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CN-121995856-A - Aspherical optical element partition processing path generation method for improving Lloyd algorithm

CN121995856ACN 121995856 ACN121995856 ACN 121995856ACN-121995856-A

Abstract

The invention provides an aspherical optical element partition processing path generation method for improving an Lloyd algorithm, which belongs to the field of aspherical optical element processing, and comprises the steps of dividing a processing area into a high residual area, a low residual area and a non-processing area through self-adaptive double-threshold and adjacent connectivity analysis based on surface shape error data of an aspherical optical element, and merging isolated areas. And (3) performing high-order iteration and low-order iteration in the high residual region and the low residual region respectively by adopting an improved Lloyd algorithm to generate the Voronoi grid with self-adaption to the region shape and controllable density. A spiral path is designed based on the centroid inside each Voronoi cell, forming a spiral path based on the Voronoi shape to ensure adequate machining. The invention can effectively avoid abrupt angle and curvature mutation in the path, and can adaptively adjust the processing density according to the surface shape error, thereby effectively inhibiting the intermediate frequency error and improving the processing surface shape quality and efficiency of the aspheric optical element.

Inventors

  • HOU XI
  • Cui Chuanyu
  • WANG JIA

Assignees

  • 中国科学院光电技术研究所

Dates

Publication Date
20260508
Application Date
20260114

Claims (10)

  1. 1. An aspherical optical element partition processing path generation method for improving an Lloyd algorithm is characterized by comprising the following steps: step 1, dividing a processing area into a high residual error area, a low residual error area and a non-processing area based on surface shape error data of an aspheric optical element through self-adaptive double-threshold and adjacent connectivity analysis, and merging isolated areas; step 2, adopting an improved Lloyd algorithm to perform high-order iteration in a high residual error region and perform low-order iteration in a low residual error region, and generating a Voronoi grid which is adaptive to the shape of the region and controllable in density; Step 3, designing a spiral path based on mass centers in each Voronoi unit to form a spiral path based on the Voronoi shape; step 4, adopting an adjacent priority and boundary close strategy, starting from a starting unit at the outer edge of the partition, and traversing all Voronoi units repeatedly; step 5, checking the path points, and when the path exceeds the boundary of the target partition, determining a safe correction point by solving the critical point and calculating the tangential direction of the critical point to generate a correction processing path without crossing the boundary; and 6, performing post-treatment on the processing path to generate an execution program which can be directly used for the optical element processing robot.
  2. 2. The method for generating the aspheric optical element partition processing path for improving the Lloyd algorithm according to claim 1 is characterized in that the self-adaptive double threshold value in the step 1 is determined by calculating the median of the surface shape error data, calculating the median of the absolute deviation from each point of the surface shape error data to the median, multiplying the median absolute deviation by a scale parameter to obtain an approximation of the standard deviation, and constructing a high residual error judgment threshold value and a low residual error lower boundary threshold value based on the approximation of the median and the standard deviation.
  3. 3. The method for generating the partitioned processing path of the aspheric optical element for improving the Lloyd algorithm according to claim 2, wherein the specific rule of merging isolated areas in the step 1 is that three types of areas of a high residual area, a low residual area and an unprocessed area are respectively marked by communicating components, the area of each communicating subset is calculated, the subset with the area smaller than a relative area threshold value and an absolute minimum area threshold value is judged as the isolated area, the isolated high residual area is merged into the low residual area, and the isolated low residual area is merged into the unprocessed area.
  4. 4. The method for generating the aspherical optical element partition processing path for improving the Lloyd algorithm according to claim 1 is characterized in that in the step 2, high-order iteration corresponds to a high residual region, low-order iteration corresponds to a low residual region, iteration orders and residual levels are in positive correlation, and the differential distribution of Voronoi grid density is realized by controlling the iteration orders.
  5. 5. The method for generating the aspherical optical element partition processing path for improving the Lloyd algorithm according to claim 1, wherein the spiral path in the step 3 is based on the design of the centroid of the Voronoi unit, and complete coverage of the inside of the Voronoi unit is realized by performing linear interpolation on the resident points between the centroid and the unit boundary.
  6. 6. The method for generating the aspherical optical element partition processing path by improving the Lloyd algorithm according to claim 1, wherein in the step 4, the adjacency priority policy determines an adjacency based on the shared boundary length of Voronoi cells, and when two Voronoi cells share a non-zero length boundary, the adjacency is determined as an adjacency cell, and an adjacency state matrix is established to record adjacency states among the cells.
  7. 7. The method for generating an aspherical optical element partition processing path for improving an Lloyd algorithm according to claim 6, wherein the traversing rule of the boundary proximity strategy in the step 4 is that Voronoi cells located at the boundary of the partition are selected as a starting cell, non-traversed adjacent cells of the current cell are selected as next processing cells each iteration, and when a plurality of non-traversed adjacent cells exist, cells farther from the center of the partition are selected as next processing cells.
  8. 8. The method for generating the partitioned processing path of the aspheric optical element for improving the Lloyd algorithm according to claim 1, wherein the cross-boundary verification in the step 5 is specifically implemented by calculating a surface shape error value of any point on the path, comparing the surface shape error value with a partition threshold value, and determining that the point exceeds a target processing area when the surface shape error value of the point does not meet the error range condition of the partition.
  9. 9. The method for generating the partitioned machining path of the aspheric optical element for improving the Lloyd algorithm according to claim 8 is characterized in that the generating mode of the corrected machining path in the step 5 is that an intersection point of a connecting line of a current machining point and a pre-determined cross-region point and a partitioned boundary is solved to be a critical point, a tangential direction of the partitioned boundary at the critical point is calculated, a safe distance is shifted along the tangential direction to determine a safe point, and the current machining point, the critical point, the safe point and a centroid of a next adjacent unit are sequentially connected to form the three-section corrected path.
  10. 10. The method for generating the partitioned processing path of the aspheric optical element for improving the Lloyd algorithm according to claim 1, wherein the post-processing of the processing path in the step 6 comprises constructing a three-dimensional model based on the parameter equation of the aspheric optical element, mapping the Voronoi spiral path to the surface of the aspheric optical element, and generating a computer numerical control processing program by combining the path parameters and the process parameters.

Description

Aspherical optical element partition processing path generation method for improving Lloyd algorithm Technical Field The invention belongs to the field of processing of aspheric optical elements, and particularly relates to a method for generating an aspheric optical element partition processing path by improving an Lloyd algorithm. Background Optical processing technology plays a key role in improving the surface quality of an aspheric optical element, and the design of a processing path is one of the central factors determining the processing performance. Reasonable path planning not only affects the uniformity of material removal, but also directly determines the level of medium frequency error (Mid-Spatial Frequency Errors, MSF) generation during processing. On the premise that the smoothing tool is well matched with the processed surface, key indexes such as corner curvature smoothness, path spacing uniformity, motion track randomness, overall periodicity and the like of the path are generally comprehensively considered in the evaluation of the processing path. Among them, the smoothness of the corner and the curvature is one of the most important factors affecting the intermediate frequency error. If a large number of sharp corners or abrupt curvature changes exist in the path, the cutter generates obvious direction jump and dynamic disturbance at the positions, so that partial material is removed unevenly, obvious medium-frequency errors are formed on the surface of the element, and the surface shape quality and the application performance of the optical element are finally affected. In order to reduce intermediate frequency errors and improve the quality of a processing surface shape, researchers in recent years propose a series of technical innovations in the aspect of processing path generation: Chinese patent application CN104155915A proposes an adaptive fairing processing path method with random dwell points in combination with curvature threshold determination. The path adopts a cubic B spline curve fairing connection to construct a continuous cubic B spline curve. The broken line connection of the traditional pseudo-random path is improved, and the processing path is smoothed. Chinese patent application CN109765839a proposes a single-row disjoint random processing path generation method suitable for arbitrary boundary regions. By constructing three sets of path points, adjacent points and non-path points and combining two random sampling and reformable point rollback mechanisms, the path can be grown step by step in any boundary area without selfing. The final path is a complex serpentine curve which extends continuously within any boundary, is single-row, is disjoint, has eight-way randomness, and integrally presents a labyrinth-like processing track. Chinese patent application CN118092315A proposes an optical processing path planning method based on area density adaptation. According to the method, the optimal path distance of each area is determined through the actual surface removal amount, point cloud data with adjustable density is generated according to the optimal path distance, triangular mapping, optimization pruning are conducted on the point cloud, and finally a continuous path which can be directly used for processing is obtained through smooth processing. The generated path appears as a flexible mesh track. However, although the above method optimizes the processing track to a certain extent, the problems of acute corners, poor randomness and the like still exist in the processing. In addition, most of the methods design a processing path based on the overall surface shape error of the effective processing caliber, are difficult to fully adapt to the local curvature change of the aspheric surface, and easily cause the phenomena of over-polishing or under-polishing in a local area, so that obvious intermediate frequency error is caused. In addition to the above methods, the common processing paths include grating shape and spiral shape, etc., but still have the problems of sharp turning angle of fixed direction and global single density distribution. Based on the above information, there is still room for significant improvement in current aspheric optical element processing path designs. Therefore, it is needed to develop a new processing path generating method for aspheric characteristics to further improve the processing stability and effectively suppress the generation of intermediate frequency errors. Disclosure of Invention In order to solve the technical problems, the invention provides an aspherical optical element partition processing path generation method for improving an Lloyd algorithm, which is characterized in that firstly, a processing area is divided into a high residual area, a low residual area and a non-processing area based on surface shape error data of an aspherical optical element through self-adaptive dual-threshold and adjacent connectivity analysis, and