Macro-micro cross-scale characterization method and system for three-dimensional profile of metal curved grating

Abstract

The application discloses a kind of metal curved grating three-dimensional profile macro-micro cross-scale characterization method and system, the present application method includes the global three-dimensional topography data of measured metal curved diffraction grating is reconstructed based on the original data of the sub-aperture splicing measurement of measured metal curved diffraction grating;Frequency domain filtering is separated into micro-diffraction structure surface data and macroscopic substrate surface data;Macroscopic substrate surface data is iteratively closest point surface shape registration grating substrate surface shape error is calculated;Micro-diffraction structure surface data is two-dimensional Gabor filtering to calculate the mean and standard deviation of grating period, local plane least square fitting is carried out to calculate the spatial distribution of grating period and glint angle;Macroscopic substrate surface data and the processing result of micro-diffraction structure surface data are output as three-dimensional profile cross-scale characterization result.The present application aims at metal curved diffraction grating microstructure, while realizing the high-precision characterization of curved grating macroscopic substrate and micro-diffraction structure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of processing and measuring optical microstructures, and in particular to a method and system for macro-micro cross-scale characterization of three-dimensional profiles of metal curved gratings. BACKGROUND

[0002] In the field of hyperspectral remote sensing detection, diffractive optical microstructures such as diffraction gratings, Fresnel lenses, and holographic optical elements are widely used in hyperspectral remote sensing, space exploration, and environmental monitoring due to their lightweight, compact structure, and excellent optical performance. Diffraction gratings are a kind of periodic, sub-wavelength microstructure optical element that can modulate the phase and amplitude of light waves, achieving spectral splitting and aberration correction. The Offner-type spectrometer system using curved diffraction gratings is the core module of the imaging spectrometer, and its performance directly determines the quality and resolution of spectral imaging. The surface topography of the grating, especially the periodicity of the micro-scale groove structure, the uniformity of the blaze angle distribution, and the macro-scale substrate surface error, are all key parameters that affect the optical performance of the grating, so they need to be accurately characterized. The development of nanoscale profile measurement technology provides an accurate and reliable means for grating microstructure surface topography measurement. High-precision three-dimensional surface topography measurement instruments such as white light interferometers, atomic force microscopes, and laser confocal microscopes have become the main means for grating microstructure detection due to their sub-nanometer spatial resolution and nanometer measurement accuracy. The measured grating surface topography is mainly divided into direct and indirect methods. The direct characterization method is based on the measured two-dimensional line profile data of the grating, directly evaluating the fitted values of key parameters such as the period and blaze angle of each grating microstructure unit, and finally calculating the mean and standard deviation of each parameter to evaluate the processing consistency. However, this method has human error in the manual fitting process of measuring diffractive structures, and is still limited to two-dimensional profile analysis, which cannot reflect the spatial distribution characteristics of diffractive microstructures on the metal curved substrate. The indirect characterization method mainly includes diffraction and interference methods, which can quickly evaluate the characteristic parameters of large-aperture diffraction gratings, but can only obtain the average grating pitch or blaze angle in the measurement laser beam irradiation area, which may cause edge effects or local outliers to be hidden.

[0003] With the development of ultra-precision machining manufacturing technology, the grating substrate topography gradually changes from a plane to a spherical surface or even a free-form surface, and the urgent demand for high-precision metrology characterization of grating microstructure is increasing, so the profile characterization of curved grating needs to change from two-dimensional to three-dimensional and from local to global. In the face of complex curved surface and micro-nano structure integrated application scene, the traditional grating profile characterization method has been difficult to meet the challenge of cross-scale and high-precision. Therefore, the development of cross-scale and high-precision profile characterization technology suitable for three-dimensional surface topography of metal curved grating has important theoretical significance and engineering value for promoting the optimization of manufacturing process and quality evaluation of high-end optical elements. SUMMARY

[0004] The technical problem solved by the present application: In view of the above problems of the prior art, a metal curved grating three-dimensional profile macro-micro cross-scale characterization method and system are provided, and the present application aims to simultaneously realize high-precision characterization of the macroscopic substrate and the microscopic diffraction structure of the metal curved diffraction grating.

[0005] In order to solve the above technical problems, the technical scheme adopted by the present application is:

[0006] A metal curved grating three-dimensional profile macro-micro cross-scale characterization method, comprising the following steps:

[0007] S101, obtaining the original data of the sub-aperture stitching measurement of the measured metal curved diffraction grating;

[0008] S102, reconstructing based on the original data to obtain the global three-dimensional topography data of the measured metal curved diffraction grating;

[0009] S103, performing frequency domain filtering on the global three-dimensional topography data, reconstructing the part higher than the preset frequency threshold as the microscopic diffraction structure surface data, and reconstructing the remaining part as the macroscopic substrate surface data;

[0010] S104, performing iterative nearest point surface registration calculation of the grating substrate surface error on the macroscopic substrate surface data; performing two-dimensional Gabor filtering on the microscopic diffraction structure surface data using a multi-scale and multi-direction Gabor filter set to calculate the mean and standard deviation of the grating period, and performing local plane least squares fitting to calculate the spatial distribution of the grating period and the blaze angle;

[0011] S105, taking the grating substrate surface error of the macroscopic substrate surface data and the spatial distribution of the grating period and the blaze angle of the microscopic diffraction structure surface data as the three-dimensional profile cross-scale characterization results of the measured metal curved diffraction grating.

[0012] Optionally, the step S104 of performing iterative nearest point surface registration calculation of the grating substrate surface error on the macroscopic substrate surface data comprises:

[0013] S201, obtaining a substrate surface point cloud set of macroscopic substrate surface data and a theoretical surface point cloud set , the substrate surface point cloud set , the first substrate surface point in the substrate surface point cloud set and the theoretical surface point cloud set , the first theoretical surface point in the theoretical surface point cloud set constitute a matched point pair, the number of points in the substrate surface point cloud set and the theoretical surface point cloud set ; ; ;

[0014] S202, by solving the objective function shown in the following formula through the coordinate transformation between the matched point pairs, the point cloud registration error convergence between the substrate surface point cloud set of macroscopic substrate surface data and the theoretical surface point cloud set is realized:

[0015] ;

[0016] wherein, is the objective function, is a rotation matrix, is a translation vector, and finally the optimal rotation matrix and translation vector are obtained when the point cloud registration error converges;

[0017] S203, the residual vector of the matched point pair is calculated according to the following formula:

[0018] ;

[0019] wherein, is the residual vector of the first matched point pair; S204, the peak-to-valley value PV and the root mean square value RMS of the macroscopic substrate surface data are calculated according to the residual vector of the matched point pair:

[0020]

[0021] ;

[0022] ;

[0023] wherein, and are the peak-to-valley value PV and the root mean square value RMS of the macroscopic substrate surface data, respectively.

[0024] ​​Optionally, the two-dimensional Gabor filtering of the micro-diffraction structure surface data in step S104 using the multi-scale and multi-direction Gabor filter set to calculate the mean and standard deviation of the grating period includes:

[0025] S301, taking the nominal grating period of the measured metal curved surface diffraction grating as the center frequency corresponding grating period range a series of reciprocal of grating periods within the range as the center frequency, a plurality of Gabor filters of continuous multi-scale and multi-direction are constructed, and de-meaning and normalization processing are performed on the two-dimensional spatial domain Ω, wherein the size of the two-dimensional spatial domain Ω is , is the length of the filtering region;

[0026] S302, the micro-diffraction structure surface data is traversed using a sliding window, and the convolution response energy of the micro-diffraction structure surface data in each sliding window and each Gabor filter in the Gabor filter set is calculated;

[0027] S303, the center frequency of the Gabor filter corresponding to the maximum convolution response energy in each sliding window is determined as the local grating period of the region in the sliding window ; all sliding windows are traversed to obtain the three-dimensional spatial distribution of the local grating period of each sliding window region, and the mean and standard deviation of the global grating period are calculated.

[0028] Optionally, the function expression of the Gabor filter in the Gabor filter set constructed in step S301 is:

[0029] ;

[0030] ;

[0031] ;

[0032] wherein, is the Gabor filtering result about , is the point coordinates of the micro-diffraction structure surface data in the plane coordinate system, is the point coordinates of the micro-diffraction structure surface data in the rotating coordinate system, is the space aspect ratio, is the grating period, is the Gaussian envelope standard deviation, is the serial number of the point, is the phase shift, is the phase shift, The grating orientation angle is given; the function expression for the mean-reduction and normalization processing in the two-dimensional spatial domain Ω is:

[0033] ;

[0034] ;

[0035] in, The result of the Gabor filter with mean removed. The length of the filtering region. For about The Gabor filtering results, This is the normalized Gabor filter result.

[0036] Optionally, step S104, which involves calculating the spatial distribution of the grating period and blaze angle using local plane least squares fitting, includes:

[0037] S401 extracts the average contour line along the grating direction from the surface data of the micro-diffraction structure, and identifies the ridge and valley positions of each grating unit through the peak finding algorithm;

[0038] S402, based on the positions of the ridge points and valley points, divide and extract each independent blazing surface unit region, and remove the blazing surface unit regions at the boundaries to reduce edge effects;

[0039] S403, for the data points within each blaze surface unit region, the least squares method is used to perform local plane fitting to obtain the normal vector of the local plane within that blaze surface unit region;

[0040] S404, Calculate the local blaze angle of the blaze surface element based on the normal vector;

[0041] S405, iterate through the local blaze angles of all blaze surface units to obtain a three-dimensional spatial distribution map of the blaze angle of the diffraction grating of the measured metal surface, and calculate the mean and standard deviation of the global blaze angle.

[0042] Optionally, in step S403, when the least squares method is used to fit the local plane to obtain the normal vector of the local plane within the blazing surface unit region, the functional expression of the fitting equation of the local plane is:

[0043] ;

[0044] in, for The height of the location The coordinates of the data points on the local plane. , and For fitting parameters, and the objective function used for local plane fitting is expressed as:

[0045] ;

[0046] wherein, is the local plane of the facet unit, and the function expression of the normal vector of the local plane in the facet unit region is obtained by fitting:

[0047] ;

[0048] wherein, is the normal vector, and the superscript T represents transposition; the function expression of the local blaze angle of the facet unit is calculated according to the normal vector in step S404:

[0049] ;

[0050] wherein, is the local blaze angle of the facet unit.

[0051] Optionally, step S105 further comprises:

[0052] S106, judging whether the three-dimensional profile cross-scale characterization result of the measured metal curved surface diffraction grating meets the requirements, if not, jumping to step S107, otherwise jumping to step S108;

[0053] S107, performing one round of processing on the measured metal curved surface diffraction grating, and performing sub-aperture stitching measurement on the measured metal curved surface diffraction grating after the completion of the round of processing, and jumping to step S101;

[0054] S108, the processing of the measured metal curved surface diffraction grating is completed, ending the processing and exiting.

[0055] In addition, the present application also provides a metal curved surface grating three-dimensional profile macro-micro cross-scale characterization system, comprising a microprocessor and a memory connected to each other, the microprocessor is programmed or configured to execute the metal curved surface grating three-dimensional profile macro-micro cross-scale characterization method.

[0056] In addition, the present application also provides a computer readable storage medium, the computer readable storage medium stores computer programs or instructions, the computer programs or instructions are programmed or configured to execute the metal curved surface grating three-dimensional profile macro-micro cross-scale characterization method by the processor.

[0057] In addition, the present application also provides a computer program product, comprising computer programs or instructions, the computer programs or instructions are programmed or configured to execute the metal curved surface grating three-dimensional profile macro-micro cross-scale characterization method by the processor. In addition, the present application also provides a computer program product, comprising computer programs or instructions, the computer programs or instructions are programmed or configured to execute the metal curved surface grating three-dimensional profile macro-micro cross-scale characterization method by the processor.

[0058] Compared with the prior art, the present application mainly has the following beneficial effects: (1) The present application expands the measurement and characterization range of the three-dimensional profile of the metal curved surface diffraction grating by combining laser confocal microscopic measurement with sub-aperture stitching algorithm, can overcome the measurement blind area and defocus blur problem caused by the narrow single view field and limited focal depth of the traditional microstructure measurement means, and is especially suitable for optical elements with high curvature base and large aperture characteristics. (2) The present application decomposes the complex profile of the curved surface grating into macroscopic base surface shape and microscopic diffraction structure based on frequency domain filtering, and independently characterizes them respectively, calculates the surface shape error between the measured base surface shape and the theoretical surface shape by using the iterative closest point (ICP) algorithm to quantify the macroscopic surface shape accuracy, and simultaneously comprehensively evaluates the microscopic diffraction structure in multiple parameters and multiple dimensions, and establishes a more comprehensive and cross-scale performance evaluation theoretical framework of the diffraction optical element. (3) The present application constructs a multi-scale and multi-directional Gabor filter bank, adaptively responds to the periodic characteristics of different regions in the frequency domain, and combines the sliding window convolution strategy to comprehensively extract the three-dimensional periodic distribution characteristics of the grating surface; the three-dimensional blaze angle spatial distribution characteristics are accurately calculated based on the local least square fitting method. The characterization method is improved from two-dimensional to three-dimensional level, and no longer depends on the manual extraction and subjective fitting of a limited number of cross-sectional lines, avoids the risk of local abnormal values being hidden, and improves the accuracy and reliability of the characterization results. For the metal curved surface diffraction grating microstructure, the present application method can overcome the limitations of the traditional two-dimensional line profile characterization method, simultaneously realize high-precision characterization of the macroscopic base and the microscopic diffraction structure of the metal curved surface diffraction grating, realize three-dimensional, global and high-precision profile characterization of the millimeter-level aperture metal curved surface grating in the sub-micron scale, and has important significance for the manufacturing process optimization and quality evaluation of the diffraction optical element. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 A three-dimensional profile cross-scale high-precision characterization method flowchart of the curved surface grating in the embodiment of the present application.

[0060] Figure 2 The original profile of the convex grating after surface reconstruction in the embodiment of the present application.

[0061] Figure 3 The profile of the macroscopic base surface shape after surface separation of the convex grating in the embodiment of the present application.

[0062] Figure 4 The profile of the microscopic diffraction structure after surface separation of the convex grating in the embodiment of the present application.

[0063] Figure 5 A point cloud position result graph after iterative closest point registration of the grating base surface shape in the embodiment of the present application.

[0064] Figure 6A surface shape error result graph of the grating substrate after surface shape iterative closest point registration in the embodiment of the present application.

[0065] Figure 7 A spatial domain real part result graph of the two-dimensional Gabor filter constructed with a center frequency in the embodiment of the present application.

[0066] Figure 8 A grating microstructure ridge valley point extraction and unit division schematic diagram in the embodiment of the present application.

[0067] Figure 9 A grating unit blaze surface local least square fitting to calculate the blaze angle result graph in the embodiment of the present application. DETAILED DESCRIPTION

[0068] In the following, a convex diffractive grating with a substrate diameter of 10 mm, a curvature radius of 24.97 mm, a period design value of 16.4 μm, a blaze angle design value of 3.65°, and a substrate material of 6061 type microcrystalline aluminum is taken as an example of the measured metal curved diffractive grating, and the present application is further described in detail. In order to make the person skilled in the art better understand the technical solutions of the present application, the technical solutions of the present application will be further described in detail in combination with the drawings in the embodiment of the present application.

[0069] As shown in Figure 1 , the metal curved grating three-dimensional profile macro-micro cross-scale characterization method of the embodiment includes the following steps:

[0070] S101, obtaining the original data of the sub-aperture stitching measurement of the measured metal curved diffractive grating;

[0071] S102, reconstructing based on the original data to obtain the global three-dimensional topography data of the measured metal curved diffractive grating;

[0072] S103, performing frequency domain filtering on the global three-dimensional topography data, reconstructing the part higher than the preset frequency threshold as the micro-diffraction structure surface data, and reconstructing the remaining part as the macro-substrate surface shape data;

[0073] S104, performing iterative closest point (ICP) surface shape registration on the macro-substrate surface shape data to calculate the grating substrate surface shape error, and performing two-dimensional Gabor filtering on the micro-diffraction structure surface data using a multi-scale and multi-direction Gabor filter set to calculate the mean and standard deviation of the grating period, and performing local plane least square fitting to calculate the spatial distribution of the grating period and the blaze angle;

[0074] S105, taking the grating substrate surface shape error of the macro-substrate surface shape data and the spatial distribution of the grating period and the blaze angle of the micro-diffraction structure surface data as the three-dimensional profile cross-scale characterization result of the measured metal curved diffractive grating and outputting.

[0075] The raw data of the sub-aperture stitching measurement of the measured metal curved diffraction grating in step S101 can be obtained by sub-aperture scanning stitching measurement of an ultra-precision three-dimensional surface topography measuring instrument. According to the size of the period and the blaze angle in the feature of the blazed grating unit, a suitable high-power objective lens is selected, a reasonable sub-aperture scanning path is planned according to the curved surface feature of the curved grating, the measurement overlap rate of adjacent sub-apertures is set, and a sub-aperture stitching layout is generated. Among them, the ultra-precision three-dimensional surface topography measuring instrument can use laser confocal microscope, white light interferometer and atomic force microscope, etc. Specifically, in this embodiment, according to the period and the blaze angle parameters of the measured grating microstructure unit, in order to ensure the measurement lateral resolution, a laser confocal microscope is selected to complete the sub-aperture stitching measurement of the curved diffraction grating with a 50-power objective lens. The measurement field of view of a single sub-aperture is 289.381x216.965 μm, and 768x1024 pixel three-dimensional point cloud data is collected. The size of the stitched rectangular area is 3.07x2.31 mm, a total of 144 sub-apertures, and an overlap rate of about 15% is set between adjacent fields of view to ensure the reliability of the measurement data. The reconstructed curved diffraction grating after stitching is separated for surface topography, and the results are shown in FIGS. 1-3. Figure 2 、 Figure 3 and Figure 4 , Figure 2 is the grating original topography after the surface reconstruction of the convex grating in this embodiment, in which the peak-to-valley value PV is 75.105 μm, the root mean square value RMS is 15.881 μm, the defocus term error Power is -72.495 μm, the X-direction size is 3.1 mm, and the Y-direction size is 2.3 mm. Figure 3 is the topography of the macroscopic base surface after the surface separation of the convex grating in this embodiment, in which the peak-to-valley value PV is 73.715 μm, the root mean square value RMS is 15.767 μm, the defocus term error Power is -71.969 μm, the X-direction size is 3.1 mm, and the Y-direction size is 2.3 mm. Figure 4 is the topography of the microscopic diffraction structure after the surface separation of the convex grating in this embodiment, in which the peak-to-valley value PV is 1.474 μm, the root mean square value RMS is 0.253 μm, the defocus term error Power is 0.001 μm, the X-direction size is 3.1 mm, and the Y-direction size is 2.3 mm. Among them, the peak-to-valley value PV refers to the difference between the peak value and the valley value of the optical surface; the root mean square value RMS refers to the standard deviation of all pixel points in the sampling range after removing the reference surface; and the defocus term error Power represents the distance deviation from the standard curvature R.

[0076] The global three-dimensional topography data of the measured metal curved diffraction grating is reconstructed in step S102 based on the original data. For example, after the system error correction of each measurement sub-aperture, the global three-dimensional topography splicing reconstruction can be realized by using the SIFT feature extraction and point cloud registration algorithm.

[0077] In step S103, the global three-dimensional topography data is subjected to frequency domain filtering. Specifically, the global three-dimensional topography data is subjected to two-dimensional fast Fourier transform, and the characteristic frequency threshold is set according to the grating processing technology characteristics. The low-frequency component lower than the threshold frequency is reconstructed as the macroscopic substrate surface data, and the high-frequency component higher than the threshold frequency is reconstructed as the microscopic diffraction structure surface data.

[0078] In step S104 of the embodiment, the optimal rotation matrix R and the translation vector t between the measured substrate surface point cloud and the theoretical design curved surface point cloud are solved by using the iterative closest point algorithm, so that the sum of the square distances of the corresponding point pairs is minimized. After the registration is completed, the point residual vectors are calculated, and then the peak-to-valley value (PV) and the root mean square value (RMS) of the surface error are obtained. Specifically, in step S104 of the embodiment, the macroscopic substrate surface data is subjected to iterative closest point surface registration to calculate the grating substrate surface error, which includes:

[0079] S201, obtaining a substrate surface point cloud set of the macroscopic substrate surface data and a theoretical surface point cloud set , wherein the th substrate surface point and the th theoretical surface point constitute a matched point pair, is the number of points; represents three dimensions, i.e., three dimensions of x, y, and z three-axis directions;

[0080] S202, solving the objective function shown in the following formula by using the coordinate transformation between the matched point pairs to realize the point cloud registration error convergence between the substrate surface point cloud set of the macroscopic substrate surface data and the theoretical surface point cloud set :

[0081] ;

[0082] wherein, is the objective function, is the rotation matrix, is the translation vector, and finally the optimal rotation matrix and the translation vector are obtained when the point cloud registration error converges.

[0083] S203, calculating the residual vector of the matched point pair according to the following formula:

[0084] ;

[0085] in, For the first The residual vector of each matching point pair;

[0086] S204, calculate the peak-to-valley values ​​(PV) and root mean square (RMS) of the macroscopic basis surface data based on the residual vectors of the matched point pairs:

[0087] ;

[0088] ;

[0089] in, and These represent the peak-to-valley values ​​(PV) and root mean square (RMS) of the macroscopic base surface data, respectively. This embodiment uses the theoretical surface point cloud set. To obtain the data based on the mathematical model of an ideal convex spherical substrate, this embodiment uses the nominal radius of curvature. R =24.97mm. Establish a mathematical model for an ideal convex spherical base, namely:

[0090] ;

[0091] in, for The height of the location The nominal radius of curvature; in this embodiment, the ICP algorithm reaches a stable convergence state after 30 iterations. The positional results of the registered point cloud and the ideal point cloud are as follows: Figure 5 As shown, the final calculated surface shape error result is as follows. Figure 6 As shown, its peak-to-valley value (PV) is 196.553 μm, its root mean square (RMS) value is 33.846 μm, its defocusing error (Power) is -2.584 μm, its X-axis dimension is 3.1 mm, and its Y-axis dimension is 2.3 mm.

[0092] In this embodiment, step S104 involves performing two-dimensional Gabor filtering on the surface data of the micro-diffraction structure using a multi-scale, multi-directional Gabor filter bank to calculate the mean and standard deviation of the grating period, including:

[0093] S301, using the nominal grating period of the diffraction grating on the metal surface under test. Corresponding grating period range The reciprocal of a series of grating periods within As the center frequency, multiple Gabor filters with continuous multi-scale and multi-directional characteristics are constructed, and mean-reduction and normalization are performed in the two-dimensional spatial domain Ω, where the size of the two-dimensional spatial domain Ω is... , is the length of the filter region;

[0094] S302, the micro-diffraction structure surface data is traversed by using a sliding window, and a convolution response energy of the micro-diffraction structure surface data in each sliding window and each Gabor filter in the Gabor filter set is calculated; a height signal of the grating data in the sliding window region is recorded as , and is calculated. The two-dimensional convolution of the filter set corresponding to the grating period is as follows:

[0095] ;

[0096] wherein, is a height signal of a position, is a Gabor filtering result of the filter set corresponding to the grating period about is a Gabor filtering result of the filter set corresponding to the grating period about is an x-axis and y-axis coordinate of the position in the sliding window, and the convolution response energy of each Gabor filter can be expressed as an energy integral of the response amplitude of the grating period to the sliding window:

[0097] ;

[0098] wherein, is the energy integral (convolution response energy), and the convolution response energy E is greater, indicating that the data in the window and the characteristics of the Gabor filter are more matched;

[0099] S303, the grating period of the local region in the sliding window is determined according to the center frequency of the Gabor filter corresponding to the maximum convolution response energy in each sliding window; all the sliding windows are traversed to obtain a three-dimensional space distribution diagram of the grating period of the local region in each sliding window, and the mean value and the standard deviation of the global grating period are calculated.

[0100] The function expression of the Gabor filter in the Gabor filter set constructed in step S301 of the embodiment is as follows:

[0101] ;

[0102] ​​​ ;

[0103] ;

[0104] wherein, is the Gabor filter result about , is the point coordinate of the micro-diffraction structure surface data in the plane coordinate system, is the point coordinate of the micro-diffraction structure surface data in the rotation coordinate system, is the space aspect ratio (used to adjust the direction sensitivity of the filter), is the grating period, is the Gaussian envelope standard deviation (determined by the filter bandwidth), is the serial number of the point, is the phase offset (controls the symmetry), is the grating direction angle; the function expression of the de-meaning and normalization processing on the two-dimensional space domain Ω is:

[0105] ;

[0106] ;

[0107] wherein, is the de-meaned Gabor filter result, is the length of the filtering region, is the Gabor filter result about , is the square of , is the normalized Gabor filter result.

[0108] In the embodiment, based on the process characteristics of the measured aluminum grating using ultra-precision single-point diamond turning, the period processing error is strictly controlled within , the period design range of the constructed multi-scale Gabor filter set is , and the sampling step is set to to meet the high-resolution detection requirement. The two-dimensional Gabor filter space domain real part constructed with the center frequency is shown in Figure 7 . The grating diffraction surface is convolved with the Gabor filter in the frequency domain through sliding windowing, and the period of the maximum response intensity is taken as the local period characteristic value of the window.

[0109] The local plane least square fitting in step S104 to calculate the spatial distribution of the grating period and the blaze angle includes:

[0110] S401, extracting the average profile line in the grating direction from the micro-diffraction structure surface data, identifying the ridge point and valley point position of each grating unit by peak searching algorithm; it should be noted that the peak searching algorithm is a known method, so the implementation details are not described here; identifying the ridge point and valley point position of each grating unit by peak searching algorithm, setting the minimum peak relative height difference greater than half of the grating height, to filter the effective maximum value point and minimum value point, that is, the ridge point and valley point of each grating unit. Finally, the number of grating ridge points and the number of grating valley points are obtained.

[0111] S402, dividing and extracting each independent blazed surface unit region according to the ridge point and valley point position, and removing the boundary blazed surface unit region to reduce the edge effect; the division region of the grating unit is defined as the region between adjacent valley points and ridge points .

[0112] S403, for each data point in the blazed surface unit region, the least square method is used for local plane fitting to obtain the normal vector of the local plane in the blazed surface unit region;

[0113] S404, calculating the local blaze angle of the blazed surface unit according to the normal vector;

[0114] S405, traversing the local blaze angles of all blazed surface units to obtain the three-dimensional space distribution diagram of the grating blaze angle of the measured metal curved surface diffraction grating, and calculating the mean value and standard deviation of the global grating blaze angle.

[0115] In this embodiment, the effective optical working surface of the blazed grating is limited to the blazed surface with a specific tilt angle, which participates in the main optical diffraction process, so the blazed surface unit needs to be extracted separately when evaluating the blaze angle. Based on the average profile detecting the ridge point and valley point of the grating, calculating the second-order difference of the data by differential peak searching algorithm, and setting the minimum peak relative height difference greater than half of the grating height, to filter the effective maximum value point and minimum value point, that is, the ridge point and valley point of each grating unit. Finally, the number of grating ridge points and the number of grating valley points are obtained. According to the positions of the grating ridge and valley points, the grating diffraction surface can be divided into independent blazed surface units, as shown in Figure 8 , wherein the first unit is defined as the region between adjacent valley points and ridge points .​​​​

[0116] In the step S403 of the embodiment, the normal vector of the local plane in the unit area of the facet is obtained by using the least square method to perform the local plane fitting. The function expression of the fitting equation of the local plane is as follows:

[0117] ;

[0118] wherein, h is the height at the point, and x and y are the plane coordinates of the data point on the local plane. , and are the fitting parameters, and the optimal plane parameters are solved by minimizing the residual sum of squares, that is, the function expression of the objective function used in the local plane fitting is as follows:

[0119] ;

[0120] wherein, h is the height at the point, and x and y are the plane coordinates of the data point on the local plane. is the local plane of the facet unit, and the function expression of the normal vector of the local plane in the unit area of the facet is as follows:

[0121] ;

[0122] wherein, h is the height at the point, and x and y are the plane coordinates of the data point on the local plane.

[0123] ;

[0124] wherein, h is the height at the point, and x and y are the plane coordinates of the data point on the local plane. is the local blaze angle of the facet unit.

[0125] As an optional embodiment, in order to solve the aforementioned objective function used in the local plane fitting, the design matrix and the observation vector are constructed as follows in the embodiment:

[0126] , ;

[0127] wherein, h is the height at the point, and x and y are the plane coordinates of the data point on the local plane. wherein, N is the number of data points, so that the optimal solution of the parameters is obtained as follows: ​​​​​​​​

[0128] ;

[0129] wherein T in superscript is the transpose operation, and has After obtaining the optimal fitting plane, the local least square fitting of the blazed facet of the grating unit obtains the result of the blaze angle as shown in Figure 9 The normal vector The local grating blaze angle of the sub-region can be derived from the normal vector .

[0130] The three-dimensional profile cross-scale characterization result of the measured metal curved surface diffraction grating in the embodiment can be used for processing and detection of the measured metal curved surface diffraction grating. As an optional implementation manner, after step S105, the method further comprises:

[0131] S106, determining whether the three-dimensional profile cross-scale characterization result of the measured metal curved surface diffraction grating meets the requirements, if not, jumping to step S107, otherwise jumping to step S108;

[0132] S107, performing one round of processing on the measured metal curved surface diffraction grating, and performing sub-aperture stitching measurement on the measured metal curved surface diffraction grating after the completion of the round of processing, and jumping to step S101;

[0133] S108, the processing of the measured metal curved surface diffraction grating is completed, ending the processing and exiting.

[0134] Based on the above description and analysis, this embodiment expands the measurement and characterization range of the three-dimensional morphology of metallic curved surface diffraction microstructures by combining laser confocal microscopy with a sub-aperture stitching algorithm. It overcomes the measurement blind spots and defocusing blurring problems caused by the narrow field of view and limited depth of focus in traditional microstructure measurement methods, making it particularly suitable for optical elements with high curvature substrates and large apertures. Based on frequency domain filtering, the composite morphology of the curved grating is decomposed into macroscopic substrate surface shape and microscopic diffraction structure, and each is characterized independently. The ICP algorithm is used to calculate the surface shape error between the measured substrate surface shape and the theoretical surface shape to quantify the macroscopic surface shape accuracy. Simultaneously, a multi-parameter, multi-dimensional comprehensive evaluation of the microscopic diffraction structure is performed, establishing a more comprehensive, cross-scale theoretical framework for evaluating the performance of diffractive optical elements. By constructing a multi-scale, multi-directional Gabor filter bank, the periodic characteristics of different regions are adaptively responded to in the frequency domain. Combined with a sliding window convolution strategy, the three-dimensional periodic distribution characteristics of the grating surface are comprehensively extracted. The spatial distribution characteristics of the three-dimensional blaze angle are accurately calculated based on the local least squares fitting method. The characterization method has been upgraded from two-dimensional to three-dimensional, eliminating reliance on manual extraction and subjective fitting of a limited number of cross-sectional traces. This avoids the risk of masking local outliers and improves the accuracy and reliability of the characterization results. The established three-dimensional global blaze angle error distribution model can be applied to the compensation processing of curved surface diffraction microstructures. By establishing a mapping relationship between blaze angle error and cutting process parameters, the manufacturing precision and diffraction efficiency of gratings are further improved, providing technical support for the optimization of manufacturing processes and quality control of diffraction microstructures, and possessing significant practical engineering application value.

[0135] Furthermore, this embodiment also provides a macro-micro scale characterization system for the three-dimensional contour of a metal curved grating, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the macro-micro scale characterization method for the three-dimensional contour of the metal curved grating.

[0136] Furthermore, this embodiment also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the macro-micro cross-scale characterization method for the three-dimensional profile of the metal curved grating via a processor.

[0137] In addition, this embodiment also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the macro-micro cross-scale characterization method of the three-dimensional profile of the metal surface grating through a processor.

[0138] Those skilled in the art will appreciate that the technology provided herein is not limited to any particular form of implementation. The technology provided herein can be implemented in hardware, software, or a combination thereof. Those skilled in the art will appreciate that the technology provided herein can be implemented in a number of different embodiments, including method embodiments, system embodiments, and computer program product embodiments. The technology provided herein can be implemented in any combination of hardware, software, or a combination thereof. The technology provided herein can be implemented in a number of different ways, including as a computer program product stored on a computer readable storage medium, as a system on chips (SOCs), as an application specific integrated circuit (ASIC), or as a cloud service. The computer program product can be implemented using two or more computer program Figure 1 one or more functions specified in the flow or flows and / or blocks Figure 1 one or more functions specified in the flow or flows and / or blocks Figure 1 one or more functions specified in the flow or flows and / or blocks Figure 1 one or more functions specified in the flow or flows and / or blocks Figure 1 one or more functions specified in the flow or flows and / or blocks Figure 1 one or more functions specified in the flow or flows and / or blocks

[0139] The above description is only preferred embodiments of the present application, the protection scope of the present application is not limited to the above-mentioned embodiments, any technical scheme falling within the concept of the present application shall be considered as falling within the protection scope of the present application. It should be noted that, for ordinary skilled in the art, some improvements and refinements without departing from the principles of the present application, these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A method for macro- and micro-scale characterization of the three-dimensional profile of a metallic curved grating, characterized in that, Includes the following steps: S101, Obtain the raw data of the sub-aperture splicing measurement of the diffraction grating on the metal surface under test; S102, Reconstruct the global three-dimensional topography data of the diffraction grating of the metal surface under test based on the original data; S103, the global three-dimensional topography data is filtered in the frequency domain, and the part above the preset frequency threshold is reconstructed as micro-diffraction structure surface data, and the remaining part is reconstructed as macro-substrate surface data. S104: Iterative nearest-point registration is performed on the macroscopic substrate surface data to calculate the grating substrate surface error; a two-dimensional Gabor filter is performed on the microscopic diffraction structure surface data using a multi-scale, multi-directional Gabor filter bank to calculate the mean and standard deviation of the grating period, and local plane least squares fitting is performed to calculate the spatial distribution of the grating period and blaze angle. S105 outputs the spatial distribution of the grating substrate surface shape error of the macroscopic substrate surface shape data and the grating period and blaze angle of the microscopic diffraction structure surface data as the three-dimensional profile cross-scale characterization result of the measured metal curved surface diffraction grating. Step S104 involves performing two-dimensional Gabor filtering on the surface data of the micro-diffraction structure using a multi-scale, multi-directional Gabor filter bank to calculate the mean and standard deviation of the grating period, including: S301, using the nominal grating period of the diffraction grating on the metal surface under test. Corresponding grating period range The reciprocal of a series of grating periods within As the center frequency, multiple Gabor filters with continuous multi-scale and multi-directional characteristics are constructed, and mean-reduction and normalization are performed in the two-dimensional spatial domain Ω, where the size of the two-dimensional spatial domain Ω is... , The length of the filtering region; S302, using a sliding window to traverse the surface data of the micro-diffraction structure, calculates the convolution response energy of the surface data of the micro-diffraction structure within each sliding window with each Gabor filter in the Gabor filter bank; S303, determine the local grating period of the region within the sliding window based on the center frequency of the Gabor filter corresponding to the maximum convolution response energy within each sliding window. ; Traverse all sliding windows to obtain the local raster period of each sliding window region. The three-dimensional spatial distribution map is obtained, and the global grating period is calculated. The mean and standard deviation.

2. The method for macro- and micro-scale characterization of the three-dimensional contour of a metal curved grating according to claim 1, characterized in that, Step S104 involves iteratively registering the macroscopic substrate surface data to the nearest point to calculate the grating substrate surface error, including: S201, Obtain the base surface shape point cloud set of macroscopic base surface shape data. and theoretical surface point cloud set basal surface point cloud set The Middle A base surface point and theoretical surface point cloud set The Middle A theoretical surface point A set of matching point pairs, representing the base surface point cloud. and theoretical surface point cloud set The number of points in each is ; S202, by matching the coordinate transformation between point pairs, solve the objective function shown in the following equation to realize the macroscopic base surface shape data base surface shape point cloud set. and theoretical surface point cloud set Point cloud registration error convergence: ； in, Let be the objective function. For rotation matrix, The translation vector is used to obtain the optimal rotation matrix when the point cloud registration error converges. Translation vector ; S203, calculate the residual vector of the matched point pair according to the following formula: ； in, For the first The residual vector of each matching point pair; S204, calculate the peak-to-valley values ​​(PV) and root mean square (RMS) of the macroscopic basis surface data based on the residual vectors of the matched point pairs: ； ； in, and These represent the peak-to-valley values ​​(PV) and root mean square values ​​(RMS) of the macroscopic base surface data.

3. The method for macro- and micro-scale characterization of the three-dimensional contour of a metal curved grating according to claim 1, characterized in that, The functional expression of the Gabor filter in the Gabor filter bank constructed in step S301 is: ； ； ； in, For about The Gabor filtering results, These are the point coordinates of the surface data of the micro-diffraction structure in a planar coordinate system. These are the point coordinates of the surface data of the micro-diffraction structure in a rotating coordinate system. The aspect ratio of the space. For the grating period, Let the standard deviation be the Gaussian envelope. The index of the point. For phase shift, The grating orientation angle is given; the function expression for the mean-reduction and normalization processing in the two-dimensional spatial domain Ω is: ； ； in, The result of the Gabor filter with mean removed. The length of the filtering region. For about The Gabor filtering results, This is the normalized Gabor filter result.

4. The method for macro- and micro-scale characterization of the three-dimensional contour of a metal curved grating according to claim 1, characterized in that, Step S104 involves calculating the spatial distribution of the grating period and blaze angle using local plane least squares fitting, including: S401 extracts the average contour line along the grating direction from the surface data of the micro-diffraction structure, and identifies the ridge and valley positions of each grating unit through the peak finding algorithm; S402, based on the positions of the ridge points and valley points, divide and extract each independent blazing surface unit region, and remove the blazing surface unit regions at the boundaries to reduce edge effects; S403, For the data points within each blaze surface unit region, the least squares method is used to perform local plane fitting to obtain the normal vector of the local plane within that blaze surface unit region; S404, Calculate the local blaze angle of the blaze surface element based on the normal vector; S405, iterate through the local blaze angles of all blaze surface units to obtain a three-dimensional spatial distribution map of the blaze angle of the diffraction grating of the measured metal surface, and calculate the mean and standard deviation of the global blaze angle.

5. The method for macro- and micro-scale characterization of the three-dimensional contour of a metal curved grating according to claim 4, characterized in that, In step S403, when the least squares method is used to fit the local plane to obtain the normal vector of the local plane within the blazing surface element region, the functional expression of the fitting equation of the local plane is: ； in, for The height of the location The coordinates of the data points on the local plane. , and The function expression for the objective function used for fitting parameters and performing local plane fitting is as follows: ； in, Let be a local plane of the blazing surface element, and the function expression for the normal vector of the local plane within the region of the blazing surface element is obtained by fitting: ； in, The normal vector is T, which indicates transpose. The functional expression for calculating the local blaze angle of the blaze element based on the normal vector in step S404 is as follows: ； in, The local blaze angle of this blaze surface element.

6. The method for macro- and micro-scale characterization of the three-dimensional contour of a metal curved grating according to claim 1, characterized in that, Step S105 is followed by: S106. Determine whether the three-dimensional profile cross-scale characterization result of the measured metal curved surface diffraction grating meets the requirements. If it does not meet the requirements, proceed to step S107; otherwise, proceed to step S108. S107, perform one round of processing on the metal surface diffraction grating to be tested, and after the completion of this round of processing, perform sub-aperture splicing measurement on the metal surface diffraction grating to be tested, then jump to step S101. S108, the processing of the diffraction grating on the curved metal surface under test is completed, the processing ends and the process exits.

7. A macro-micro scale characterization system for three-dimensional contours of a metallic curved grating, comprising an interconnected microprocessor and a memory, characterized in that, The microprocessor is programmed or configured to execute the macro-micro scale characterization method for three-dimensional profiles of metallic curved gratings as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the macro-micro scale characterization method for three-dimensional profiles of metallic curved gratings as described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the macro-micro scale characterization method for three-dimensional profiles of metallic curved gratings as described in any one of claims 1 to 6.

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