A sampling planning method for CGH error calibration

Abstract

The present application relates to the technical field of optical detection, and more particularly to a sampling planning method for CGH error calibration, comprising: based on CGH ideal phase design data, obtaining local grating period corresponding to each coordinate of CGH full aperture and corresponding spatial frequency, and then constructing global process feature atlas; determining spatial frequency coverage range; dividing the spatial frequency coverage range into N continuous and non-overlapping spatial frequency intervals according to equal frequency width; traversing all coordinates of CGH full aperture, according to the spatial frequency corresponding to the coordinates, grouping each coordinate into the coordinate candidate set corresponding to the spatial frequency interval according to the spatial frequency, and extracting M coordinates in each coordinate candidate set as sampling points; integrating all sampling points into a list, and sorting the sampling order of the sampling points by using a path optimization algorithm to complete sampling planning. The present application is at least beneficial to realize frequency domain balanced sparse sampling.

Description

Technical Field

[0001] This invention belongs to the field of optical detection technology, and in particular relates to a sampling planning method for CGH error calibration. Background Technology

[0002] In high-end optical manufacturing, computational holograms are the core technology for zero-position interferometry detection of aspherical and free-form surfaces. Computational hologram (CGH) optical elements are a type of diffractive optical element. The wavefront control accuracy of CGH depends strictly on the geometric parameters (etching depth and duty cycle) of its surface micro-nano grating structure. Due to the physical limitations of micro-nano fabrication processes (such as electron beam lithography and reactive ion etching), structural errors closely related to local pattern features will occur on the CGH surface. For example, the micro-loading effect of reactive ion etching causes the etching depth to become shallower as the local grating period decreases, and the proximity effect of electron beam lithography causes the duty cycle to change as the pattern density increases.

[0003] To accurately calibrate and compensate for these manufacturing errors, it is typically necessary to use equipment such as white light interferometers or atomic force microscopes to discretely sample and measure the geometric parameters of the micro- and nanostructures on the CGH surface to obtain error distribution data in key areas. However, CGHs, which are aspherical or have complex curved surfaces, exhibit extremely strong spatial inhomogeneity. The micro- and nanostructures on the CGH surface show a geometrical imbalance. Specifically, more than 90% of the physical area of ​​the CGH is occupied by the central large-period region (low-frequency region), while the small-period edge regions (high-frequency regions) containing significant process errors often account for less than 5% of the physical area. Figure 2 The spatial uniform sampling method used in related technologies (i.e., points are arranged according to equally spaced grids) causes most sampling points to fall in the low-frequency region with low error, resulting in a large amount of redundant data. Meanwhile, the edge high-frequency region that truly determines the slope of the process model is often assigned very few sampling points due to its small area, leading to insufficient capture of key error information and a lack of sampling samples. Ultimately, this severely restricts the accuracy of the error inversion model. From a statistical point of view, spatial uniform sampling results in extremely uneven distribution of data points in the spatial frequency domain and a lack of data in the edge high-frequency region. This makes the identification of physical model parameters extremely sensitive to measurement noise and makes it difficult to accurately predict the wavefront error of the edge key region.

[0004] Therefore, there is an urgent need for a sampling point selection method that can overcome the area limitation of the CGH to be detected and directly achieve balanced sampling based on the distribution of process characteristics (i.e., spatial frequency) to solve the above problems. Summary of the Invention

[0005] In view of this, the present invention aims to provide a sampling planning method for CGH error calibration, which is at least beneficial for achieving sparse sampling with frequency domain equalization.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0007] This invention provides a sampling planning method for CGH error calibration, comprising: Step 1, obtaining the spatial frequency corresponding to each coordinate of the CGH full aperture based on the ideal phase design data of the CGH, and then constructing a full-domain process feature map; Step 2, statistically analyzing the spatial frequencies of all coordinates in the full-domain process feature map to determine the spatial frequency coverage range; Step 3, dividing the spatial frequency coverage range into N continuous and non-overlapping spatial frequency intervals with equal frequency widths; Step 4, traversing all coordinates of the CGH full aperture, and according to the spatial frequency corresponding to the coordinate, assigning each coordinate to the corresponding coordinate candidate set of the corresponding spatial frequency interval, and extracting M coordinates as sampling points from each coordinate candidate set; Step 5, integrating all sampling points into a list, and using a path optimization algorithm to sort the sampling order of the sampling points to complete the sampling planning.

[0008] Furthermore, in step one, based on the ideal phase design data of CGH, the local grating period corresponding to each coordinate of the full aperture of CGH is obtained, and the spatial frequency is obtained based on the local grating period.

[0009] Furthermore, in step one, based on the CGH ideal phase design data, gradient calculation is performed on each coordinate within the full aperture range to obtain the local grating period Λ(x, y) corresponding to the corresponding coordinate, and the spatial frequency f corresponding to each coordinate is obtained according to f=1 / Λ(x, y).

[0010] Furthermore, in step two, the spatial frequencies of all coordinates in the global process feature map are traversed to obtain the minimum and maximum values ​​of the spatial frequencies, thereby determining the spatial frequency coverage range.

[0011] Furthermore, in step four, when extracting M coordinates from each set of candidate coordinates, the following condition must be met: the Euclidean distance between the newly selected coordinates and the already selected coordinates is greater than a set threshold.

[0012] Furthermore, the path optimization algorithm in step five includes the nearest neighbor algorithm.

[0013] Furthermore, the ideal phase design data for CGH includes substrate aperture, operating wavelength, and phase distribution.

[0014] Furthermore, in step four, M coordinates are randomly selected or uniformly sampled from each set of candidate coordinates as sampling points.

[0015] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0016] The sampling planning method for CGH error calibration provided by this invention helps reduce regression analysis errors. Specifically, this invention artificially constructs high-weighted observation data by forcibly allocating sufficient sampling weights in the high-frequency region at the edge of the physical surface with very small physical dimensions. This helps to significantly reduce the variance of physical model parameter identification. Moreover, this invention greatly reduces the number of sampling points required while ensuring the accuracy of model prediction. Experiments show that only a small number of frequency-equalized sampling points need to be measured to achieve the calibration effect of tens of thousands of points in traditional full-field scanning. Furthermore, the sampling planning method provided by this invention only depends on the design data of CGH and does not require modification of the measurement hardware. The control instruction file generated based on the planned sampling points and sampling sequence can be directly imported into mainstream white light interferometers or atomic force microscopes, making it highly universal. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0018] Figure 1 A flowchart of the sampling planning method for CGH error calibration described in the embodiments of the present invention;

[0019] Figure 2 This is a histogram of sampling point distribution in the frequency domain for a traditional spatial uniform sampling method.

[0020] Figure 3 The histogram of sampling points in the frequency domain is obtained by the sampling planning method for CGH error calibration described in the embodiments of the present invention.

[0021] Figure 4 This is a schematic diagram of the spatial distribution of sampling points on the physical surface of the CGH in the traditional spatial uniform sampling method.

[0022] Figure 5 This is a schematic diagram of the spatial distribution of sampling points on the physical surface of the CGH obtained by the sampling planning method for CGH error calibration according to the embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0025] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0026] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0027] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] refer to Figure 1 This invention provides a sampling planning method for CGH error calibration, comprising: Step 1, obtaining the spatial frequency corresponding to each coordinate of the CGH full aperture based on the ideal phase design data of the CGH, and then constructing a full-domain process feature map; Step 2, statistically analyzing the spatial frequencies of all coordinates in the full-domain process feature map to determine the spatial frequency coverage range; Step 3, dividing the spatial frequency coverage range into N continuous and non-overlapping spatial frequency intervals with equal frequency widths; Step 4, traversing all coordinates of the CGH full aperture, and according to the spatial frequency corresponding to the coordinate, assigning each coordinate to the corresponding spatial frequency interval's coordinate candidate set, and extracting M coordinates as sampling points from each coordinate candidate set; Step 5, integrating all sampling points into a list, and using a path optimization algorithm to sort the sampling order of the sampling points to complete the sampling planning.

[0029] This invention addresses the challenge of spatial and frequency domain mismatch by providing a sampling planning method for CGH error calibration. This method achieves balanced sparse sampling in the frequency domain, breaking free from the constraints of physical space area on sampling distribution. Instead, it establishes a sampling allocation mechanism based on local spatial frequencies. This is achieved by dividing the frequency domain into equally spaced frequency intervals and forcibly constraining the number of samples in each interval. Figure 3 This achieves sampling equalization in the frequency domain, redistributing sampling points from low-value, low-frequency, large-area regions to high-value, high-frequency, sensitive regions. Without increasing the total sampling workload, it significantly improves the ability of the sampling data to characterize micro / nano structure process errors (especially edge errors) and the accuracy of model fitting. Utilizing the prior knowledge of CGH design, the sampling probability density is transformed from "physical spatial uniformity" to "process frequency domain uniformity," which helps ensure that the measurement points uniformly cover the complete process dynamic range from the large period at the center to the small period at the edge.

[0030] The ideal phase design data for a CGH is designed based on specific optical inspection requirements. For example, a CGH designed to inspect a parabolic mirror with a focal ratio of 1 means that the ideal phase design data is prior knowledge obtained by forward design calculation using optical design software based on the optical surface requirements of the aspherical or freeform surface to be inspected. The ideal phase design data for a CGH includes physical substrate parameters and optical design parameters. In some embodiments, the ideal phase design data for a CGH includes substrate aperture, operating wavelength, and phase distribution.

[0031] It should be noted that each spatial frequency interval in step three represents a specific process feature segment, not a physical area segment; in step four, each spatial frequency interval has a corresponding set of coordinate candidates. For each spatial frequency interval, all coordinates falling within the spatial frequency interval within the full aperture range of CGH are retrieved, and the coordinates that meet the requirements are assigned to the corresponding set of coordinate candidates.

[0032] Furthermore, in step one, based on the ideal phase design data of CGH, the local grating period corresponding to each coordinate of the full aperture of CGH is obtained, and the spatial frequency is obtained based on the local grating period.

[0033] Furthermore, in step one, based on the CGH ideal phase design data, gradient calculation is performed on each coordinate within the full aperture range to obtain the local grating period Λ(x, y) corresponding to the corresponding coordinate, and the spatial frequency f corresponding to each coordinate is obtained according to f=1 / Λ(x, y).

[0034] Furthermore, in step two, the spatial frequencies of all coordinates in the global process feature map are traversed to obtain the minimum and maximum values ​​of the spatial frequencies, thereby determining the spatial frequency coverage range.

[0035] Furthermore, in step four, M coordinates are randomly selected or uniformly sampled from each set of candidate coordinates as sampling points.

[0036] Furthermore, in step four, when extracting M coordinates from each candidate coordinate set, the following condition must be met: the Euclidean distance between the newly selected coordinates and the already selected coordinates is greater than a set threshold. That is, spatial dispersion constraints are applied during the extraction process to ensure the dispersion of the sampling points in the azimuth angle and avoid introducing systematic errors from a single direction.

[0037] The number of sampling points M can be flexibly set according to the actual total number of sampling points and the number of bins N, as long as the final detection accuracy requirements are met (such as the reconstruction residual RMS being less than 2.0 nm). The sampling planning method provided by this invention is based on the CGH physical parameters (periodic function), and has stronger physical correlation compared with the existing uniform dense sampling points. Under the same inversion reconstruction method, the number of sampling points of this invention can be much lower than the number of sampling points of the traditional method.

[0038] Furthermore, the path optimization algorithm in step five includes the nearest neighbor algorithm.

[0039] It should be noted that after completing the sampling planning in step five of this invention, a control instruction file can be formed based on the sampling points and the sampling order of the sampling points. Subsequently, the corresponding detection equipment moves according to the planned sampling points and sampling order based on the control instruction file to perform detection.

[0040] This embodiment constructs a high-precision numerical simulation environment and, with the goal of achieving the same detection accuracy, compares and analyzes the number of sampling points and sampling efficiency of traditional spatial uniform sampling versus the sampling planning method for CGH error calibration provided by this invention.

[0041] The specific steps are as follows:

[0042] The first step is to construct an ideal phase model of the CGH to be tested. The element to be tested is set as a large-aperture binary phase-type aspherical CGH, and its physical substrate parameters and optical design parameters are as follows:

[0043] Base diameter: ;

[0044] Operating wavelength: ;

[0045] Phase distribution: Designed for detecting parabolic mirrors with a focal ratio of 1, this phase distribution, calculated according to the grating equation, results in a local grating period on the CGH surface. It exhibits non-linear changes, specifically from the central region Continuously and rapidly decreasing to the edge region ;

[0046] Process dynamic range: The corresponding spatial frequency range is ;

[0047] The second step is to construct a virtual truth surface containing frequency-dependent errors, as follows:

[0048] Based on the principles of micro-load effect and proximity effect in micro-nano fabrication, a synthetic error surface strongly correlated with the local spatial frequency distribution is constructed as the true value for this simulation. This true value model includes systematic error components and random noise components. The systematic error component represents the geometric parameter errors of the micro-nano structure (such as etching depth error or duty cycle error) that exhibit a monotonic change with increasing local spatial frequency. This simulates the characteristics of real manufacturing processes, where larger processing structure errors accumulate in the small but densely striped high-frequency edge region, while the errors are relatively flat in the central low-frequency region. The random noise component is the random noise following a normal distribution superimposed across the entire aperture on top of the aforementioned systematic errors, simulating the surface roughness or system noise floor of the testing instrument in actual processing. Therefore, the constructed error distribution map exhibits significant frequency dependence characteristics, indicating that the high-frequency ring at the edge converges the main morphological errors and is the key sensitive area for detection.

[0049] The third step is to execute the sampling planning method for CGH error calibration proposed in this invention. Specifically, N=10, which means the spatial frequency range... The sample was divided into 10 spatial frequency intervals, M=4, meaning that the number of samples in each spatial frequency interval was 4, and spatial dispersion constraints were applied. Obtain the set of sampling points Sampling point set Total number of sampling points Based on the set of sampling points Taking the radial basis function interpolation algorithm as an example, the error sampling value at the point is used to invert the full-caliber error distribution, and the root mean square residual of the true value surface in the second step is calculated based on this. It can be understood that other interpolation algorithms and inversion methods are also applicable.

[0050] The fourth step, as a control group, involves sampling and reconstruction using traditional methods with uniform spatial sampling. Specifically, a sampling grid conforming to a uniform spatial distribution is generated within a 100mm aperture, and the grid density is gradually increased to increase the total number of sampling points. Starting from 50, the error distribution is inverted based on spatial sampling point sets of different densities using the same interpolation algorithm as in the second step, and the corresponding root mean square residuals are recorded.

[0051] The fifth step is to compare and analyze the sampling efficiency under the same precision. Specifically, the convergence criterion for passing the test is set as: reconstructed residual. After comparison, it was found that if the same standard is achieved, the present invention requires at least 40 sampling points, while traditional spatial uniform sampling requires 827 sampling points.

[0052] refer to Figure 4 and Figure 5 Traditional spatial uniform sampling generates a large number of sampling points (blue squares) in the central low-frequency region, while the sampling points generated by this invention achieve frequency domain equalized sparse sampling, and the sampling points (red squares) are intelligently clustered in the edge high-frequency region.

[0053] In summary, simulation results show that traditional methods suffer from undersampling in the high-frequency region at the edge where the physical area is small but the error weight is high, requiring a very large total number of samples to meet the accuracy requirements. However, this invention, through a frequency domain equalization strategy, only requires about 1 / 20 of the sampling points of the traditional method to achieve the same physical model inversion accuracy (RMS < 2.0 nm). This significantly reduces the displacement travel and measurement time of the detection equipment, verifying the efficiency and accuracy of this invention in CGH detection.

[0054] In the detection of aspherical and freeform CGHs, the frequency domain equalized sparse sampling method proposed in this invention has significant technical advantages over traditional spatial uniform sampling. Under the premise of ensuring the same physical model inversion accuracy (e.g., RMS < 2.0 nm), this invention can reduce the number of sampling points by more than an order of magnitude. In this embodiment, the efficiency is improved by about 21 times. This invention effectively solves the contradiction between undersampling of high-frequency errors at the edges and data redundancy in the low-frequency region at the center. It captures key information covering the entire dynamic range of the CGH process with extremely low measurement cost, providing a new technical path for achieving efficient and high-precision online calibration of large-aperture complex optical components.

[0055] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0056] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A sampling planning method for CGH error calibration, characterized in that, include: Step 1: Based on the ideal phase design data of CGH, obtain the spatial frequency corresponding to each coordinate of the full aperture of CGH, and then construct a full-domain process feature map; Step 2: Calculate the spatial frequencies of all coordinates in the global process feature map to determine the spatial frequency coverage area. ; Step 3: Expand the spatial frequency coverage area Divide the space frequency into N consecutive and non-overlapping intervals with equal frequency widths; Step 4: Traverse all coordinates of the CGH full aperture. Based on the spatial frequency corresponding to the coordinate, classify each coordinate into the corresponding spatial frequency interval coordinate candidate set. Extract M coordinates from each coordinate candidate set as sampling points. Step 5: Combine all sampling points into a list, and use a path optimization algorithm to sort the sampling order of the sampling points to complete the sampling plan.

2. The sampling planning method for CGH error calibration according to claim 1, characterized in that, In step one, based on the ideal phase design data of CGH, the local grating period corresponding to each coordinate of the full aperture of CGH is obtained, and the spatial frequency is obtained based on the local grating period.

3. The sampling planning method for CGH error calibration according to claim 2, characterized in that, In step one, based on the CGH ideal phase design data, gradient calculation is performed on each coordinate within the full aperture range to obtain the local grating period Λ(x, y) corresponding to the corresponding coordinate, and the spatial frequency f corresponding to each coordinate is obtained according to f=1 / Λ(x, y).

4. The sampling planning method for CGH error calibration according to claim 1, characterized in that, In step two, the spatial frequencies of all coordinates in the global process feature map are traversed to obtain the minimum spatial frequency. and maximum value This allows for the determination of the spatial frequency coverage area. .

5. The sampling planning method for CGH error calibration according to claim 1, characterized in that, In step four, when extracting M coordinates from each candidate coordinate set, the following condition must be met: the Euclidean distance between the newly selected coordinates and the already selected coordinates is greater than a set threshold. .

6. The sampling planning method for CGH error calibration according to claim 1, characterized in that, The path optimization algorithm in step five includes the nearest neighbor algorithm.

7. The sampling planning method for CGH error calibration according to claim 1, characterized in that, The ideal phase design data for the CGH includes the substrate aperture, operating wavelength, and phase distribution.

8. The sampling planning method for CGH error calibration according to claim 1, characterized in that, In step four, M coordinates are randomly selected or uniformly sampled from each set of candidate coordinates as sampling points.

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