Method for calculating processing residence time of large-aperture optical element by convolution gradient method

Abstract

The invention relates to the technical field of optical processing, in particular to a method for calculating the processing residence time of a large-aperture optical element through a convolution gradient method, and the method comprises the steps: obtaining the surface shape residual error and a removal function of a to-be-processed workpiece according to the surface shape and the processing technology of the to-be-processed workpiece; a polishing track and polishing track parameters are set according to the surface shape sampling size of the workpiece to be machined; according to the surface shape residual error, the removal function and the polishing track, an objective function is determined, and iteration conditions are set based on the gradient of the objective function; and optimizing the target function by utilizing an iteration condition, and calculating to obtain the final residence time. According to the method, the original residual iteration condition is set as the gradient iteration condition, so that the calculation precision of the residence time is ensured, the calculation and optimization process of the residence time is accelerated, and the engineering period is shortened.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing, and particularly relates to a method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method. Background Art

[0002] Computer-controlled optical surface forming technology is mainly applied to the processing of large-aperture and high-steep aspherical surfaces (especially off-axis aspherical surfaces). Its working principle is to select appropriate processing parameters according to quantitative surface shape detection data, and use a computer to control a small grinding head to move on the optical surface at a specific path, speed and pressure, so as to grind or polish the optical element, and control the material removal amount by controlling the relative pressure, speed between the grinding head and the workpiece, and the dwell time of the grinding head on the workpiece surface. In actual processing, for simplicity of control, a fixed pressure and grinding head rotation speed are generally used, and only the dwell time is controlled. The traditional dwell time problem model is: ; Wherein, represents the convolution operation, E ( x , y ) represents the surface shape error of the optical element to be processed, ( x , y ) represents the surface shape coordinates, R ( ω , ν ) represents the removal function, ([[]] ω , ν ) represents the removal function coordinates, T ( ε , η ) represents the dwell time, ([[]] ε , η ) represents the position coordinates of the processing tool, Re represents the effective radius of the circular optical element to be processed.

[0003] Among the existing common dwell time calculation methods, the polynomial fitting method (disclosed in the paper "Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics" in the journal "Optics Express"), the Bayesian method (disclosed in the paper "Algorithm for ion beam figuring of low-gradient mirrors" in the journal "Applied Optics"), the matrix method (disclosed in the paper "Algorithm for solving the dwell time of magnetorheological machining of large-aperture optical elements" in the journal "Acta Optica Sinica"), and the Fourier transform method (disclosed in the paper "Iterative blind deconvolution method for dwell-time adjustment" in the journal "Applied Optics") are all difficult to quickly calculate the dwell time in the processing application of large-aperture optical elements. In the direct convolution method (disclosed in the paper "Dwell-time algorithm for polishing large optics" in the journal "Applied Optics"), the residual iteration condition is disclosed as the optimization condition. This method depends on the selection of the initial value. Sometimes this selection leads to too slow convergence speed, and often there are errors of very small magnitude that copy the initial surface shape.

[0004] For optical elements in the meter scale, especially for the existing 4m optical elements and the larger-sized optical elements that will appear in the future, the surface shape data is very large. The need to quickly calculate the dwell time should be emphasized to develop corresponding algorithms. Summary of the Invention

[0005] In view of this, the present invention aims to provide a method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method, modifying the original residual iteration condition in the direct convolution method to a gradient iteration condition, while ensuring the calculation accuracy of the dwell time, accelerating the calculation and optimization process of the dwell time, and reducing the engineering cycle.

[0006] To achieve the above object, the technical solution of the present invention is realized as follows: A method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method, comprising: S1: Obtain the surface shape residual and the removal function of the workpiece to be processed according to the surface shape and processing technology of the workpiece to be processed; S2: Set the polishing trajectory and polishing trajectory parameters according to the surface shape sampling size of the workpiece to be processed; S3: Determine the objective function based on the surface shape residual and removal function obtained in step S1 and the polishing trajectory obtained in step S2, and set the iteration conditions based on the gradient of the objective function; S4: Optimize the objective function using the iteration conditions obtained in step S3 to determine the final dwell time.

[0007] Further, the objective function in step S3 is: ; where f ( T ) represents the objective function, T represents the dwell time to be solved, R represents the removal function, E represents the surface shape residual, represents the convolution operation.

[0008] Further, in step S3, the iteration conditions include: ; where T k represents the dwell time of the k th iteration, ξ k represents the damping factor of the k th iteration, represents the gradient of the objective function of the k th iteration.

[0009] Further, the gradient of the objective function is iterated through the following formula: ; where gu represents the set maximum allowable gradient, represents the removal function R the matrix obtained by inverting each element of up, down, left, and right, Δ k represents the surface shape residual of the kth iteration, obtained through the following formula: .

[0010] Further, the damping factor is iterated through the following formula: ; where σ represents the learning parameter reduction ratio.

[0011] Further, step S3 also includes: sampling the surface shape residual, removal function, and polishing trajectory at the same sampling interval; determining the objective function and iteration conditions based on the sampled surface shape residual, removal function, and polishing trajectory.

[0012] Further, step S4 includes: calculating the convergence rate of the surface shape residual at the k-th iteration by removing the function and the dwell time of the k-th iteration; when the convergence rate exceeds a preset convergence rate threshold or the number of iterations reaches the upper limit K, the current dwell time is the final dwell time.

[0013] Further, the convergence rate is: ; where C k represents the convergence rate at the k-th iteration, RMS (·) represents calculating the root mean square.

[0014] Further, the range of the convergence rate threshold is [0, 1].

[0015] Compared with the prior art, the present invention can achieve the following beneficial effects: The method for calculating the dwell time for processing a large-aperture optical element by the convolution gradient method according to the present invention changes the original residual iteration condition to a gradient iteration condition, while ensuring the calculation accuracy of the dwell time, accelerating the calculation and optimization process of the dwell time, reducing the engineering cycle, and being better applied to the processing calculation of meter-level optical elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a schematic flow chart of the method for calculating the dwell time for processing a large-aperture optical element by the convolution gradient method according to the embodiment of the present invention; Figure 2 is a schematic diagram of the surface shape residual of the circular workpiece according to the embodiment of the present invention; Figure 3 is a schematic diagram of the surface shape residual of the annular workpiece according to the embodiment of the present invention; Figure 4 is a schematic diagram of the distribution of the removal function according to the embodiment of the present invention; Figure 5 is a schematic diagram of the distribution of the dwell time for processing the circular workpiece according to the embodiment of the present invention; Figure 6 is a schematic diagram of the surface shape residual of the processed circular workpiece according to the embodiment of the present invention; Figure 7 is a schematic diagram of the distribution of the dwell time for processing the annular workpiece according to the embodiment of the present invention; Figure 8Schematic diagram of the surface form residual of the processed annular workpiece according to the embodiment of the present invention Detailed implementation manners

[0017] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present 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 only used to explain the present invention and do not constitute a limitation to the present invention.

[0018] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0019] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0020] In the description of the present invention, it should be noted that, unless otherwise clearly defined and limited, the terms "installation", "connection", and "connection" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0021] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0022] As Figure 1 shown, the method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to the embodiment of the present invention includes: S1: Obtain the surface form residual and the removal function of the workpiece to be processed according to the surface form and processing technology of the workpiece to be processed.

[0023] Among them, the surface residual of the workpiece to be processed is measured by an interferometer; the removal function is related to the processing technology, and the processing technology includes magnetorheological polishing, small grinding head polishing, ion beam polishing, etc.

[0024] S2: Set the polishing trajectory and polishing trajectory parameters according to the surface sampling size of the workpiece to be processed.

[0025] S3: Determine the objective function based on the surface residual and removal function obtained in step S1, and the polishing trajectory obtained in step S2, and set the iteration conditions based on the gradient of the objective function.

[0026] In some embodiments, step S3 further includes: sampling the surface residual, removal function, and polishing trajectory at the same sampling interval; determining the objective function and iteration conditions according to the sampled surface residual, removal function, and polishing trajectory.

[0027] In some embodiments, the objective function in step S3 is: ; Among them, f ( T ) represents the objective function, T represents the dwell time, which is the quantity to be solved, R represents the removal function, E represents the surface residual, represents the convolution operation.

[0028] In a certain embodiment, a convolution operation conv2_same(·) on the removal function R and the dwell time T is adopted, where conv2_same(·) represents a convolution operation with the same dimension and size. In the convolution operation, the removal function R is the convolution kernel, that is, the dwell time T is convolved with the removal function R, and the dimension and size of the result after convolution are the same as those of the dwell time T. It can be understood that the objective function f (T) is further expressed as: ; The iteration conditions include: ; Among them, T k represents the k -th iteration of the dwell time, ξ k represents the k -th iteration of the damping factor, represents the k -th iteration of the gradient of the objective function.

[0029] The initial dwell time (i.e., the dwell time of the 0-th iteration) T0 is: ; Among them, VR represents the removal rate of the function volume, which is expressed as: ; Among them, Δ x and Δ y represent the sampling interval of the removal function in two dimensions.

[0030] The gradient of the objective function is iterated through the following formula: ; Among them, gu represents the set maximum allowable gradient, represents the removal function R after each element in it is flipped up and down and then flipped left and right. min(·) represents taking the minimum value. Δ k represents the surface shape residual corresponding to the k-th iteration, which is obtained through the following formula: .

[0031] In a certain embodiment, in the objective function k of the -th iteration, a conv2_same(·) convolution operation is performed on the surface shape residual Δ k corresponding to the k-th iteration and the matrix R * , that is: ; In the surface shape residual Δ k corresponding to the k-th iteration, a conv2_same(·) convolution operation is performed on the dwell time k corresponding to the T k -th iteration and the removal function R, that is: ; The damping factor is iterated through the following formula: ; Among them, σ represents the learning parameter reduction ratio.

[0032] The damping factor ξ k , as well as the learning parameter reduction ratio σ , are related to the peak value of the removal rate and need to be adjusted according to the actual situation of the removal function. The maximum allowable gradient gu depends on the distribution of the removal function values and is adjusted according to the actual distribution of the removal function.

[0033] S4: Optimize the objective function using the iteration conditions obtained in step S3 to determine the final dwell time.

[0034] In some embodiments, step S4 includes: calculating the convergence rate of the surface shape residual at the k-th iteration by removing the function and the dwell time at the k-th iteration; when the convergence rate exceeds a preset convergence rate threshold, or the number of iterations reaches the upper limit K, the current dwell time is the final dwell time. The value of the upper limit K is determined according to the actual situation.

[0035] In some embodiments, the convergence rate is: ; where C k represents the convergence rate at the k-th iteration, RMS (·) represents calculating the root mean square. When the convergence rate exceeds the convergence rate threshold, the current dwell time is the final dwell time. For a reasonable processing, the range of the convergence rate threshold is [0, 1]. The convergence rate threshold is obtained by comprehensively considering the actual situation of the calculation cost and optical processing experience, and is preferably set to 0.9. In a certain embodiment, the convergence rate C k at the k-th iteration can be obtained by the following formula: .

[0036] To clearly illustrate the calculation of the dwell time for large-aperture optical element processing by the convolution gradient method described in the embodiments of the present invention, the method provided by the present invention is respectively used to process a circular workpiece with a diameter of 840 mm and an annular workpiece with an outer diameter of 3556 mm and an inner diameter of 460 mm. The surface shape residual of the circular workpiece is as Figure 2 shown. Its peak-to-valley value PV of the surface shape residual is 1.5714λ, and the root mean square value RMS is 0.020096λ, where λ represents the wavelength of the laser emitted by the interferometer, λ = 632.8 nm; the surface shape residual of the annular workpiece is as Figure 3 shown. Its peak-to-valley value PV of the surface shape residual is 2.6772λ, and the root mean square value RMS is 0.053978λ. The same processing technology is used to process the two workpieces, and the removal function is 5 mm × 15 mm for both, as Figure 4 shown. The polishing trajectory uses a grating trajectory. In the process of using the method provided by the present invention to calculate the dwell time for the circular workpiece and the annular workpiece, the parameters are the same, that is: the sampling interval of the surface shape residual, the removal function, and the polishing trajectory is 1 mm, that is, Δ x and Δ y are both 1 mm, and the maximum allowed sampling pitch is 1 mm × 3 mm (that is, the maximum value of Δ x is 1 mm, and the maximum value of Δ y is 3 mm), and the maximum allowed gradientgu = 10 4 , the learning parameter reduction ratio σ = 0.98, the initial damping factor (i.e., the damping factor at the 0th iteration) ξ 0 = 0.1, the convergence rate threshold is set to 0.9, and the upper limit K of the number of iterations is 20.

[0037] For circular workpieces, the final dwell time distribution calculated using the algorithm provided by the present invention is as follows Figure 5 shown. The final total dwell time is 30.89 h, and the calculation time of the entire method reaches 6 s. The surface form residual of the circular workpiece after being processed with the final dwell time determined by the method provided by the present invention is as follows Figure 6 shown. The PV corresponding to its surface form residual is 1.34159λ, and the RMS is 0.00233λ. Calculate the difference between the surface form residual of the unprocessed circular workpiece and the surface form residual of the circular workpiece after being processed with the final dwell time determined by the method provided by the present invention through the following formula to prove the convergence of the method provided by the present invention RSE = E - E’ = E - conv2_same(T, R) .

[0038] Among them, RSE represents the difference, E represents the surface form residual of the unprocessed workpiece, E’ represents the surface form residual of the workpiece after being processed.

[0039] And calculate the convergence rate at the kth iteration through the following formula C k : ; The surface form convergence rate of the processed circular workpiece C K is 0.8841. The calculation stops when the upper limit of the number of iterations is reached. Although the ideal convergence rate is not achieved, its calculation time is acceptable. The calculation results can be made to better meet the calculation requirements by adjusting other parameters and performing multiple calculations.

[0040] For annular workpieces, the final dwell time distribution calculated using the algorithm provided by the present invention is as follows Figure 7 shown. The final total dwell time is 530.69 h, and the calculation time of the entire method reaches 198 s. The surface form residual of the annular workpiece after being processed with the final dwell time determined by the method provided by the present invention is as follows Figure 8 shown. The PV corresponding to its surface form residual is 2.43062λ, and the RMS is 0.00503λ. Calculate the difference between the surface form residual of the unprocessed annular workpiece and the surface form residual of the annular workpiece after being processed with the final dwell time determined by the method provided by the present invention through the above formula. The surface form convergence rate of the processed annular workpiece isC K = 0.9068.

[0041] For the above two embodiments, the sampling intervals used are Δ x and Δ y both being 1 mm. If the sampling interval is relaxed to the maximum allowable sampling interval, Δ x being 1 mm and Δ y being 3 mm, then the calculation time for the circular element embodiment can reach 2 s, and the calculation time for the annular element embodiment can reach 100 s. However, it should be noted that the initial learning rate needs to be increased because the relative gradient decreases when the data becomes sparse, and the learning intensity needs to be increased.

[0042] It should be understood that various forms of the processes shown above can be used, with steps reordered, added, or deleted. For example, the steps recited in the disclosure of the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution disclosed in the present invention can be achieved. No limitation is made herein.

[0043] The above specific embodiments do not constitute a limitation on the protection scope of the present 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 the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for calculating the dwell time of large-aperture optical element processing by convolution gradient method, characterized in that Including: S1: Obtain the surface form residual and the removal function of the workpiece to be processed according to the surface form and processing technology of the workpiece to be processed; S2: Set the polishing trajectory and polishing trajectory parameters according to the surface form sampling size of the workpiece to be processed; S3: Determine the objective function according to the surface form residual and removal function obtained in step S1 and the polishing trajectory obtained in step S2, and set the iteration condition based on the gradient of the objective function; S4: Optimize the objective function using the iteration condition obtained in step S3 to determine the final dwell time.

2. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 1, wherein The objective function in step S3 is: ； Among them, f ( T ) represents the objective function, T represents the residence time to be solved, R represents the removal function, E represents the surface form residual, represents the convolution operation.

3. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 2, characterized in that In step S3, the iteration condition includes: ； Among them, T k represents the residence time of the k th iteration, ξ k represents the damping factor of the k th iteration, represents the gradient of the objective function of the k th iteration.

4. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 3, characterized in that The gradient of the objective function is calculated by the following formula: ； Among them, gu represents the set maximum allowable gradient, represents the removal function R is the matrix obtained by inverting each element of the matrix k represents the surface residual of the k-th iteration, which is obtained by the following formula: 。 5. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 3, characterized in that, The damping factor is calculated by the following formula: ； Among them, σ represents the learning parameter reduction ratio.

6. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 1, wherein Step S3 further includes: Sample the surface form residual, the removal function, and the polishing trajectory at the same sampling interval; Determine the objective function and the iteration condition according to the sampled surface form residual, removal function, and polishing trajectory.

7. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 3, wherein Step S4 includes: Calculate the convergence rate of the surface form residual at the k-th iteration through the removal function and the dwell time at the k-th iteration; When the convergence rate exceeds the preset convergence rate threshold or the number of iterations reaches the upper limit K, the current dwell time is the final dwell time.

8. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 7, characterized in that The convergence rate is: ； Among them, C k represents the convergence rate at the k-th iteration, RMS (·) represents the calculation of the root mean square.

9. The method for calculating the dwell time of large-aperture optical element processing by the convolution gradient method according to claim 7, characterized in that, The range of the convergence rate threshold is [0, 1].

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