Method and device for processing surface shape data of diffraction optical element based on least square method

Abstract

According to the least square method-based diffractive optical element surface shape data processing method and device disclosed by the invention, the pose error of the surface shape data measured by the contourgraph can be corrected only by loading the surface shape data file measured by the contourgraph and the design parameter file of the diffractive optical element; and each evaluation index of the surface shape is calculated at the same time, so that the operation process is simplified, and the accuracy of surface shape evaluation of the diffractive optical element is improved. The method comprises the following steps: (1) reading measurement data and design parameters; (2) fitting by a least square method; (3) compensating pose errors; (4) extracting a step part; (5) detecting gradient abrupt change points to determine the position of an annular belt; (6) calculating the step height; (7) eliminating part data near each step of the surface shape data after the pose error compensation; and (8) calculating a 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 profiler and gives corresponding evaluation indicators. Background Art

[0002] Diffractive Optical Elements (DOE) is a phase-type optical element based on the diffraction effect of light. It modulates the output thin surface through the micro-relief structure on the surface to obtain the desired wavefront. In order to achieve richer optical functions and increase the freedom of optical design, the microstructure of the diffractive optical element is usually superimposed on an aspherical substrate.

[0003] Compared with traditional optical elements, diffractive optical elements have many unique advantages. They are small in size and light in weight, which can effectively simplify the structure of the optical system. At the same time, they have unique dispersion characteristics and ambient temperature characteristics, which can bring more design freedom to optical design, thereby realizing special optical functions. With the continuous development of processing technology, the application of diffractive optical elements has become more mature. Today, diffractive optical elements have been widely used in beam shaping, spatial imaging, optical computing and other fields.

[0004] The imaging effect of a diffractive optical element is directly affected by its diffraction efficiency, which is closely related to its surface shape. Therefore, it is extremely important to measure the surface shape of a diffractive optical plane. As the most commonly used surface shape measurement method, profilometer measurement often inevitably has posture errors during measurement. Therefore, the subsequent processing of the profilometer's detection data is particularly important for the surface shape evaluation of the diffractive optical plane. 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 profiler and the design parameter file of the diffractive optical element to correct the posture error of the surface shape data measured by the profiler, 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: the least square method-based diffractive optical element surface data processing 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 read measurement data through a composite optimization function to optimize the translation and deflection posture errors and vertex curvature radius errors of the measurement data;

[0009] (3) Compensating for posture errors: Based on the posture error data optimized in step (2), the translation and deflection posture errors 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 diffractive 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) Calculating step height: For each ring belt, the average value of the data in 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 compensating for the posture error: According to the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after compensating for the posture error in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center;

[0014] (8) Calculating the surface error evaluation index, using 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 square method by sequentially reading measurement data and design parameters, fitting by the least square method, compensating for posture errors, extracting step parts, detecting gradient mutation points to determine the position of the annular zone, calculating step heights, eliminating the data of the parts near each step of the surface data after compensating for posture errors, and calculating surface error evaluation indicators. The present invention uses the least square method to perform surface fitting on the surface data of the diffractive optical element detected by the profiler, compensates for the posture errors of the translation and deflection obtained by the fitting, and calculates various surface evaluation indicators based on the compensated surface data, thereby improving the accuracy of the 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 error of the surface data measured by the profiler, and simultaneously calculate various evaluation indicators of the surface, thereby simplifying the operation process, lowering the operation threshold, and improving the accuracy of the surface evaluation of the diffractive optical element.

[0016] A device for processing surface data of a diffractive optical element based on the least square method is also provided, 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 shape 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 translation and deflection posture errors and vertex curvature radius errors of the measurement data;

[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 compensating for the posture error to extract a step portion of the diffractive surface of the diffractive optical element;

[0022] a ring zone position determination module configured to first perform Gaussian filtering on the extracted diffraction surface step portion of the diffractive optical element, then perform gradient processing on it and detect the position of the gradient mutation point to determine the ring zone position of the diffractive optical element;

[0023] The step height calculation module is configured to use the average value of 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;

[0024] A data removal module near the step is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensating for the posture error according to the read removal width parameter;

[0025] The surface error evaluation index calculation module is configured to calculate various surface error evaluation indexes of the diffractive optical element by eliminating the surface data near the step. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] 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.

[0027] Figure 2 It is a schematic diagram of the translation and deflection posture errors of the surface data of the diffractive optical element.

[0028] Among them: 1-only compensation for translation error effect diagram, 2-simultaneous compensation for translation and deflection errors effect diagram

[0029] Figure 3 It is a result diagram after the present invention processes a specific example.

[0030] Among them: 3- surface error diagram of diffractive optical element, 4- surface diagram of diffractive optical element surface data after removing the non-spherical substrate, 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

[0031] like Figure 1 As shown, the least squares method-based diffractive optical element surface data processing method comprises the following steps:

[0032] (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;

[0033] (2) Least squares fitting: The least squares fitting is performed on the read measurement data through a composite optimization function to optimize the translation and deflection posture errors and vertex curvature radius errors of the measurement data;

[0034] (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

[0035] compensation;

[0036] (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 diffractive surface of the diffractive optical element;

[0037] (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;

[0038] (6) Calculating step height: For each ring belt, the average value of the data in 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.

[0039] (7) Eliminating the data near each step of the surface shape data after compensating for the posture error: According to the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after compensating for the posture error in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center;

[0040] (8) Calculating the surface error evaluation index, using 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.

[0041] The present invention establishes a method for processing surface data of a diffractive optical element based on the least square method by sequentially reading measurement data and design parameters, fitting by the least square method, compensating for posture errors, extracting step parts, detecting gradient mutation points to determine the position of the annular zone, calculating step heights, eliminating the data of the parts near each step of the surface data after compensating for posture errors, and calculating surface error evaluation indicators. The present invention uses the least square method to perform surface fitting on the surface data of the diffractive optical element detected by the profiler, compensates for the posture errors of the translation and deflection obtained by the fitting, and calculates various surface evaluation indicators based on the compensated surface data, thereby improving the accuracy of the 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 error of the surface data measured by the profiler, and simultaneously calculate various evaluation indicators of the surface, thereby simplifying the operation process, lowering the operation threshold, and improving the accuracy of the surface evaluation of the diffractive optical element.

[0042] Preferably, in the 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.

[0043] Preferably, in step (2), the read measurement data is fitted by 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 translation and deflection posture errors of the measurement data and the vertex curvature radius error.

[0044] Preferably, in step (3), the obtained posture error is used to compensate for the translation and deflection posture errors in the measurement data by using the coordinate transformation shown in formula (1).

[0045]

[0046] 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 adjust The surface data of the diffractive optical element after compensating for the posture error.

[0047] Preferably, in step (4), the face shape data y after compensating for the posture error is adjust Subtract x adjust The non-step part in the corresponding theoretical diffraction surface is used to extract the step part y of the diffraction surface of the diffraction optical element stair The theoretical equation of the diffraction surface and its non-step part are respectively (2) and (3)

[0048]

[0049] 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, 6th phase coefficients of the diffraction surface respectively.

[0050] Preferably, in step (5), firstly, 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 and the position of the gradient mutation point is detected to determine the position of the diffractive optical element ring zone.

[0051] Preferably, in step (6), with the positive direction of the x-axis from left to right, for each level of the annular band, the average value of the data in a window of a certain length is used as the height of the previous level of the annular band and the next level of the annular band, wherein the detected step positions are respectively used as the right end point of the previous level of the annular band window and the left end point of the next level of the annular band window, and the heights of two adjacent levels of the annular bands are subtracted to obtain the height of each step.

[0052] Preferably, in step (7), the x obtained in step (3) is adjusted according to the removal width parameter read in step (1). adjust and adjustData is removed. The removed part is the data with a certain 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 remain .

[0053] Preferably, in step (8), the surface shape data y after removing the data near the step 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 surface shape of the diffractive optical element.

[0054] Those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes the steps of the above-mentioned embodiment method, and the storage medium can be: ROM / RAM, magnetic disk, optical disk, memory card, etc. Therefore, corresponding to the method of the present invention, the present invention also includes a device for processing surface data of a diffractive optical element based on the least squares method, and the device is usually represented in the form of functional modules corresponding to the steps of the method. The device includes:

[0055] 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 shape fitting and data processing system;

[0056] 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 translation and deflection posture errors and vertex curvature radius errors of the measurement data;

[0057] A posture error compensation module configured to compensate for translation and deflection posture errors in the measurement data through coordinate transformation;

[0058] A step portion extraction module configured to subtract a non-step portion in a theoretical plane from the surface shape data after compensating for the posture error to extract a step portion of the diffractive surface of the diffractive optical element;

[0060] a ring zone position determination module configured to first perform Gaussian filtering on the extracted diffraction surface step portion of the diffractive optical element, then perform gradient processing on it and detect the position of the gradient mutation point to determine the ring zone position of the diffractive optical element;

[0061] The step height calculation module is configured to use the average value of 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;

[0062] A data removal module near the step is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensating for the posture error according to the read removal width parameter;

[0063] The surface error evaluation index calculation module is configured to calculate various surface error evaluation indexes of the diffractive optical element by eliminating the surface data near the step.

[0064] 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 square method is implemented in the following manner:

[0065] 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:

[0066] Step 1: Read measurement data and design parameters

[0067] In the 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.

[0068] Step 2: Least Squares Fitting

[0069] In this example, the translation of the measured data in the x-axis and y-axis directions of the ideal surface shape, the polarization direction around the origin, and the vertex curvature radius are taken as optimization targets, and 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 to perform least squares fitting on the data. 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.

[0070] Step 3: Compensate for posture errors

[0071] In the example, the position and posture 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.

[0072] Step 4: Extract the steps

[0073] In the example, the non-step portion of the theoretical diffraction surface is subtracted from the surface shape data after compensating for the posture error to extract the step portion of the diffraction surface of the diffraction optical element.

[0074] Step 5: Detect the gradient mutation point to determine the ring position

[0075] In this example, Gaussian filtering is used to smooth the extracted step data. The standard deviation of the Gaussian kernel is set to 20. Then, the gradient mutation point is detected with a threshold of 0.01, and a total of 6 groups of ring positions are obtained, such as Figure 3 shown.

[0076] Step 6: Calculate step height

[0077] In the example, the average value of the data in 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 symmetrical to the y-axis represent the same level, so the final step height is the average value of the step heights of the same level on both sides calculated separately.

[0078] Step 7: Eliminate the data near each step of the surface data after compensating for the posture error

[0079] In the example, the surface data after compensation of the posture error is centered on the detected step positions, and the data of the rejection width are read on the left and right sides, and the rejection width is 50μm.

[0080] Step 8: Calculate the surface error evaluation index

[0081] In the example, the various evaluation indicators of the surface error of the diffractive optical element are calculated by 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.

[0082] The beneficial effects of the present invention are as follows:

[0083] 1. The least squares method-based diffractive optical element surface shape fitting and data processing method disclosed in the present invention performs surface shape fitting on the surface shape data of the diffractive optical element detected by a profilometer using the least squares method and compensates for the translation and deflection posture errors obtained from the fitting, and calculates various surface shape evaluation indicators based on the compensated surface shape data, thereby improving the accuracy of the surface shape evaluation of the diffractive optical element.

[0084] 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 profiler and the design parameter file of the diffractive optical element to automatically correct the posture error of the surface shape data measured by the profiler, and calculate various evaluation indicators of the surface shape at the same time, thereby simplifying the operation process and lowering the operation threshold.

[0085] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any simple modification, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention are still within the protection scope 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 in that: 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 read measurement data through a composite optimization function to optimize the translation and deflection posture errors and vertex curvature radius errors of the measurement data; (3) Compensating for posture errors: Based on the posture error data optimized in step (2), the translation and deflection posture errors 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 diffractive 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) Calculating step height: For each ring belt, the average value of the data in 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 compensating for the posture error: According to the elimination width parameter read in step (1), the surface shape data of the diffractive optical element after compensating for the posture error in step (3) is respectively eliminated with the position of each gradient mutation point detected in step (5) as the center; (8) Calculating the surface error evaluation index, using 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 square method according to claim 1, characterized in that: In the step (1), the measurement data is 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.

3. The method for processing surface data of a diffractive optical element based on the least square method according to claim 2, characterized in that: In the step (2), the read measurement data is fitted by the least square 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, so as to optimize the translation and deflection posture errors 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 square method according to claim 3, characterized in that: In the step (3), the translation and deflection posture errors in the measurement data are compensated by the coordinate transformation shown in formula (1) according to the obtained posture 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 adjust 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 square method according to claim 4, characterized in that: In the step (4), the face shape data y after compensating the posture error is adjust Subtract x adjust The non-step part in the corresponding theoretical diffraction surface is used to extract the step part y of the diffraction surface of the diffraction optical element stair The theoretical equation of the diffraction surface and its non-step part are respectively (2) and (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 phase coefficients of the diffraction surface respectively.

6. The method for processing surface data of a diffractive optical element based on the least square method according to claim 5, characterized in that: In step (5), firstly, the step part data y extracted in step (4) is stair Gaussian filtering is performed to eliminate the interference of outliers, and then gradient processing is performed and the position of the gradient mutation point is detected 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 square method according to claim 6, characterized in that: In the step (6), from left to right is the positive direction of the x-axis, for each level of the ring band, the average value of the data in a window of a certain length is used as the height of the previous level of the ring band and the next level of the ring band, wherein the detected step position is respectively used as the right end point of the previous level of the ring band window and the left end point of the next level of the ring band window, and the heights of two adjacent levels of the ring band are subtracted to obtain the height of each step.

8. The method for processing surface data of a diffractive optical element based on the least square method according to claim 7, characterized in that: In step (7), the x obtained in step (3) is adjusted according to the removal width parameter read in step (1). adjust and adjust Data is removed. The removed part is the data with a certain 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 remain .

9. The method for processing surface data of a diffractive optical element based on the least square method according to claim 8, characterized in that: In step (8), the surface data y after removing the data near the step 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 surface shape of the diffractive optical element.

10. A device for processing surface data of a diffractive optical element based on the least square 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 shape 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 translation and deflection posture errors and vertex curvature radius errors of the measurement data; 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 extract the step portion of the diffractive surface of the diffractive optical element by subtracting the non-step portion in the theoretical plane from the surface shape data after compensating for the posture error; a ring zone position determination module configured to first perform Gaussian filtering on the extracted diffraction surface step portion of the diffractive optical element, then perform gradient processing on it and detect the position of the gradient mutation point to determine the ring zone position of the diffractive optical element; The step height calculation module is configured to use the average value of 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 the step is configured to remove data centered on each step position of the surface data of the diffractive optical element after compensating for 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 indexes of the diffractive optical element by eliminating the surface data near the step.

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