Method and device for processing surface data of diffractive optical element based on least squares method

Abstract

The present invention discloses a method and device for processing surface shape data of a diffractive optical element based on the least squares method. By simply loading the surface shape data file measured by the profiler and the design parameter file of the diffractive optical element, the posture error of the surface shape data measured by the profiler can be corrected, and various evaluation indices of the surface shape can be calculated at the same time, thereby simplifying the operation process and improving the accuracy of the surface shape evaluation of the diffractive optical element. The method comprises: (1) reading the measurement data and design parameters; (2) fitting the least squares method; (3) compensating for the posture error; (4) extracting the step portion; (5) detecting the gradient mutation point to determine the annular zone position; (6) calculating the step height; (7) eliminating the data near each step of the surface shape data after the posture error compensation; and (8) calculating the surface shape error evaluation index.

Description

Technical Field

[0001] The present invention relates to the technical field of surface shape detection and analysis of optical elements, and in particular to a method for processing surface shape data of a diffractive optical element based on the least squares method, and also to a device for processing surface shape data of a diffractive optical element based on the least squares method, which uses the least squares method to process the surface shape data of the diffractive optical element collected by a profilometer and provide corresponding evaluation indicators. Background Art

[0002] Diffractive optical elements (DOEs) are phase-shifting optical elements based on the diffraction effect of light. They modulate the output surface through micro-relief structures on their surfaces to achieve a desired wavefront. To achieve more diverse optical functions and increase the freedom of optical design, the microstructure of a DOE is often superimposed on an aspheric substrate.

[0003] Compared to traditional optical elements, diffractive optical elements offer numerous unique advantages. Their small size and light weight effectively simplify the structure of optical systems. Furthermore, their unique dispersion and ambient temperature characteristics provide greater design freedom for optical design, enabling the realization of specialized optical functions. With the continuous advancement of processing technology, the application of diffractive optical elements has matured, and they are now widely used in fields such as beam shaping, spatial imaging, and optical computing.

[0004] The imaging effect of a diffractive optical element is directly affected by its diffraction efficiency, which in turn is closely related to its surface shape. Therefore, measuring the surface shape of a diffractive optical element is extremely important. Profilometry is the most commonly used surface shape measurement method, but pose errors are often unavoidable during measurement. Therefore, subsequent processing of profilometry data is particularly important for surface shape evaluation of diffractive optical surfaces. Summary of the Invention

[0005] In order to overcome the defects of the prior art, the technical problem to be solved by the present invention is to provide a method for processing the surface shape data of a diffractive optical element based on the least squares method. It only needs to load the surface shape data file measured by the profilometer and the design parameter file of the diffractive optical element to correct the posture error of the surface shape data measured by the profilometer, and at the same time calculate various evaluation indicators of the surface shape, which simplifies the operation process and improves the accuracy of the surface shape evaluation of the diffractive optical element.

[0006] The technical solution of the present invention is: this method for processing surface data of a diffractive optical element based on the least squares method comprises the following steps:

[0007] (1) Reading measurement data and design parameters: Reading the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file;

[0008] (2) Least squares fitting: The least squares fitting is performed on the measured data through a composite optimization function to optimize the position error of the translation and deflection of the measured data and the error of the vertex curvature radius;

[0009] (3) Compensating for posture errors: Based on the posture error data optimized in step (2), the posture errors of translation and deflection in the measurement data are compensated by coordinate transformation;

[0010] (4) Extracting the step portion: subtracting the non-step portion in the theoretical plane from the surface shape data after compensating for the posture error to extract the step portion of the diffraction surface of the diffractive optical element;

[0011] (5) Detecting the gradient mutation point to determine the annular zone position: first, Gaussian filtering is performed on the step portion extracted in step (4), and then gradient processing is performed on it and the gradient mutation point position is detected to determine the annular zone position of the diffractive optical element;

[0012] (6) Calculation of step height: For each ring belt, the average value of the data within a certain length window is used as the height of the previous ring belt and the next ring belt, and the height of each step is calculated by subtracting the two;

[0013] (7) Eliminating the data near each step of the surface shape data after the posture error is compensated: Based on the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after the posture error is compensated in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center;

[0014] (8) Calculate the surface error evaluation index, and use the surface data after eliminating the data near the step in step (7) to calculate the surface error evaluation index of the diffractive optical element.

[0015] The present invention establishes a method for processing surface data of a diffractive optical element based on the least squares method by sequentially reading measurement data and design parameters, fitting using the least squares method, compensating for posture errors, extracting step portions, detecting gradient mutation points to determine annular zone positions, calculating step heights, eliminating data near each step of the surface data after posture error compensation, and calculating surface error evaluation indices. The present invention uses the least squares method to perform surface fitting on the surface data of the diffractive optical element detected by the profiler, compensates for the posture errors of translation and deflection obtained by the fitting, and calculates various surface evaluation indices based on the compensated surface data, thereby improving the accuracy of surface evaluation of the diffractive optical element. The present invention only needs to load the surface data file measured by the profiler and the design parameter file of the diffractive optical element to automatically correct the posture errors of the surface data measured by the profiler, and simultaneously calculate various evaluation indices of the surface, thereby simplifying the operation process, lowering the operation threshold, and improving the accuracy of surface evaluation of the diffractive optical element.

[0016] Also provided is a device for processing surface data of a diffractive optical element based on the least squares method, comprising:

[0017] a measurement data and design parameter reading module configured to read the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file into the diffractive optical element surface fitting and data processing system;

[0018] A least squares fitting module is configured to perform least squares fitting on the read measurement data through a composite optimization function to optimize the position errors of translation and deflection of the measurement data and the vertex curvature radius error;

[0019] A posture error compensation module configured to compensate for translation and deflection posture errors in the measurement data through coordinate transformation;

[0020] a step portion extraction module configured to subtract a non-step portion in a theoretical plane from the surface shape data after compensation for the posture error to extract the step portion of the diffraction surface of the diffractive optical element;

[0021] a zone position determination module configured to first perform Gaussian filtering on the extracted step portion of the diffractive surface of the diffractive optical element, then perform gradient processing on the extracted step portion and detect the position of the gradient mutation point to determine the position of the zone of the diffractive optical element;

[0022] The step height calculation module is configured to use the average value of the data in a certain length window as the height of the previous and next ring belts for each ring belt, and calculate the height of each step by subtracting the two;

[0023] A data removal module near steps is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensation of the posture error according to the read removal width parameter;

[0024] The surface error evaluation index calculation module is configured to calculate various surface error evaluation indices of the diffractive optical element by using the surface data after eliminating the data near the steps. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of the method for processing surface shape data of a diffractive optical element based on the least squares method according to the present invention.

[0026] Figure 2 It is a schematic diagram of the translation and deflection posture errors of the surface data of the diffractive optical element.

[0027] Among them: 1-only compensation for translation error effect diagram, 2-simultaneous compensation for translation and deflection error effect diagram

[0028] Figure 3 It is a result diagram after the present invention processes a specific example.

[0029] Among them: 3- surface error diagram of the diffractive optical element, 4- surface diagram of the diffractive optical element after removing the non-spherical substrate from the surface data, 5- evaluation index of the surface shape of the diffractive optical element, 6- evaluation index of the diffractive structure of the diffractive optical element. DETAILED DESCRIPTION

[0030] like Figure 1 As shown, the least squares method-based diffractive optical element surface data processing method comprises the following steps:

[0031] (1) Reading measurement data and design parameters: Reading the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file;

[0032] (2) Least squares fitting: The least squares fitting is performed on the measured data through a composite optimization function to optimize the position error of the translation and deflection of the measured data and the error of the vertex curvature radius;

[0033] (3) Compensation of posture error: Based on the posture error data optimized in step (2), the translation and deflection posture errors (such as Figure 2 Place

[0034] compensation;

[0035] (4) Extracting the step portion: subtracting the non-step portion in the theoretical plane from the surface shape data after compensating for the posture error to extract the step portion of the diffraction surface of the diffractive optical element;

[0036] (5) Detecting the gradient mutation point to determine the annular zone position: first, Gaussian filtering is performed on the step portion extracted in step (4), and then gradient processing is performed on it and the gradient mutation point position is detected to determine the annular zone position of the diffractive optical element;

[0037] (6) Calculation of step height: For each ring belt, the average value of the data within a certain length window is used as the height of the previous ring belt and the next ring belt, and the height of each step is calculated by subtracting the two;

[0038] (7) Eliminating the data near each step of the surface shape data after the posture error is compensated: Based on the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after the posture error is compensated in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center;

[0039] (8) Calculate the surface error evaluation index, and use the surface data after eliminating the data near the step in step (7) to calculate the surface error evaluation index of the diffractive optical element.

[0040] The present invention establishes a method for processing surface data of a diffractive optical element based on the least squares method by sequentially reading measurement data and design parameters, fitting using the least squares method, compensating for posture errors, extracting step portions, detecting gradient mutation points to determine annular zone positions, calculating step heights, eliminating data near each step of the surface data after posture error compensation, and calculating surface error evaluation indices. The present invention uses the least squares method to perform surface fitting on the surface data of the diffractive optical element detected by the profiler, compensates for the posture errors of translation and deflection obtained by the fitting, and calculates various surface evaluation indices based on the compensated surface data, thereby improving the accuracy of surface evaluation of the diffractive optical element. The present invention only needs to load the surface data file measured by the profiler and the design parameter file of the diffractive optical element to automatically correct the posture errors of the surface data measured by the profiler, and simultaneously calculate various evaluation indices of the surface, thereby simplifying the operation process, lowering the operation threshold, and improving the accuracy of surface evaluation of the diffractive optical element.

[0041] Preferably, in step (1), the measurement data are read from the .prf file, and the design parameters of the diffractive optical element are read from the .design and .diff files respectively by reading specific fields in the files.

[0042] Preferably, in step (2), the read measurement data is fitted by least squares method using a composite optimization function that combines the standard deviation between the measurement data and the ideal surface shape with the symmetry of the diffraction surface of the optical element to optimize the position error of the translation and deflection of the measurement data and the vertex curvature radius error.

[0043] Preferably, in step (3), the obtained posture error is used to compensate for the translation and deflection posture errors in the measurement data by the coordinate transformation shown in formula (1).

[0044]

[0045] Among them, θ is the deflection angle error, x0 and y0 are the translation errors, and x data with y data For the imported measurement data, x adjust and y adjust This is the surface data of the diffractive optical element after compensating for the posture error.

[0046] Preferably, in step (4), the face shape data y after compensating for the posture error is adjust Subtract x adjust The non-step portion of the corresponding theoretical diffraction surface is used to extract the step portion y of the diffraction surface of the diffraction optical element. stair The theoretical equations of the diffraction surface and its non-step part are respectively Equation (2) and Equation (3)

[0047]

[0048] Among them, CC and k are coefficients; A4, A6, A8, A 10 is the aspheric high-order coefficient; n1 and n2 are the refractive index of the medium before the diffraction surface and the refractive index of the medium after the diffraction surface, respectively; λ0 is the equivalent design wavelength; c1, c2, c3 are the 2nd, 4th, and 6th order phase coefficients of the diffraction surface, respectively.

[0049] Preferably, in step (5), first the step portion data y extracted in step (4) is stair Gaussian filtering is performed to eliminate the interference of outliers, and then gradient processing is performed to detect the position of the gradient mutation point to determine the position of the diffractive optical element ring zone.

[0050] Preferably, in step (6), with the positive direction of the x-axis from left to right, for each level of annular band, the average value of the data in a window of a certain length is used as the height of the previous level annular band and the next level annular band, wherein the detected step position is respectively used as the right end point of the previous level annular band window and the left end point of the next level annular band window, and the heights of the two adjacent levels of annular bands are subtracted to obtain the height of each step.

[0051] Preferably, in step (7), the x obtained in step (3) is adjusted according to the removal width parameter read in step (1). adjust and y adjustThe data is removed. The removed part is the data with the specified removal width on both sides, with each gradient mutation point detected in step (5) as the center. The data after removal is recorded as x remain and y remain .

[0052] Preferably, in step (8), the surface shape data y after removing the data near the steps in step (7) is used. remain Calculate the surface error evaluation indexes of each diffractive optical element, such as the peak-to-valley value PV and the root mean square value RMS of the diffractive optical element.

[0053] Those skilled in the art will appreciate that all or part of the steps in the above-described embodiment method can be implemented by instructing the relevant hardware through a program. The program can be stored in a computer-readable storage medium. When executed, the program includes each step of the above-described embodiment method. The storage medium can be: ROM / RAM, a magnetic disk, an optical disk, a memory card, etc. Therefore, corresponding to the method of the present invention, the present invention also includes a device for processing surface shape data of a diffractive optical element based on the least squares method. The device is generally represented in the form of functional modules corresponding to the steps of the method. The device includes:

[0054] a measurement data and design parameter reading module configured to read the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file into the diffractive optical element surface fitting and data processing system;

[0055] A least squares fitting module is configured to perform least squares fitting on the read measurement data through a composite optimization function to optimize the position errors of translation and deflection of the measurement data and the vertex curvature radius error;

[0056] A posture error compensation module configured to compensate for translation and deflection posture errors in the measurement data through coordinate transformation;

[0057] a step portion extraction module configured to subtract a non-step portion in a theoretical plane from the surface shape data after compensation for the posture error to extract the step portion of the diffraction surface of the diffractive optical element;

[0058] a zone position determination module configured to first perform Gaussian filtering on the extracted step portion of the diffractive surface of the diffractive optical element, then perform gradient processing on the extracted step portion and detect the position of the gradient mutation point to determine the position of the zone of the diffractive optical element;

[0059] The step height calculation module is configured to use the average value of the data in a certain length window as the height of the previous and next ring belts for each ring belt, and calculate the height of each step by subtracting the two;

[0060] A data removal module near steps is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensation of the posture error according to the read removal width parameter;

[0061] The surface error evaluation index calculation module is configured to calculate various surface error evaluation indices of the diffractive optical element by using the surface data after eliminating the data near the steps.

[0062] A specific embodiment of the present invention is described in detail below. A method for processing surface data of a diffractive optical element based on the least squares method is implemented in the following manner:

[0063] The process of establishing the surface data processing method of diffractive optical elements based on the least squares method is as follows: Figure 1 As shown, the specific implementation steps are:

[0064] Step 1: Read measurement data and design parameters

[0065] In this example, the profile data is read from the .prf file and the design parameters of the diffractive optical element are read from the .design and .diff files by reading specific fields in the file, and then imported into the diffractive optical element surface fitting and data processing system. The design parameters include the aspheric high-order coefficients of the diffractive optical element, the medium refractive index, the equivalent design wavelength, etc.

[0066] Step 2: Least Squares Fitting

[0067] In this example, the x-axis and y-axis translation of the measured data relative to the ideal surface shape, the polarization direction around the origin, and the vertex curvature radius are used as optimization targets. The standard deviation between the measured data and the ideal surface shape and the symmetry of the optimized diffraction surface are used as composite evaluation functions. The data are fitted using the least squares method, and the weight of the evaluation function is the standard deviation: Taking the right, top and clockwise as the positive directions of x-axis translation, y-axis translation and deflection respectively, the optimized x-axis translation error is 16.676433mm, the y-axis translation error is -1.971218mm, the deflection error is -0.2538°, and the vertex curvature radius is 28.981554mm.

[0068] Step 3: Compensate for pose errors

[0069] In this example, the position error of the surface data of the diffractive optical element is compensated by the coordinate transformation shown in formula (1), so that the vertex of the data is located at the origin.

[0070] Step 4: Extract the steps

[0071] In this example, the non-step portion of the theoretical diffraction surface is subtracted from the surface shape data after the posture error is compensated to extract the step portion of the diffraction surface of the diffraction optical element.

[0072] Step 5: Detect the gradient mutation point to determine the ring position

[0073] In this example, Gaussian filtering is used to smooth the extracted step data. The standard deviation of the Gaussian kernel is set to 20, and then the gradient mutation point is detected with a threshold of 0.01, resulting in a total of 6 groups of ring positions, such as Figure 3 shown.

[0074] Step 6: Calculate step height

[0075] In this example, the average value of the data within a certain length window is used as the height of each ring belt, and the heights of adjacent ring belts are subtracted to obtain the height of each step, such as Figure 3 As shown, the window length is 1 / 10 of the width of the smallest step of the diffractive optical element. Since the diffractive optical element is circular and symmetrical, the corresponding steps on both sides of the y-axis represent the same level. Therefore, the final step height is the average of the calculated step heights of the same level on both sides.

[0076] Step 7: Eliminate the data near each step of the surface data after compensating for the pose error

[0077] In this example, the surface data after compensation of the posture error is centered on the detected step positions, and the data of the rejection width on the left and right sides are read, and the rejection width is 50μm.

[0078] Step 8: Calculate the surface error evaluation index

[0079] In this example, the various evaluation indicators of the surface error of the diffractive optical element are calculated using the calculation formula, and the results are as follows: Figure 3 As shown, the calculated PV value is 0.7919 μm and the RMS value is 0.0960 μm.

[0080] The beneficial effects of the present invention are as follows:

[0081] 1. The present invention discloses a method for surface shape fitting and data processing of a diffractive optical element based on the least squares method. The method uses the least squares method to perform surface shape fitting on the surface shape data of the diffractive optical element detected by a profilometer and compensates for the translation and deflection posture errors obtained from the fitting. The method also calculates various surface shape evaluation indicators based on the compensated surface shape data, thereby improving the accuracy of surface shape evaluation of the diffractive optical element.

[0082] 2. The least squares method-based diffractive optical element surface shape fitting and data processing device disclosed in the present invention only needs to load the surface shape data file measured by the profilometer and the design parameter file of the diffractive optical element to automatically correct the posture error of the surface shape data measured by the profilometer, and calculate various evaluation indicators of the surface shape at the same time, thereby simplifying the operation process and lowering the operation threshold.

[0083] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the scope of protection of the technical solution of the present invention.

Claims

1. A method for processing surface data of a diffractive optical element based on the least squares method, characterized by: It includes the following steps: (1) Reading measurement data and design parameters: Reading the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file; (2) Least squares fitting: The least squares fitting is performed on the measured data through a composite optimization function to optimize the position error of the translation and deflection of the measured data and the error of the vertex curvature radius; (3) Compensating for posture errors: Based on the posture error data optimized in step (2), the posture errors of translation and deflection in the measurement data are compensated by coordinate transformation; (4) Extracting the step portion: subtracting the non-step portion in the theoretical plane from the surface shape data after compensating for the posture error to extract the step portion of the diffraction surface of the diffractive optical element; (5) Detecting the gradient mutation point to determine the annular zone position: first, Gaussian filtering is performed on the step portion extracted in step (4), and then gradient processing is performed on it and the gradient mutation point position is detected to determine the annular zone position of the diffractive optical element; (6) Calculation of step height: For each ring belt, the average value of the data within a certain length window is used as the height of the previous ring belt and the next ring belt, and the height of each step is calculated by subtracting the two; (7) Eliminating the data near each step of the surface shape data after the posture error is compensated: Based on the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after the posture error is compensated in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center; (8) Calculate the surface error evaluation index, and use the surface data after eliminating the data near the step in step (7) to calculate the surface error evaluation index of the diffractive optical element.

2. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 1, characterized in that: In the step (1), measurement data are read from the .prf file and design parameters of the diffractive optical element are read from the .design and .diff files respectively by reading specific fields in the file.

3. The method for processing surface shape data of a diffractive optical element based on the least squares method according to claim 2, characterized in that: In the step (2), the read measurement data is fitted by the least squares method through a composite optimization function that combines the standard deviation between the measurement data and the ideal surface shape with the symmetry of the diffraction surface of the optical element to optimize the position errors of the translation and deflection of the measurement data and the vertex curvature radius error.

4. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 3, characterized in that: In the step (3), the position errors of translation and deflection in the measurement data are compensated by the coordinate transformation shown in formula (1) according to the obtained position error. Among them, θ is the deflection angle error, x0 and y0 are the translation errors, and x data with y data For the imported measurement data, x adjust and y adjust This is the surface data of the diffractive optical element after compensating for the posture error.

5. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 4, characterized in that: In the step (4), the face shape data y after the posture error is compensated is adjust Subtract x adjust The non-step portion of the corresponding theoretical diffraction surface is used to extract the step portion y of the diffraction surface of the diffraction optical element. stair The theoretical equations of the diffraction surface and its non-step part are respectively Equation (2) and Equation (3) Among them, CC and k are coefficients; A4, A6, A8, A 10 is the aspheric high-order coefficient; n1 and n2 are the refractive index of the medium before the diffraction surface and the refractive index of the medium after the diffraction surface, respectively; θ0 is the equivalent design wavelength; c1, c2, c3 are the 2nd, 4th, and 6th order phase coefficients of the diffraction surface, respectively.

6. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 5, characterized in that: In the step (5), first the step portion data y extracted in the step (4) is stair Gaussian filtering is performed to eliminate the interference of outliers, and then gradient processing is performed to detect the position of the gradient mutation point to determine the position of the diffractive optical element ring zone.

7. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 6, characterized in that: In the step (6), from left to right is the positive direction of the x-axis, and for each level of the annular band, the average value of the data in a certain length window is used as the height of the previous level annular band and the next level annular band, wherein the detected step position is respectively used as the right end point of the previous level annular band window and the left end point of the next level annular band window, and the heights of two adjacent levels of the annular band are subtracted to obtain the height of each step.

8. The method for processing surface shape data of a diffractive optical element based on the least squares method according to claim 7, characterized in that: In the step (7), the x obtained in the step (3) is adjusted according to the culling width parameter read in the step (1). adjust and y adjust Data is removed. The removed part is the data with the specified removal width on both sides of the gradient mutation point detected in step (5) as the center. The data after removal is recorded as x remain and y remain .

9. The method for processing surface data of a diffractive optical element based on the least squares method according to claim 8, characterized in that: In the step (8), the surface data y after removing the data near the steps in step (7) is used. remain Calculate the surface error evaluation indexes of each diffractive optical element, such as the peak-to-valley value PV and the root mean square value RMS of the diffractive optical element.

10. A device for processing surface data of a diffractive optical element based on the least squares method, characterized in that: It includes: a measurement data and design parameter reading module configured to read the measurement data of the profilometer and the design parameters of the diffractive optical element from the record file into the diffractive optical element surface fitting and data processing system; A least squares fitting module is configured to perform least squares fitting on the read measurement data through a composite optimization function to optimize the position errors of translation and deflection of the measurement data and the vertex curvature radius error; A posture error compensation module configured to compensate for translation and deflection posture errors in the measurement data through coordinate transformation; a step portion extraction module configured to subtract a non-step portion in a theoretical plane from the surface shape data after compensation for the posture error to extract the step portion of the diffraction surface of the diffractive optical element; a zone position determination module configured to first perform Gaussian filtering on the extracted step portion of the diffractive surface of the diffractive optical element, then perform gradient processing on the extracted step portion and detect the position of the gradient mutation point to determine the position of the zone of the diffractive optical element; The step height calculation module is configured to use the average value of the data in a certain length window as the height of the previous and next ring belts for each ring belt, and calculate the height of each step by subtracting the two; A data removal module near steps is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensation of the posture error according to the read removal width parameter; The surface error evaluation index calculation module is configured to calculate various surface error evaluation indices of the diffractive optical element by using the surface data after eliminating the data near the steps.

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