Computer-aided alignment denoising method for high-precision optical systems

Abstract

The present application relates to a kind of computer-aided alignment denoising methods for high-precision optical system, first, build the simulation model of misalignment optical system, calculate sensitivity matrix by difference method, construct imaging quality evaluation objective function;Interferometer multiple field multiple acquisition system wave aberration is used, constructs multiple aberration matrix and is spliced to generate observation matrix;Observation matrix is sequentially implemented dense noise denoising, matrix row average processing, spliced to further complete sparse noise denoising after full field aberration matrix is obtained;Compensation amount is solved relying on sensitivity matrix, effective compensation amount is screened in combination with objective function and is carried out system alignment, after alignment, test imaging quality, not meet the index then repeat wave aberration measurement and denoising process iterative correction.The advantage is that: it can effectively reduce the negative influence of interferometer measurement noise on alignment accuracy, improve the alignment accuracy of high-precision optical system, and the method can maintain stable denoising performance under different noise intensity.

Description

Technical Field

[0001] This invention relates to the field of optical system assembly and adjustment technology, and in particular to a noise reduction method for computer-aided assembly and adjustment of high-precision optical systems. Background Technology

[0002] Wavelength aberration is a core indicator determining the imaging performance of high-precision optical systems. With increasingly stringent imaging quality requirements, the accurate detection and control of wavelength aberration has become a key technological bottleneck restricting the system resolution of high-precision optical systems. As the core measurement device in the assembly and adjustment of optical systems, the interferometer's measurement accuracy is closely related to the final imaging quality. However, in practical engineering environments, interferometric measurement data are inevitably affected by both systematic errors and random noise, leading to deviations in the extraction of Zernike coefficients.

[0003] Because the sensitivity matrix typically exhibits ill-conditioned characteristics, even small errors will be significantly amplified, thus affecting the stability of the compensation solution and severely impacting the alignment accuracy. To address the challenges posed by noise in Computer Aided Alignment (CAA), a series of noise suppression techniques have been developed to optimize measurement methods or improve algorithms and enhance signal quality. These include: 1. Real-time measurement of the optical path difference ratio using a reference interferometer to adaptively suppress light source phase noise; 2. An adaptive noise cancellation technique that dynamically adjusts the cancellation gain to maintain optimal suppression by real-time monitoring of the optical path difference ratio between the sensing arm and the reference arm; 3. A typical phase measurement interferometry algorithm that directly calculates the wavefront phase distribution by acquiring multiple frames of phase-shifted interferograms and using least-squares fitting; 4. For the calibration of the interferometer's own systematic errors, by establishing a rotational symmetry model, applying multi-angle sampling to the test mirror or reference mirror, and taking the average, the inherent specific angular harmonic errors of the interferometer can be effectively eliminated.

[0004] However, existing methods are mainly limited to error suppression at the level of interferometric images or phase reconstruction, lacking a systematic modeling and denoising strategy based on the overall structure of the Zernike coefficient matrix. Furthermore, a unified and effective processing framework is lacking for mixed scenarios of dense and sparse noise. Therefore, there is a need to develop a denoising method for computer-aided assembly in high-precision optical systems to achieve layered suppression of multiple types of noise, thereby improving the stability and accuracy of computer-aided assembly. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a computer-aided assembly and noise reduction method for high-precision optical systems, specifically comprising the following steps: S1: Construct a simulation model based on the misaligned optical system to be adjusted, sequentially adjust the values ​​of each compensator in the simulation model, and calculate the sensitivity matrix using the difference method. And set the objective function; S2: The wave aberration of the misaligned optical system is measured multiple times under multiple fields of view using an interferometer. The Zernike coefficients are fitted and multiple aberration matrices F1 are constructed. The column vectors of the multiple aberration matrices in the same field of view are extracted and spliced ​​together to form the observation matrix F2. S3: Perform dense noise denoising on the observation matrix F2 of each field of view obtained in step S2 to obtain the single field of view dense denoising matrix F3; S4: Take the average value of each row of the single-view dense denoising matrix F3 to obtain the one-dimensional dense denoising matrix F4, and then stitch the one-dimensional dense denoising matrix F4 of each view in the order of the view to obtain the full-view aberration matrix F5. S5: Perform sparse noise denoising on the full-field aberration matrix F5 to obtain a low-rank aberration matrix. ; S6: Combine the sensitivity matrix J and the low-rank aberration matrix Substitute the compensation amount into the compensation amount calculation formula to solve for the compensation amount. Select the effective compensation amount through the objective function. Use the effective compensation amount to adjust the misaligned optical system. Stop the adjustment when the imaging quality meets the standard. Otherwise, repeat steps S2 to S5.

[0006] Preferably, the sensitivity matrix in step S1 The dimension is n Zernike ×m, sensitivity matrix Middle elements The calculation formula is: ; Where, n Zernike The number of terms representing the Zernike coefficient. Represents the number of compensators. Elements representing the Zernike coefficient matrix, Elements representing compensators.

[0007] Preferably, in step S2, the wavelet aberration of the misaligned optical system is measured n times to construct n sets of aberration matrices F1, each set of aberration matrices F1 having a dimension of n. Zernike ×n field , where n Zernike n is the number of terms in the Zernike coefficients. field The number of fields of view acquired; extract the column vectors of the same field of view from each aberration matrix F1, and concatenate the extracted n column vectors to obtain the observation matrix F2, which has an n-dimensional dimension. Zernike ×n.

[0008] Preferably, step S3 includes the following sub-steps: S31: Extract the mean of each row of the observation matrix F2, and subtract the mean of each row from the mean of the row in the observation matrix F2 to obtain the mean-reduced matrix. The expression is as follows: ; in, It is the mean vector of each row, with dimension n. Zernike ×1, It is an n x 1 column vector containing only 1s. Each element in the vector has a value of 1. The superscript T indicates that the vector is empty. Transpose; S32: The mean-removed matrix obtained in step S31 Perform singular value decomposition: ; in, Let be the first singular value matrix, represented as: , Represents singular values, Represents a diagonal matrix; Represents the first left singular vector matrix; Denotes the first right singular vector matrix; S33: Preserve the first singular value matrix Center front Set one singular value to zero and the rest to zero to obtain the first truncated singular value matrix. , is represented as: ; Use the first truncated singular value matrix Reconstruct the matrix to obtain the mean-reduced matrix. The low-rank approximation matrix when taking the first k ranks , is represented as: ; S34: Let the low-rank approximation matrix Adding the mean of the corresponding row in the observation matrix F2 to each row yields the single-view dense denoising matrix F3 when taking the first k ranks, as shown in the following formula: ; The same operation is performed on the observation matrix of each field of view to obtain the single-field dense denoising matrix of each field of view.

[0009] Preferably, the dimension of each one-dimensional dense denoising matrix F4 in step S4 is n. Zernike ×1, the dimension of the full-field aberration matrix F5 is n. Zernike ×n field .

[0010] Preferably, step S5 specifically includes the following sub-steps: S51: Using the augmented Lagrange multiplier method, the full-field aberration matrix F5 obtained in step S4 is processed to obtain the augmented Lagrange function, expressed as: ; in, Represents the denoised low-rank aberration matrix; N represents the sparse noise matrix; This represents the calculation of the nuclear norm; represent Norm; It is a regularization parameter; Indicates the inner product; Denotes the Frobenius norm; S52: In the augmented Lagrangian function, the sparse matrix is ​​fixed. , multiplier and penalty parameters The value of remains unchanged, low-rank aberration matrix The update rules are as follows: ; in, yes The optimal solution at the (k+1)th iteration; The meaning is the smallest time within the curly braces. The value of ; S53: In the augmented Lagrangian function, fix the low-rank aberration matrix. , multiplier and penalty parameters The values ​​of remain unchanged, sparse matrix The update rules are as follows: ; in, It is the optimal solution for N in the (k+1)th iteration; S54: The results obtained in steps S52 and S53 Substituting N into the formula Increase the penalty parameter The following formula is used to determine whether the iteration has converged: ; in, If the above formula is satisfied or the maximum number of iterations is reached, and the set tolerance is met, then the low-rank aberration matrix is ​​output. This is the aberration matrix after denoising the sparse noise; otherwise, continue to repeat steps S52~S54 until the convergence requirement is met.

[0011] Preferably, step S51 further includes: Step S511: Set the low-rank aberration matrix The initial values ​​of the sparse noise matrix N and the multipliers Y are both zero matrices with the same dimensions as F5; the regularization parameter... The initialization formula is as follows: ; For penalty parameters The initialization formula is as follows: .

[0012] Preferably, in step S6, the low-rank aberration matrix obtained in step S5 is... Convert to a single-column vector. Calculate the compensation amount using the compensation amount calculation formula. The formula is as follows: ; in, An identity matrix whose main diagonal elements are all 1s; It is the damping factor; , J is the ideal aberration matrix of the simulation model; J is the sensitivity matrix. Determine the compensation amount based on the preset objective function The effectiveness of this compensation amount depends on whether the objective function value decreases. The effective compensation amount is used to complete the system setup and adjustment; if the objective function value increases, the damping factor D is adjusted and the compensation amount is recalculated. Until an effective compensation amount is obtained; after assembly and adjustment, the imaging quality is detected and compared with the preset assembly and adjustment index. If the index is met, the assembly and adjustment ends; if the index is not met, the iteration correction from step S2 to step S5 is repeated.

[0013] Compared with the prior art, the present invention can achieve the following beneficial effects: The noise reduction method for computer-aided assembly and adjustment of high-precision optical systems of the present invention can effectively reduce the negative impact of interferometer measurement noise on assembly and adjustment accuracy, and improve the assembly and adjustment accuracy of high-precision optical systems; moreover, the method can maintain stable noise reduction performance under different noise intensities. Attached Figure Description

[0014] Figure 1 This is a flowchart of a noise reduction method for computer-aided assembly and adjustment of a high-precision optical system according to an embodiment of the present invention; Figure 2 This is a flowchart of computer-aided assembly and adjustment for a high-precision optical system provided according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a noise reduction process for computer-aided assembly and adjustment of a high-precision optical system according to an embodiment of the present invention; Figure 4This is a simulation example optical system provided according to an embodiment of the present invention; Figure 5 This is a comparison of simulation results between the noise reduction method for computer-aided assembly and adjustment of high-precision optical systems provided by the embodiments of the present invention and conventional computer-aided assembly and adjustment methods; Figure 6 This is a comparison of the image quality of a noise reduction method for computer-aided assembly and adjustment of a high-precision optical system provided by an embodiment of the present invention with that of conventional computer-aided assembly and adjustment results at different noise levels. Detailed Implementation

[0015] In the following description, embodiments of the invention will be described with reference to the accompanying drawings. In the description below, the same modules are denoted by the same reference numerals. Where the same reference numerals are used, their names and functions are also the same. Therefore, their detailed description will not be repeated.

[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0017] This invention provides a denoising method for computer-aided assembly and adjustment of high-precision optical systems. By first performing dense noise denoising and then sparse noise denoising, it achieves layered suppression of multiple types of noise, thereby improving the stability and accuracy of computer-aided assembly and adjustment. See the flowchart of the denoising method. Figure 1 See the computer-aided assembly flowchart. Figure 2 See the diagram for the noise reduction process. Figure 3 Specifically, it includes the following steps: S1: Construct a simulation model in simulation software based on the misaligned optical system to be adjusted, sequentially adjust the values ​​of each compensator in the simulation model, and calculate the sensitivity matrix using the finite difference method (first order). ; Sensitivity matrix The dimension is n Zernike ×m,n Zernike The number of terms representing the Zernike coefficient. Represents the number of compensators; elements in the sensitivity matrix The calculation formula is: ; in, Elements representing the Zernike coefficient matrix, Elements representing compensators; In some implementations, the calculation of the sensitivity matrix can be extended from first order to second order, depending on the accuracy requirements. The compensator is the eccentricity of the lens or the air gap between adjacent lenses in the simulation model; Meanwhile, an objective function is constructed to subsequently determine the degradation of imaging quality after the optical system is assembled and adjusted; In the evaluation system of computer-aided optical assembly and adjustment, the objective function needs to be constructed by comprehensively considering three dimensions: image quality evaluation index, wavefront error data, and system assembly tolerance. The appropriate function construction form can be selected according to the actual engineering accuracy requirements, and the corresponding numerical optimization algorithm can be used to complete the solution. The optional optimization algorithms include, but are not limited to, the least squares algorithm and the orthogonal descent (coordinate descent) algorithm.

[0018] S2: The wavefront aberration of the misaligned system is measured multiple times using an interferometer to extract Zernike coefficients and construct an aberration matrix. The wavefront aberration of the misaligned optical system to be installed is measured n times under multiple fields of view using an interferometer. The corresponding Zernike coefficients are fitted to obtain the values, and n sets of aberration matrices F1 for the misaligned optical system are constructed. Each set of aberration matrices F1 has a dimension of n. Zernike ×n field ; where n Zernike n is the number of terms in the Zernike coefficients. field The number of fields of view captured; Extract the column vectors of the same field of view from each set of aberration matrices F1, and concatenate the extracted n column vectors sequentially to obtain the observation matrix F2, which has an n-dimensional dimension. Zernike ×n; Specifically, the Zernike coefficient is either the standard Zernike coefficient or the striped Zernike coefficient, with the striped Zernike coefficient being preferred.

[0019] S3: Perform dense noise denoising on the observation matrix F2 of the same field of view. The specific steps are as follows: Step S31: Extract the mean of each row of the observation matrix F2. Subtract the mean of each row from the mean of the observed matrix F2 to obtain the mean-reduced matrix. , represented as: ; in, It is the mean vector of each row, with dimension n. Zernike ×1, It is an n x 1 column vector containing only 1s. Each element in the vector has a value of 1. The superscript T indicates that the vector is empty. Transpose.

[0020] Step S32: The mean-removed matrix obtained in step S31 is processed... The formula for performing singular value decomposition is as follows: ; in, Let be the first singular value matrix, represented as: , These represent singular values, which reflect the magnitude of the contribution of the orthogonal pattern to the matrix transformation. Represents a diagonal matrix; Represents the first left singular vector matrix; Let represent the first right singular vector matrix.

[0021] Step S33: Retain the first singular value matrix Center front Set one singular value to zero and the rest to zero to obtain the first truncated singular value matrix. , is represented as: ; Use the first truncated singular value matrix Reconstructing the mean-reduced matrix The mean-removed matrix is ​​obtained. The low-rank approximation matrix when taking the first k ranks , is represented as: .

[0022] Step S34: Let the low-rank approximation matrix Adding the mean of the corresponding row in the observation matrix F2 to each row yields the single-view dense denoising matrix F3 when taking the first k ranks, as shown in the following formula: ; The same operation is performed on the observation matrix of each field of view to obtain the single-field dense denoising matrix of each field of view.

[0023] S4: Stitch together the aberration matrices of each field of view.

[0024] The average value of each row of the single-view dense denoising matrix F3 is taken to obtain the one-dimensional dense denoising matrix F4 for that view. The dimension of the one-dimensional dense denoising matrix F4 is n. Zernike ×1; Perform the same operation on the single-view dense denoising matrix for each field of view to obtain n field A one-dimensional dense denoising matrix F4 for each field of view will be used to denoise n field The one-dimensional dense denoising matrix F4 for each field of view is concatenated sequentially according to the field of view order to obtain the full-field aberration matrix F5, where the dimension of F5 is n. Zernike ×n field .

[0025] S5: Perform sparse noise denoising on the full-field aberration matrix F5 to obtain a low-rank aberration matrix. Specifically, the steps include the following: S51: Decompose the full-field aberration matrix F5 obtained in step S4 using robust principal component analysis, expressed as: F5 = +N; in, The sparse noise matrix represents the noise components separated from the full-field aberration matrix F5.

[0026] If directly based on the robust principal component analysis model F5= +N Solve for the low-rank aberration matrix The optimization problem corresponding to the sparse noise matrix N possesses both non-convex and non-smooth characteristics, making it difficult to solve directly. Therefore, a convex relaxation technique is employed to transform it into a solvable convex optimization problem under the given constraints. Next, solve the objective function. The low-rank aberration matrix corresponding to the minimum value With sparse noise matrix N; in, The matrix represents the calculation of the nuclear norm. The sum of all singular values ​​is used to induce a low-rank aberration matrix. ; represent Norms are used to induce sparse noise matrices. ; It is a regularization parameter used to balance the importance of low-rank terms and sparse terms.

[0027] Due to constraints It is difficult to strictly satisfy the equality constraint, so Lagrange multipliers are used to handle the equality constraint. The augmented Lagrange function after using Lagrange multipliers Y is defined as follows: ; in: represents the Frobenius norm, which is the square root of the sum of the squares of the absolute values ​​of all elements in the matrix. This represents the inner product, which is the sum of the elements multiplied at corresponding positions of two matrices. This represents the penalty parameter.

[0028] Set the low-rank aberration matrix The initial values ​​of the sparse noise matrix N and the Lagrange multipliers Y are both all-zero matrices. These all-zero matrices have the same dimension as the full-field aberration matrix F5. ​​The regularization parameter... The initialization formula is as follows: ; For penalty parameters The initialization formula is as follows: ; Different initial values ​​can also be set depending on the situation.

[0029] S52: Solving for the low-rank aberration matrix .

[0030] In augmented Lagrange function First, fix the sparse noise matrix. , multiplier and penalty parameters The values ​​of remain unchanged, only the low-rank aberration matrix With variables as variables, the original multivariate joint optimization problem is transformed into solving only the low-rank aberration matrix. Independent subproblems, low-rank aberration matrix The update and iteration rules are as follows: ; in, yes The optimal solution at the (k+1)th iteration; The meaning is the smallest time within the curly braces. The value of , low-rank aberration matrix The calculation process for the independent subproblems is as follows: Solving low-rank matrices using the singular value thresholding method Let temporary intermediate variables Perform singular value decomposition on the temporary intermediate variable B: ; in, The second left singular vector matrix, It is the second right singular vector matrix. The second singular value matrix is ​​represented as: , Represents singular values; calculate The formula is as follows: ; in, Indicates taking The larger value between 0 and 0.

[0031] S53: Solving the sparse noise matrix .

[0032] In augmented Lagrange function In the middle, the low-rank aberration matrix is ​​fixed. , multiplier Penalty parameters The value of remains unchanged; at this point, only the sparse noise matrix remains. With variables as variables, the original multivariate joint optimization problem is transformed into solving only the sparse noise matrix. Independent subproblems, sparse noise matrix The update and iteration rules are as follows: ; in, It is the optimal solution for N in the (k+1)th iteration; Calculate the sparse noise matrix using the soft thresholding method. The formula is as follows: ; in, (N) is the sign function: when N > 0 ;when hour, When N=0, ; Indicates taking The larger of the two values.

[0033] S54: The formula for the Lagrange multiplier Y is expressed as: The low-rank aberration matrix obtained in step S52 The sparse noise matrix obtained in step S53 Substituting into the above equation updates the Lagrange multiplier Y, and simultaneously increases the penalty parameter. The value of the convergence criterion is determined, and the convergence criterion formula is used to determine whether the iteration meets the termination condition. The convergence criterion formula is expressed as follows: ; in, The tolerance is set; if the low-rank aberration matrix obtained after steps S52 and S53 is... and sparse noise matrix If the above formula is satisfied, or the maximum number of iterations is reached, then the low-rank aberration matrix is ​​output. This is the aberration matrix after denoising the sparse noise; otherwise, continue to cycle through steps S52~S54 until the requirements are met.

[0034] In summary, for the optimization problem of the augmented Lagrangian function, an alternating iterative approach is adopted, applying it to the low-rank aberration matrix respectively. and sparse noise matrix Each corresponding independent subproblem is solved to update the variables; the Lagrange multipliers are dynamically adjusted synchronously. and penalty parameters The iteration continues until the preset convergence condition is met.

[0035] S6: Calculate the compensation amount, verify its effectiveness by changing the objective function value, adjust the misaligned optical system using the effective compensation amount, and check the image quality after adjustment. If the predetermined standard is met, stop the adjustment; otherwise, repeat steps S2 to S5. Specifically, this includes the following steps: The low-rank aberration matrix obtained in step S5 Convert to a single-column vector. The compensation amount is calculated using the compensation amount calculation formula. , represented as: ; Where J is the sensitivity matrix; The identity matrix has elements on its main diagonal with a value of 1, and all other elements with a value of 0. It is the damping factor; , This is the ideal aberration matrix of the simulation model, free from noise error factors.

[0036] Adjust compensation amount Then, if the value of the objective function decreases, the compensation amount is determined. This is an effective compensation quantity; if the value of the objective function increases, then the damping factor... Make corrections and recalculate the compensation amount. This process is repeated until an effective compensation amount that can reduce the objective function is calculated.

[0037] The offset optical system is compensated and adjusted using the effective compensation amount. After adjustment, the imaging quality of the optical system is detected and compared with the preset adjustment index. If the measured imaging quality meets the adjustment index requirements, the whole machine adjustment process is terminated. Otherwise, steps S2 to S5 are repeated.

[0038] Example 1 The optical system used in this embodiment is a high-precision microscope lens with a working wavelength of deep ultraviolet (266 nm), such as... Figure 4 As shown.

[0039] In this embodiment, the Fringe Zernike polynomial is used as the optimization parameter. The first four terms mainly characterize the placement error of the misaligned system to be installed, so they are removed from the objective function definition. The constructed objective function formula is as follows: ; in, Indicates the first The Zernike coefficient vector from the 5th to the 37th terms in each field of view. Represents the L2 norm; the optical system in this embodiment acquires a total of 9 fields of view, namely... Take 9.

[0040] The measurement error between the Zernike coefficient values ​​obtained by the interferometer's actual fitting and the true aberration coefficients of the optical system is shown in Table 1.

[0041] Table 1. Measurement error of individual Zernike coefficients

[0042] The image quality of the simulation model, calculated according to the objective function formula, is 0.036661. , The operating band of the simulation model is specified in this embodiment. =266 nm.

[0043] Based on the given processing and assembly tolerances, as shown in Table 2, 1000 sets of misaligned systems were randomly generated using the Monte Carlo method. The Zernike coefficients of each misaligned system were calculated under multiple fields of view, constructing a set of misalignment aberration matrices. The average objective function value for the 1000 misaligned systems was statistically analyzed to be 0.177096. .

[0044] Table 2. Range of machining error and assembly / adjustment error

[0045] During computer-aided assembly and adjustment Figure 4 The eccentricity of the fifth lens from left to right and all air gaps were selected as compensators. In this embodiment, 1000 sets of simulation experiments were conducted to verify the impact of the noise reduction method of this invention on the accuracy of computer-aided assembly.

[0046] To verify the effectiveness of the denoising method of the present invention, the computer-aided assembly and adjustment results under two modes were compared. Mode 1 is the conventional computer-aided assembly and adjustment method, and Mode 2 is the computer-aided assembly and adjustment method of the present invention with denoising processing.

[0047] To clearly demonstrate the experimental results, the objective function of a portion of the experimental results was randomly selected. Plot a scatter plot, such as Figure 5 As shown, Figure 5 In conventional computer-aided assembly and adjustment, the results are represented by circular markers, indicating noisy CAA; in this method, the results are represented by triangular markers, indicating denoised CAA; and in ideal simulation, the results are represented by square markers, indicating noiseless CAA. Statistical analysis of the simulation results yields the objective function of 1000 sets of experiments in Mode 1. The mean is 0.038154. The objective function of 1000 sets of experiments in Mode 2 The mean is 0.037959 The image quality of Mode 2 is improved by approximately 0.512% compared to Mode 1. These results statistically validate that the denoising process described in this method can effectively improve the computer-aided assembly accuracy of high-precision microscope lenses.

[0048] To comprehensively evaluate the statistical properties of the method proposed in this invention, Figure 6 Box plots of the computer-aided assembly and adjustment results of this method under different noise levels are presented. The upper and lower boundaries of the left box in the figure correspond to the objective function after computer-aided assembly and adjustment, respectively. The first and third quartiles, with horizontal lines inside the boxes representing the median and cubes inside the boxes representing the mean; the objective function after computer-aided assembly is shown on the right. The distribution scatter plot; the conventional computer-aided assembly and adjustment results are represented as noisy CAA; the computer-aided assembly and adjustment results of this method are represented as denoised CAA. Observing the line graph, as the noise level increases from 1 to 3 times, in the conventional computer-aided assembly and adjustment results (noisy CAA), the objective function... The mean is 0.038154 Rising to 0.039430 In the computer-aided assembly and adjustment results (denoised CAA) of this method, the objective function is... The mean is only 0.037959 It rose slightly to 0.038030 The overall distribution range remained stable. This indicates that the proposed method can effectively suppress the interference of measurement noise on the computer-aided assembly and adjustment process even with increased noise, demonstrating excellent robustness.

[0049] Experimental results show that by introducing the denoising method of the present invention for computer-aided assembly and adjustment of high-precision optical systems into the computer-aided assembly and adjustment process of high-precision microscope heads, the negative impact of interferometer measurement noise on assembly and adjustment accuracy can be effectively reduced, and the assembly and adjustment accuracy of high-precision optical systems can be improved. Moreover, the method can maintain stable denoising performance under different noise intensities.

[0050] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0051] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A computer-aided assembly and noise reduction method for high-precision optical systems, characterized in that, Includes the following steps: S1: Construct a simulation model based on the misaligned optical system to be adjusted, sequentially adjust the values ​​of each compensator in the simulation model, and calculate the sensitivity matrix using the difference method. And set the objective function; S2: The wave aberration of the misaligned optical system is measured multiple times under multiple fields of view using an interferometer. The Zernike coefficients are fitted and multiple aberration matrices F1 are constructed. The column vectors of the multiple aberration matrices in the same field of view are extracted and spliced ​​together to form the observation matrix F2. S3: Perform dense noise denoising on the observation matrix F2 of each field of view obtained in step S2 to obtain a single field of view dense denoising matrix F3; S4: Take the average value of each row of the single-view dense denoising matrix F3 to obtain the one-dimensional dense denoising matrix F4, and then stitch the one-dimensional dense denoising matrix F4 of each view in the order of the view to obtain the full-view aberration matrix F5. S5: Perform sparse noise denoising on the full-field aberration matrix F5 to obtain a low-rank aberration matrix. ; S6: Combine the sensitivity matrix J and the low-rank aberration matrix Substitute the compensation amount into the compensation amount calculation formula to solve for the compensation amount. Use the objective function to select the effective compensation amount. Use the effective compensation amount to adjust the misaligned optical system. Stop the adjustment when the imaging quality meets the standard. Otherwise, repeat steps S2 to S5.

2. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, The sensitivity matrix mentioned in step S1 The dimension is n Zernike ×m, sensitivity matrix Middle elements The calculation formula is: ； Where, n Zernike The number of terms representing the Zernike coefficient. Represents the number of compensators. Elements representing the Zernike coefficient matrix, Elements representing compensators.

3. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, In step S2, the wavelet aberration of the misaligned optical system is measured n times to construct n sets of aberration matrices F1, each of which has a dimension of n. Zernike ×n field , where n Zernike n is the number of terms in the Zernike coefficients. field The number of fields of view acquired; extract the column vectors of the same field of view from each aberration matrix F1, and concatenate the extracted n column vectors to obtain the observation matrix F2, which has an n-dimensional dimension. Zernike ×n.

4. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, Step S3 includes the following sub-steps: S31: Extract the mean of each row of the observation matrix F2, and subtract the mean of each row from the mean of the observed matrix F2 to obtain the mean-reduced matrix. The expression is as follows: ； in, It is the mean vector of each row, with dimension n. Zernike ×1, It is an n x 1 column vector containing only 1s. Each element in the vector has a value of 1. The superscript T indicates that the vector is empty. Transpose; S32: The mean-removed matrix obtained in step S31 Perform singular value decomposition: ； in, Let be the first singular value matrix, represented as: , Represents singular values, Represents a diagonal matrix; Denotes the first left singular vector matrix; Denotes the first right singular vector matrix; S33: Preserve the first singular value matrix Center front Set one singular value to zero and the rest to zero to obtain the first truncated singular value matrix. , represented as: ； Use the first truncated singular value matrix Reconstruct the matrix to obtain the mean-reduced matrix. The low-rank approximation matrix when taking the first k ranks , represented as: ; S34: Let the low-rank approximation matrix Adding the mean of the corresponding row in the observation matrix F2 to each row yields the single-view dense denoising matrix F3 when taking the first k ranks, as shown in the following formula: ； The same operation is performed on the observation matrix of each field of view to obtain the single-field dense denoising matrix of each field of view.

5. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, In step S4, each one-dimensional dense denoising matrix F4 has a dimension of n. Zernike ×1, the dimension of the full-field aberration matrix F5 is n. Zernike ×n field .

6. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, Step S5 specifically includes the following sub-steps: S51: Using the augmented Lagrange multiplier method, the full-field aberration matrix F5 obtained in step S4 is processed to obtain the augmented Lagrange function, expressed as: ； in, Represents the denoised low-rank aberration matrix; N represents the sparse noise matrix; This represents the calculation of the nuclear norm; represent Norm; It is a regularization parameter; Indicates the inner product; Denotes the Frobenius norm; S52: In the augmented Lagrangian function, the sparse matrix is ​​fixed. , multiplier and penalty parameters The value of remains unchanged, low-rank aberration matrix The update rules are as follows: ； in, yes The optimal solution at the (k+1)th iteration; The meaning is the smallest time within the curly braces. The possible values ​​of ; S53: In the augmented Lagrangian function, fix the low-rank aberration matrix. , multiplier and penalty parameters The values ​​of remain unchanged, sparse matrix The update rules are as follows: ； in, It is the optimal solution for N in the (k+1)th iteration; S54: The results obtained in steps S52 and S53 Substituting N into the formula Increase the penalty parameter The following formula is used to determine whether the iteration has converged: ； in, If the above formula is satisfied or the maximum number of iterations is reached, and the set tolerance is met, then the low-rank aberration matrix is ​​output. This is the aberration matrix after denoising the sparse noise; otherwise, continue to repeat steps S52~S54 until the convergence requirement is met.

7. A computer-aided assembly and noise reduction method for high-precision optical systems according to claim 6, characterized in that, Step S51 also includes: Step S511: Set the low-rank aberration matrix The initial values ​​of the sparse noise matrix N and the multipliers Y are both zero matrices with the same dimensions as F5; the regularization parameter... The initialization formula is as follows: ； For penalty parameters The initialization formula is as follows: 。 8. The computer-aided assembly and noise reduction method for high-precision optical systems according to claim 1, characterized in that, In step S6, the low-rank aberration matrix obtained in step S5 is... Convert to a single-column vector. Calculate the compensation amount using the compensation amount calculation formula. The formula is as follows: ； in, An identity matrix whose main diagonal elements are all 1s; It is the damping factor; , J is the ideal aberration matrix of the simulation model; J is the sensitivity matrix; Determine the compensation amount based on the preset objective function The effectiveness of this compensation amount depends on whether the objective function value decreases. The effective compensation amount is used to complete the system setup and adjustment; if the objective function value increases, the damping factor D is adjusted and the compensation amount is recalculated. Until an effective compensation amount is obtained; after assembly and adjustment, the imaging quality is detected and compared with the preset assembly and adjustment index. If the index is met, the assembly and adjustment ends; if the index is not met, the iteration correction from step S2 to step S5 is repeated.

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