the accurate wavefront Zernike coefficient a is output; if E t <TH, then the optimization ends and the accurate wavefront Zernike coefficient a is output.

[0042] Furthermore, the filter in step S3 is a Gaussian high-pass filter.

[0043] Furthermore, the number of terms j of the Zernike polynomial is selected to be 36 terms.

[0044] Furthermore, in step S2, the image-side checkerboard grating is moved by a piezoelectric ceramic actuator.

[0045] The beneficial effects of the present invention are:

[0046] The present invention realizes wavefront reconstruction by using a non-linear optimization method, avoids the problem that the reconstruction accuracy is affected by multi-stage parasitic interference in the prior art, and improves the detection accuracy; and only two-step phase shifting is required, solving the problem that the number of phase shifting steps required by the existing method is too many and the phase shifting time is too long, thus easily introducing noise during the phase shifting process. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a schematic diagram of the optical device of the present invention.

[0048] Figure 2It is the flowchart of the method of the present invention.

[0049] Figure 3 It is the result diagram of an embodiment of the present invention. Among them, (a) is the two-step phase-shifting interference diagram, (b) is the original wavefront phase diagram, (c) is the roughly extracted wavefront phase diagram, and (d) is the wavefront phase diagram after iterative optimization.

[0050] In the figure, there are incoherent light source 1, object-side Ronchi grating 2, lens to be measured 3, image-side checkerboard grating 4, and image sensor 5. Specific embodiments

[0051] The present invention will be described in detail below according to the accompanying drawings and preferred embodiments. The purpose and effect of the present invention will become more clear. The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0052] As Figure 1 shown, the optical system used in the present invention includes an incoherent light source 1, an object-side Ronchi grating 2, a lens to be measured 3, an image-side checkerboard grating 4, and an image sensor 5 arranged in sequence along the optical axis. The lens to be measured 3 is fixedly arranged on the optical platform to be measured of the Ronchi phase-shifting shearing interference measurement system. The incoherent light emitted by the incoherent light source 1 passes through the object-side Ronchi grating 2, the lens to be measured 3, and the image-side checkerboard grating 4 in sequence and is received by the image sensor. Among them, the object-side Ronchi grating 2 is two sets of one-dimensional grating lines with perpendicular directions. The optical axis direction is the z-axis. According to the right-hand rule, the two directions perpendicular to the z-axis are the x-axis and the y-axis respectively; the two diagonals of the image-side checkerboard grating 4 are perpendicular to the x-axis and the y-axis directions respectively; the magnification ratio is equal to the ratio of the grating constant of the image-side checkerboard grating 4 to that of the object-side Ronchi grating 2.

[0053] As Figure 2 shown, the method of the present invention includes the following steps:

[0054] S1: Build an optical system so that the image-side checkerboard grating 4 and the object-side Ronchi grating 2 satisfy the object-image relationship with respect to the lens to be measured 3, and the specific arrangement is as described above.

[0055] S2: Respectively set the light source wavelength λ, the normalized shear rate S, the phase shift amount δ of the two interference diagrams, the optimization judgment threshold TH, the total number of optimizations N, the moment decay coefficients β1 and β2, the learning rate α, the constant ε added to maintain numerical stability, and the initial optimization number t = 1 for wavefront detection.

[0056] S3: Use the object-side Ronchi grating 2 with rulings in the x and y directions to capture interference patterns respectively. Move the object-side Ronchi grating 2 to allow light to pass through the one-dimensional grating lines perpendicular to the x direction, and move the image-side checkerboard grating 4 in the y direction through a piezoelectric ceramic actuator (PZT) to obtain the interference pattern in the x direction; move the image-side checkerboard grating 4 to allow light to pass through the one-dimensional grating lines perpendicular to the y direction, and move the object-side Ronchi grating 2 in the x direction through a piezoelectric ceramic actuator (PZT) to obtain the interference pattern in the y direction.

[0057] If only considering the ±1 order interference, the light intensity expressions before and after phase shift are as follows:

[0058]

[0059] In the formula, (x, y) are the coordinates on the interference plane, is the light intensity of the interference pattern before phase shift recorded, is the light intensity of the interference pattern after phase shift recorded; I'(x, y) is the background light intensity, that is, the slowly varying part; I”(x, y) is the light intensity coefficient varying with the phase, is the phase of the wavefront to be measured, and δ is the phase shift amount.

[0060] S4: Use a filter to process the spectrum of the light intensity, filter out the slowly varying part, and obtain the light intensities before and after phase shift after filtering, and their expressions are as follows:

[0061]

[0062] In the formula, I1(x, y) is the light intensity of the interference pattern before phase shift after filtering, and I2(x, y) is the light intensity of the interference pattern after phase shift after filtering.

[0063] In this embodiment, a Gaussian high-pass filter is used to accurately filter out the DC term.

[0064] From equations (3) and (4), the expression of the roughly extracted wavefront phase is as follows:

[0065]

[0066] S5: Use the image sensor 5 to obtain the actual measurement value of the light intensity, generate the estimated value of the light intensity through the roughly extracted phase, and construct an error function based on the actual measurement value and the estimated value of the light intensity, and its expression is as follows: In the formula, x, y are the position coordinates of the interference spot on the interference plane, n is the interference order, k is a natural number; τ

[0067]

[0068] is the interference amplitude coefficient, and its value is equal to sinc(n / 2) |n| 2 ​; S is the shear rate.

[0069] S6: The coarsely extracted wavefront phase obtained according to step S4 Express it with Zernike polynomials, and the expression is as follows:

[0070]

[0071] a = [a1, a2,..., a j (8)

[0072] In the formula, (ρ, θ) are the polar coordinates within the unit circle, a j is the Zernike coefficient, Z j (ρ, θ) is the Zernike polynomial, a is the vector composed of all Zernike coefficients, which can uniquely represent the wavefront; in order to balance the running time and accuracy, the number of terms j of the Zernike polynomial is preferably 36 terms.

[0073] Perform non - linear iterative optimization on the Zernike coefficient a j The optimization algorithm is implemented through the following sub - steps:

[0074] (6.1) Linear fitting. Multiply the initial values of all calculated Zernike coefficients by the same constant k, that is, a = ka, to minimize the value of the error function E.

[0075] (6.2) Optimize the Zernike coefficient using the gradient descent algorithm. The numerical gradient is defined as:

[0076]

[0077] g = [g1, g2,…, g j (10)

[0078] In the formula, h is a small positive number, acting on the Zernike coefficient a j to generate the wavefront phase g is the vector composed of all numerical gradients.

[0079] (6.3) The series of expressions for updating the Zernike coefficients after gradient descent are as follows:

[0080] m t = β1·m t-1 +(1 - β1)·g t (11)

[0081]

[0082] In the formula, t is the number of optimization times, m t is the first - order moment of g t v t is g tThe second moment, where both β1 and β2 are moment decay coefficients, is m t for bias correction, is v t for bias correction; a t is the Zernike coefficient after the t-th optimization, α is the learning rate, and ε is a constant added to maintain numerical stability.

[0083] (6.4) Substitute the Zernike coefficient a after the t-th optimization t into Eqs. (6) - (8) to obtain the error function E after the t-th optimization t ; Judge the relationship between the error function E t and the optimization judgment threshold TH. If E t ≥TH, then judge the relationship between the optimization times t and the total number of optimizations N. If t < N, recalculate the gradient and continue the next optimization, i.e., t = t + 1, and repeat steps (6.2) - (6.4); if t ≥ N, end the optimization and output the accurate wavefront Zernike coefficient a; if E t < TH, then the optimization is completed and the optimization ends.

[0084] S7: According to the accurate wavefront Zernike coefficient a obtained in step S6, combine Eqs. (7) and (8) to reconstruct the wavefront to be measured with high precision

[0085] The following gives a specific embodiment of the present invention to illustrate the technical effects of the present invention.

[0086] S1: Construct an optical path, where the lens 3 to be measured is a 10× microscope objective.

[0087] S2: Set the light source wavelength λ = 452 nm, the normalized shear rate S = 0.0745, the phase shift amount δ of the two interference patterns = 3π / 2, the optimization judgment threshold TH = 10 -10 , the total number of optimizations N = 150, the moment decay coefficients β1 = 0.9, β2 = 0.999, the learning rate α = 1, the constant ε added to maintain numerical stability = 10 -8 , and the initial optimization times t of wavefront detection = 1.

[0088] S3: Use the object-side Ronchi grating 2 with rulings in the x and y directions to capture interference patterns respectively, and use two Ronchi shearing interference patterns to reconstruct the wavefront phase.

[0089] S4: Use a Gaussian high-pass filter to filter out the DC term and process the spectrum of the light intensity.

[0090] S5: Use the image sensor 5 to obtain the actual measured value of the light intensity, and extract the phase roughly Generate an estimated value of the light intensity, and construct an error function based on the actual measured value and the estimated value of the light intensity.

[0091] S6: Represent the roughly extracted wavefront phase using a 36th-order Zernike polynomial and perform non-linear iterative optimization on the Zernike coefficient a j

[0092] S7: Based on the accurate Zernike coefficients a of the wavefront obtained in step S6, reconstruct the wavefront to be measured with high precision.

[0093] As Figure 3 shown, this is the result graph of this embodiment. The PV value and RMS value of the error between the wave surface after iterative optimization and the original wave surface are both below 10 -5 nm, which proves that the present invention can achieve accurate wavefront phase reconstruction with only two Ronchi shearing interferograms.

[0094] The present invention overcomes the influence of high-order interference on phase detection, thereby achieving high-precision reconstruction of the wavefront phase. It can achieve accurate wavefront reconstruction with only two interferograms, and its reconstruction accuracy and robustness are higher than those of the existing eight-step, ten-step, and thirteen-step phase-shifting methods.

[0095] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing examples, or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.​

Claims

1. A non-linear optimization wavefront reconstruction method for a shearing interferometry system, characterized in that, It includes the following steps: S1: Fix the lens to be measured on the optical platform to be measured of the shear interferometry system. The incoherent light emitted by the incoherent light source sequentially passes through the object-side Ronchi grating, the lens to be measured, and the image-side checkerboard grating, and is received by the image sensor. The object-side Ronchi grating is composed of two sets of one-dimensional grating lines with perpendicular directions; The optical axis direction is the z-axis. According to the right-hand rule, the two directions perpendicular to the z-axis are the x-axis and the y-axis respectively. The two diagonals of the image-side checkerboard grating are perpendicular to the x-axis and the y-axis directions respectively. The magnification is equal to the ratio of the grating constant of the image-side checkerboard grating to that of the object-side Ronchi grating; S2: Move the object-side Ronchi grating so that the light passes through the one-dimensional grating line perpendicular to the x-direction, and move the image-side checkerboard grating along the y-direction to obtain the interference pattern in the x-direction. Move the image-side checkerboard grating so that the light passes through the one-dimensional grating line perpendicular to the y-direction, and move the object-side Ronchi grating along the x-direction to obtain the interference pattern in the y-direction; S3: Use a filter to process the spectrum of the light intensity, filter out the slow-varying part, and obtain the light intensity before and after phase shift after filtering, so as to obtain the roughly extracted wavefront phase; S4: Use the image sensor to obtain the actual measured value of the light intensity, generate the estimated value of the light intensity through the roughly extracted wavefront phase, and construct an error function according to the actual measured value and the estimated value of the light intensity; S5: Represent the roughly extracted wavefront phase by Zernike polynomials, and perform non-linear iterative optimization on the Zernike coefficients. Specifically: after linearly fitting the Zernike coefficients, perform gradient descent algorithm optimization. For the error function after each optimization, judge its relationship with the optimization judgment threshold. If the optimized error function is greater than or equal to the optimization judgment threshold, judge the relationship between the number of optimizations and the total number of optimizations. If the number of optimizations is less than the total number of optimizations, perform the next optimization, and repeat step S5; otherwise, end the optimization and output the accurate wavefront Zernike coefficients. If the optimized error function is less than the optimization judgment threshold, end the optimization and output the accurate wavefront Zernike coefficients; S6: Reconstruct the wavefront to be measured according to the accurate wavefront Zernike coefficients obtained in step S5.

2. The non - linear optimization wavefront reconstruction method for a shearing interferometry system according to claim 1, characterized in that, In step S2, if only considering the ±1 order interference, the expressions of the light intensity before and after phase shift are where (x, y) are the coordinates on the interference plane, is the light intensity of the interference pattern before phase shift, is the light intensity of the interference pattern after phase shift, I'(x, y) is the background light intensity, i.e., the slow-varying part, and I”(x, y) is the light intensity coefficient varying with the phase, is the phase of the wavefront to be measured, and δ is the phase shift amount.

3. The non - linear optimized wavefront reconstruction method for a shearing interferometry system according to claim 2, characterized in that, In step S3, the expressions of the light intensity before and after phase shift after filtering are as follows: Wherein, (x, y) are the coordinates on the interference plane, I1(x, y) is the light intensity of the filtered interference pattern before phase shift, I2(x, y) is the light intensity of the filtered interference pattern after phase shift, and I”(x, y) is the light intensity coefficient varying with the phase, is the phase of the wavefront to be measured, and δ is the phase shift amount; The roughly extracted wavefront phase is obtained from the above formula The expression is as follows:

4. The non - linear optimized wavefront reconstruction method for a shearing interferometry system according to claim 1, wherein, The expression of the error function in step S4 is as follows: where x and y are the position coordinates of the interference light spot on the interference plane, n is the interference order, k is a natural number; τ |n| is the interference amplitude coefficient, and its value is equal to sinc(n / 2) 2 ; is the wavefront phase of the rough extraction; S is the shear rate.

5. The non - linear optimized wavefront reconstruction method for a shearing interferometry system according to claim 4, wherein In the step S5, the roughly extracted wavefront phase is represented by Zernike polynomials The expression is as follows: a = [a1, a2, …, a j ​ where (ρ,θ) are the polar coordinates within the unit circle, and a j is the Zernike coefficient, and Z j (ρ,θ) is the Zernike polynomial, and a is the vector composed of all Zernike coefficients.

6. The non-linear optimized wavefront reconstruction method for a shearing interferometry system according to claim 5, characterized in that The non-linear iterative optimization algorithm in step S5 is realized through the following sub-steps: (5.1) Linear fitting: Multiply the initial values of all calculated Zernike coefficients by the same constant k, that is, a = ka, to make the value of the error function E the smallest; (5.2) Perform gradient descent algorithm optimization on the Zernike coefficients. The numerical gradient is defined as: g = [g1, g2,..., g j ​ In the formula, E is the error function, h is a positive number; g is the vector composed of all numerical gradients; (5.3) The series expressions for updating the Zernike coefficients after gradient descent are as follows: m t = β1·m t-1 +(1 - β1)·g t where t is the number of optimization times, m t is the first moment of g t , v t is the second moment of g t , both β1 and β2 are moment decay coefficients, is the bias correction of m t , is the bias correction of v t ; a t is the Zernike coefficient after the t-th optimization, α is the learning rate, and ε is a constant added to maintain numerical stability; (5.4) According to the Zernike coefficient a optimized at the t-th time t obtain the error function E optimized at the t-th time t , and judge the relationship between the error function E t and the optimization judgment threshold TH. If E t ≥TH, then judge the relationship between the optimization times t and the total number of optimizations N. If t < N, then perform the next optimization, that is, t = t + 1, and repeat steps (5.2) to (5.4); if t ≥ N, end the optimization and output the accurate wavefront Zernike coefficient a; if E t <TH, then end the optimization and output the accurate wavefront Zernike coefficient a.

7. The non-linear optimized wavefront reconstruction method for a shearing interferometry system according to claim 1, characterized in that The filter in step S3 is a Gaussian high-pass filter.

8. The non-linear optimized wavefront reconstruction method for a shear interferometry system according to claim 5, characterized in that The number of terms j of the Zernike polynomial is selected as 36 terms.

9. The non - linear optimization wavefront reconstruction method for a shearing interferometry system according to claim 1, characterized in that, In step S2, the image-side checkerboard grating is moved by a piezoelectric ceramic actuator.

Images