Calculation Method for Flatness Error of Optical Surface Based on Minimum Zone

Abstract

The present invention discloses a method for calculating the flatness error of an optical surface based on a minimum area, comprising the following steps: using an optical profiler to scan and obtain a data point set of the optical part surface; calculating the least square plane from these point sets, and determining two initial iteration points and upper and lower containing planes; determining the rotation axis and search area of ​​the containing plane with these two points, and traversing and searching for the third iteration point; if the three points meet the straight line discrimination criterion, directly calculating the final result; if not, determining the rotation axis and search area of ​​the containing plane with three iteration points, and searching for the fourth iteration point; if the four points do not meet the minimum area discrimination criterion, removing one iteration point and returning to the previous step to continue iteration; finally calculating the distance between the upper and lower containing planes as the final flatness error. The present invention uses the least square plane as a starting point, saves a lot of preliminary calculations, and reduces invalid calculations by selecting the search area, so that the overall calculation can converge faster.

Description

Technical Field

[0001] The present invention belongs to the field of precision measurement, and particularly relates to a method for calculating the flatness error of an optical surface based on the minimum zone. Background Art

[0002] At present, with the continuous development of precision manufacturing technology, the digital measurement of parts has long become a key step in the product life cycle. In the surface shape detection of optical manufacturing, PV and RMS have long been used to represent the performance of optical surfaces, but these parameters are not applicable in fields such as mechanical manufacturing and processing. Among the evaluation elements of parts, flatness is a key geometric tolerance element for the error evaluation of box-shaped parts, block-shaped parts, etc. Its evaluation result is very important for the quality and service life of products. Therefore, it is of great practical significance to effectively and accurately evaluate the flatness error. The national standard Product Geometric Technology Specifications (GPS) Appendix B describes the evaluation of flatness error as follows: When a single measured feature is between two planes with a distance less than or equal to the given tolerance value, its flatness is qualified. The direction of these two planes depends on the maximum distance between them being as small as possible.

[0003] The problem of flatness evaluation that satisfies the minimum zone method belongs to a non-differentiable complex optimization problem. When the ISO standard describes the minimum zone attribute, it does not specify any specific calculation method to determine the flatness error. Currently, domestic and foreign scholars mainly use traditional optimization methods, intelligent algorithms, computational geometry methods, etc. Gan Yongli introduced four computational geometry methods in the book "Shape and Position Error Detection": the least squares method, the diagonal method, the three-far-point plane method, and the minimum zone method. Among them, the least squares method is the simplest, but it is different from the definition of flatness error. The results of the diagonal method and the three-far-point plane method are often greater than those of the minimum zone method. However, the minimum zone method introduced in the book requires manual intervention and fails to achieve full automation. In the article "Research on Flatness Error Evaluation Based on Improved Particle Swarm Optimization Algorithm" by Xia Yatao, an improved particle swarm optimization algorithm was used. Although the accuracy of flatness error evaluation was improved, there are still problems such as poor stability, inaccurate results, and difficulty in practical application. Currently, the least squares method is generally used in the market to approximately calculate the flatness error of parts. Although the least squares method is widely used to determine geometric and dimensional tolerances, it does not strictly comply with the minimum zone judgment criterion required by the ANSI Y14.5 standard. Summary of the Invention

[0004] The present invention proposes a method for calculating the flatness error of an optical surface based on the minimum zone, which solves the problems of non-compliance with standards, poor calculation stability, low efficiency, inaccuracy, and impracticality of common current algorithms.

[0005] The technical solution for implementing the present invention is as follows: An optical surface flatness error calculation method based on the minimum zone, comprising the following steps:

[0006] Step S1: Use an optical profiler to scan and measure the surface of the optical component to be measured, and obtain a three-dimensional data point set of the surface of the optical component to be measured.

[0007] Step S2: Calculate the least squares plane M based on the above three-dimensional data point set, and successively calculate the distances from the points in the three-dimensional data point set to the least squares plane M. Determine the positive highest point and the negative highest point as two initial iteration points A and B. If there are multiple identical points, any one can be selected arbitrarily. Make a plane parallel to the least squares plane through these two initial iteration points as the upper containing plane Pu and the lower containing plane Pd.

[0008] Step S3: Use the two initial iteration points A and B as rotation points, synchronously rotate the upper containing plane and the lower containing plane, and respectively select appropriate search regions for the two containing planes through the first region selection algorithm. Search for the points in these two regions that are in contact with the corresponding plane and have the smallest rotation angle. If there are multiple points with the same and smallest angle, any one can be selected; at this time, two points are selected in the two search regions. Select the point with a smaller rotation angle as the third iteration point C, and finally synchronously update the equations of the upper containing plane and the lower containing plane.

[0009] Step S4: Determine whether the three points A, B, and C satisfy the minimum zone straight line criterion. If satisfied, jump to step S7 to calculate the flatness error. If not satisfied, continue with S5 to find the fourth iteration point.

[0010] Step S5: After finding the third iteration point, there will be two iteration points in one of the containing planes. Take the line connecting these two iteration points as the rotation axis of this containing plane; while there is only one iteration point on the other containing plane, also make a rotation axis through this iteration point, and make the rotation axes of the upper containing plane and the lower containing plane parallel to each other; respectively select appropriate search regions for the upper containing plane and the lower containing plane through the second region selection algorithm. Search for the points in these two regions that are in contact with the corresponding containing plane and have the smallest rotation angle. If there are multiple points with the same and smallest angle, any one can be selected; after two points are selected in the two search regions, select the point with a smaller rotation angle as the fourth iteration point D; finally synchronously update the equations of the upper containing plane and the lower containing plane.

[0011] Step S6: Determine whether the four points A, B, C, and D satisfy the triangle criterion or the cross criterion discrimination criterion. If not satisfied, remove a point according to a certain rule, and then jump to step S5 to continue the rotation iteration until the four iteration points all satisfy the minimum zone discrimination criterion.

[0012] Step S7: Calculate the distance between the two rotated planes containing the points in space using the distance formula from a point to a plane, which is the final flatness error.

[0013] Compared with the prior art, the remarkable advantages of the present invention are as follows:

[0014] (1) In step S2 of the present invention, starting from the least-squares plane, an approximate solution is quickly obtained, saving a large amount of preliminary calculations.

[0015] (2) In steps S3 and S5 of the present invention, a region selection algorithm is used respectively, reducing nearly half of the invalid calculations and enabling the overall calculation to converge faster. Description of the Drawings

[0016] Figure 1 is a flowchart of the flatness error algorithm based on the most region in the embodiment of the present invention.

[0017] Figure 2 is a schematic diagram of the first region search algorithm for traversing and finding iteration points in the embodiment of the present invention.

[0018] Figure 3 is a schematic diagram of the second region search algorithm for traversing and finding iteration points in the embodiment of the present invention.

[0019] Figure 4 is a calculation model of the rotation angles of the upper and lower containing planes when finding the third iteration point in the embodiment of the present invention.

[0020] Figure 5 is a calculation model of the rotation angles of the upper and lower containing planes when finding the fourth iteration point in the embodiment of the present invention.

[0021] Figure 6 is a schematic diagram of removing invalid points when the triangle criterion is not satisfied in the embodiment of the present invention.

[0022] Figure 7 is a schematic diagram of removing invalid points in two cases when the cross criterion is not satisfied in the embodiment of the present invention, where (a) is the case where the cross point is on a certain line segment, and (b) is the case where the cross points are not on both line segments. Detailed Embodiments

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0024] It should be noted that all directional indications (such as up, down, left, right, front, back...) in the embodiments of the present invention are only used to explain the relative positional relationship and movement conditions between components in a certain specific posture (as shown in the attached drawings). If this specific posture changes, the directional indications will also change accordingly.

[0025] In addition, in the present invention, descriptions such as "first" and "second" are only for descriptive purposes and should not be construed as indicating or implying their relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0026] Next, the specific implementation manner, as well as the technical difficulties and inventive points of the present invention, will be further introduced in combination with the design examples.

[0027] Combined with Figures 1 to 7 , for a method for calculating the flatness error of an optical surface based on the minimum zone in the present invention, the steps are as follows:

[0028] Step S1: Use an optical profiler to scan and measure the surface of the optical component to be measured, and obtain a three-dimensional data point set of the surface of the optical component to be measured. The specific method is as follows: Place the optical component to be measured on the loading platform of the optical profiler, adjust the measurement height and position, use professional measurement software to perform phase-shifting scanning measurement on the surface of the optical component to be measured, obtain the contour data of the surface of the optical component to be measured through the phase unwrapping algorithm built in the software, then filter out the burr noise on the contour data to obtain a three-dimensional data point set of the surface of the optical component to be measured, and finally output a measurement data file, which contains the length, width, height, and scanning sampling interval of the optical surface data set. After reading this measurement data file, subsequent processing analysis and information extraction can be carried out.

[0029] Step S2: Substitute the three-dimensional data point set measured in Step S1 into the least squares plane fitting function to calculate the least squares plane M. At this time, the points in the three-dimensional data point set are separated into upper and lower parts by the least squares plane M. Respectively traverse and calculate the distances from the points in these two parts to the least squares plane M. The point corresponding to the maximum distance in the upper part is used as the initial iteration point A, and the point corresponding to the maximum distance in the lower part is used as the initial iteration point B. If there are multiple identical maximum values, any one of them can be selected; Make a plane parallel to the least squares plane M through the iteration point A as the upper inclusion plane Pu, and make a plane parallel to the least squares plane M through the iteration point B as the lower inclusion plane Pd.

[0030] Step S3: Using two initial iteration points A and B as rotation points, synchronously rotate the upper containing plane and the lower containing plane, and respectively select appropriate search regions for the two containing planes through the first region selection algorithm. As shown in Figure 2 The specific method of the first region selection algorithm is as follows: Project the data point set onto the XOY plane of the coordinate axis. Connect the projection points of the iteration points A and B on the XOY plane to obtain the straight line equation L. Calculate the straight line equations perpendicular to L with A and B as the feet of the perpendiculars respectively, denoted as l a and l b . These are used as the two dividing lines. The search region for the containing plane where point A is located is: on the side where the projection point of point B is located with l a as the dividing line, but not including the points on the line. Similarly, the search region for the containing plane where point B is located is: on the side where the projection point of point A is located with l b as the dividing line, but not including the points on the line. Selecting appropriate search regions makes it easier for subsequent iteration points to meet the minimum region discrimination criterion, that is, the iteration results stably tend to converge.

[0031] Then, traverse and search in these two regions for the points that are in contact with the corresponding containing planes and have the smallest rotation angle. If there are multiple points with the same and smallest angle, choose any one. The specific method for traversing and calculating the rotation angle is as follows: As shown in Figure 4 , taking the iteration point A as an example, traverse all the points in the search region corresponding to the upper containing plane Pu, denoted as i. Taking point A as the rotation point, calculate the rotation angle θ i when in contact with point i. Its calculation formula is:

[0032]

[0033] where d i is the distance from point i to the upper containing plane Pu, S i is the distance from point i to point A, and sin -1 is to calculate the arcsine function. The rotation search method for point B and the lower containing plane Pd is the same. At this time, two points are selected in the two search regions, and the point with the smaller rotation angle is selected as the third iteration point C.

[0034] Finally, synchronously update the equations of the upper containing plane and the lower containing plane. The specific method is as follows: Assume that point C is in the upper containing plane. Calculate the normal vector n of the upper containing plane Pu. Cross-multiply the vector n by the AC vector formed by points A and C to obtain the rotation axis vector r of Pu. Then cross-multiply the vector r by the AC vector to obtain the normal vector of the rotated Pu. From point A, calculate the equation of the rotated upper containing plane Pu. Since the upper containing plane and the lower containing plane rotate synchronously and always remain parallel, the equation of the rotated Pd can be obtained from point B. The calculation method is the same when point C is in the lower containing plane Pd.

[0035] Step S4. Determine whether the minimum area straight line discrimination criterion is satisfied based on the iterative points A, B, and C. The specific method is as follows: Assume that the iterative points A and C are located on the upper inclusion plane. Project the iterative point B onto the upper inclusion plane Pu, and determine whether the three points on the upper inclusion plane are on the same straight line, and the projected point of point B needs to be between points A and C. If so, the minimum area straight line discrimination criterion is satisfied; otherwise, it is not satisfied. When point C is on the lower inclusion plane, the calculation method is the same. If the minimum area straight line discrimination criterion is satisfied, jump to step S7; if not, continue with step S5 to find the fourth iterative point.

[0036] Step S5. After finding the third iterative point, there will be two iterative points in one of the inclusion planes. Connect the two iterative points as the rotation axis of this inclusion plane. And there is only one iterative point on the other inclusion plane, and also make a rotation axis through this iterative point, and make the rotation axes of the upper inclusion plane and the lower inclusion plane parallel to each other. The second region selection algorithm selects appropriate search regions for the upper inclusion plane and the lower inclusion plane respectively. The specific steps of the second region selection algorithm are as follows: Project the iterative points A, B, and C onto the XOY plane. As Figure 3 shown, assume that A and C are on the upper inclusion plane Pu. Set the straight line connecting the projected points of the iterative points A and C as the dividing line l a2 , and make a straight line parallel to l a2 through the projected point of point B as the dividing line l b2 ; then the search region of Pu is: with l a2 as the dividing line and on the same side as the projected point of point B, but not including the points on the line; the search region of the lower inclusion plane is: with l b2 as the dividing line and on the same side as the projected point of point A, but not including the points on the line; the calculation method is the same when points B and C are in the same inclusion plane.

[0037] Then traverse and search in these two regions for the point that contacts the corresponding inclusion plane and has the minimum rotation angle. If there are multiple points with the same and minimum angles, choose any one. The specific steps of traversing and calculating the rotation angle are as follows: As Figure 5 shown, assume that the iterative point A and the iterative point C are both on the upper inclusion plane. Connect points A and C, and use the straight line AC as the rotation axis. At this time, the rotation axis of the lower inclusion plane passes through point B and is parallel to the straight line AC; through the second region selection algorithm, select an appropriate search region for the upper inclusion plane Pu, traverse all points in the region, denoted as j, and calculate the rotation angle θ j of Pu rotating around the rotation axis AC to point j. Its calculation formula is:

[0038]

[0039] where d j is the distance from point j to the inclusion plane, and D jis the distance from point j to the straight line where the rotation axis AC is located, sin -1 is to calculate the arcsine function. The rotation search method of Pd is the same. At this time, two points are selected in the two search areas, and the point with the smaller rotation angle is selected as the fourth iteration point D; the calculation method for the case where point C and point B are in the same plane is the same; finally, the equations of the upper inclusion plane and the lower inclusion plane are updated synchronously according to the method in step S3.

[0040] Step S6: Determine whether the four points A, B, C, and D satisfy the triangle criterion or the cross criterion discrimination criterion. If satisfied, continue to step S7.

[0041] The judgment method of the triangle criterion is as follows: When three of the iteration points are in the same inclusion plane, according to the second search area selection method in step S5, the situation where three points are on the same straight line is avoided. The iteration point on the other plane is projected onto this plane. If the projection point is inside or on the triangle formed by the other three points, the minimum area triangle criterion is satisfied; otherwise, it is not satisfied. At this time, an invalid iteration point needs to be removed according to certain rules, and then jump to S5 to continue the rotation iteration. The rules for removing invalid iteration points are as follows: As Figure 6 shown, assume that A, C, and D are all on the upper inclusion plane Pu. Project point B onto the upper inclusion plane to obtain the projection point B'. Connect the three points A, C, and D to form a triangle. At this time, point B' is outside the triangle. Select the side of the triangle that is closest to point B' as the new rotation axis. In the figure, it is the straight line AD. At the same time, discard the point that is not on the rotation axis. In the figure, it is the iteration point C.

[0042] The judgment method of the cross criterion is as follows: When the four iteration points are distributed in two inclusion planes in pairs, it is necessary to judge the cross criterion. Project all the iteration points onto the same inclusion plane, and connect the two points on the same inclusion plane respectively. If the two formed line segments intersect, the minimum area cross criterion is satisfied; otherwise, it is not satisfied. At this time, an invalid iteration point also needs to be removed according to certain rules, and then jump to S5 to continue the rotation iteration. The rules for removing invalid iteration points are as follows: Assume that point A and point D are on the upper inclusion plane Pu, and point B and point C are on the lower inclusion plane Pd. Project all the points onto the upper inclusion plane to obtain the projection points B' and C'. Connect the two points on the same inclusion plane respectively to form two line segments AD and B'C'. According to the second area selection algorithm in step S5, the parallelism of the two line segments is effectively avoided, but the two line segments have no intersection point. Extend these two line segments to obtain an intersection point. According to the position of the intersection point, it can be divided into the following two situations: Situation a: The intersection point is on one of the line segments, as Figure 7 shown in (a) of it. Select the straight line where this line segment is located as the rotation axis. In the figure, it is the line segment AD. Then discard the iteration point corresponding to the point on the line segment B'C' that is farther from the rotation axis AD. In the figure, it is the iteration point C; Situation b: The intersection points are not on both line segments, asFigure 7 As shown in (b) of , in this case, a straight line can be randomly selected as the rotation axis, and the iteration points corresponding to the points farther from the rotation axis on the other straight line can be discarded.

[0043] Step S7: Through the rotation iteration of the previous six steps, four iteration points that meet the minimum zone discrimination criterion and the upper and lower containing planes are obtained. The distance between these two containing planes is the flatness error of the surface of the measured part. The final result can be calculated only by using the distance formula from a spatial point to a plane.

Claims

1. A method for calculating the flatness error of an optical surface based on the minimum zone, characterized in that, Including the following steps: Step S1: Use an optical profiler to scan and measure the surface of the optical component to be measured, and obtain a three-dimensional data point set of the surface of the optical component to be measured; Step S2: Calculate the least squares plane M according to the above three-dimensional data point set, calculate the distances from the points in the three-dimensional data point set to the least squares plane M in turn, determine the forward highest point and the reverse highest point as two initial iteration points A and B. If there are multiple identical points, arbitrarily select one. Pass through these two initial iteration points to make a plane parallel to the least squares plane as the upper inclusion plane Pu and the lower inclusion plane Pd; Step S3: Use the two initial iteration points A and B as the rotation points, synchronously rotate the upper inclusion plane and the lower inclusion plane, and use the first region selection algorithm to select appropriate search regions for the two inclusion planes respectively. Search for the points that are in contact with the corresponding plane and have the smallest rotation angle in these two regions. If there are multiple points with the same and smallest angle, arbitrarily select one; At this time, two points are selected in the two search regions, and the point with the smaller rotation angle is selected as the third iteration point C. Finally, synchronously update the equations of the upper inclusion plane and the lower inclusion plane; Step S4: Judge whether the three points A, B, and C satisfy the minimum region straight line criterion. If they satisfy, jump to step S7 to calculate the flatness error. If they do not satisfy, continue with S5 to find the fourth iteration point; Step S5: After finding the third iteration point, there will be two iteration points in one of the inclusion planes. Connect the two iteration points as the rotation axis of the inclusion plane; while there is only one iteration point on the other inclusion plane, also make a rotation axis through this iteration point, and make the rotation axes of the upper inclusion plane and the lower inclusion plane parallel to each other; Use the second region selection algorithm to select appropriate search regions for the upper inclusion plane and the lower inclusion plane respectively. Search for the points that are in contact with the corresponding inclusion plane and have the smallest rotation angle in these two regions. If there are multiple points with the same and smallest angle, arbitrarily select one; After two points are selected in the two search regions, select the point with the smaller rotation angle as the fourth iteration point D; Finally, synchronously update the equations of the upper inclusion plane and the lower inclusion plane; Step S6: Judge whether the four points A, B, C, and D satisfy the triangle criterion or the cross criterion discrimination criterion. If they do not satisfy, remove a point according to a certain rule, and then jump to step S5 to continue the rotation iteration until the four iteration points all satisfy the minimum region discrimination criterion; Step S7: Calculate the distance between the two rotated inclusion planes through the distance formula from a spatial point to a plane, which is the final flatness error.

2. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S1, use an optical profiler to scan and measure the surface of the optical component to be measured, and obtain a three-dimensional data point set of the surface of the optical component to be measured, specifically as follows: Place the optical component to be measured on the optical profiler, adjust the measurement position, scan and measure the optical component to be measured, then solve the phase to obtain the data of the surface of the optical component to be measured, and save the measurement file, which includes the length, width, height and scanning sampling pitch of the optical surface data set, and then perform filtering to remove burr noise points, and finally obtain a three-dimensional data point set of the surface of the optical component to be measured.

3. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S2, the least-squares plane M is calculated based on the above three-dimensional data point set. The distances from the points in the three-dimensional data point set to the least-squares plane M are calculated in sequence, and the forward highest point and the reverse highest point are determined as two initial iteration points A and B, specifically as follows: The least-squares plane M is a three-dimensional plane equation obtained by fitting the three-dimensional data point set into the least-squares method formula. The points in the three-dimensional data point set are separated into upper and lower parts by the least-squares plane M. The points in these two parts are traversed respectively, and the distances from the points to the least-squares plane are calculated. The point corresponding to the maximum value in the upper part is the initial iteration point A, and the point corresponding to the maximum value in the lower part is the initial iteration point B. If there are multiple identical maximum values, any one of them can be selected.

4. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S3, appropriate search regions are selected for the two containing planes respectively through the first region selection algorithm. The specific steps are as follows: Project the three-dimensional data point set onto the XOY plane of the coordinate axes, calculate the straight-line equation L of the line connecting the iterative points A and B on the XOY plane, and calculate the straight-line equations perpendicular to L with A and B as the feet of the perpendiculars respectively, denoted as l a and l b , which are used as the two dividing lines; the search region of the upper inclusion plane where point A is located is: with l a as the dividing line, on the side where the projection point of point B is located, but does not include the points on the line; The search area of the lower inclusion plane where point B is located is: with l b as the dividing line, and on the same side as the projection point of point A, but not including the points on the line.

5. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S3, with the two initial iteration points A and B as rotation points, the upper containing plane and the lower containing plane are rotated, and the point that contacts a certain containing plane and has the smallest rotation angle is searched as the third iteration point C, and the equations of the upper containing plane and the lower containing plane are updated synchronously, specifically as follows: Step 31: Through the first region selection algorithm, traverse all points in the search region, denoted as i. Taking point A as the rotation point, calculate the minimum rotation angle θ when contacting point i. i , and its calculation formula is: ； where d i is the distance from point i to the upper inclusion plane Pu, S i is the distance from point i to point A, is to calculate the arcsine function; The rotation search method of point B and the lower containing plane Pd is the same as that in step 31. Finally, the point corresponding to the smallest of all the rotation angles is combined as the third iteration point C.

6. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 5, characterized in that, In step S3, the equations of the upper containing plane and the lower containing plane are updated synchronously, specifically as follows: In step 32, calculate the normal vector n of the upper containing plane Pu, cross-multiply the vector n by the AC vector formed by the iteration point A and the iteration point C to obtain the rotation axis vector r of Pu, and then cross-multiply the vector r by the AC vector to obtain the normal vector of the rotated Pu. The equation of the rotated Pu can be calculated from the iteration point A; since the upper containing plane and the lower containing plane rotate synchronously and always remain parallel, the equation of the rotated Pd can be obtained from the iteration point B; If the iteration point C is within the lower containing plane, the calculation method is the same as that in step 32.

7. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S4, the discrimination method of the minimum region straight line criterion is as follows: Assume that the iteration points A and C are located on the upper containing surface, project the iteration point B onto the upper containing plane, and judge whether the three points on the upper containing surface are on the same straight line, and the projection point of point B needs to be between point A and C. If so, the minimum region straight line discrimination criterion is satisfied, otherwise it is not satisfied; when point C is on the lower containing plane, the judgment method is the same as above; if the minimum region straight line discrimination criterion is satisfied, jump to step S7, if not, continue step S5 to find the fourth iteration point.

8. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, characterized in that, In step S5, appropriate search regions are selected for the upper containing plane and the lower containing plane respectively through the second region selection algorithm. The specific steps are as follows: Step 51: Project the three-dimensional data point set onto the XOY plane of the coordinate axis. Assume that the iterative points A and C are both on the upper inclusion plane. The line connecting the projection points of points A and C is set as the demarcation line l. a2 , draw a line parallel to l a2 through the projection point of point B as the demarcation line l. b2 ; Then the search area of the upper inclusion plane where point A is located is: with l a2 as the demarcation line and on the same side as the projection point of point B, but not including the points on the line; the search area of the lower inclusion plane where point B is located is: with l b2 as the demarcation line and on the same side as the projection point of point A, but not including the points on the line; The calculation method for the case where points B and C are in the same inclusion plane is the same as that in Step 51.

9. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, wherein, In step S5, search for the point that contacts the corresponding containing plane and has the smallest rotation angle in the two regions. The specific calculation method of the rotation angle is as follows: In Case 1, assume that the iterative point C and the iterative point A are in the same containing plane. With AC as the rotation axis, at this time, the rotation axis of the lower containing plane passes through the iterative point B and is parallel to the AC axis. Through the second region selection algorithm, a suitable search region is selected for the upper containing plane Pu, and all points in the region are traversed, denoted as j. Calculate the rotation angle θ when Pu rotates around the rotation axis AC to point j j , and its calculation formula is: ； where d j is the distance from point j to the containing plane, and D j is the distance from point j to the straight line where the rotation axis AC is located, is the arcsine function for calculation; The rotation search method of the plane Pd is the same as that of the plane Pu. Since the rotation axis of the plane Pd is parallel to the AC of Pu and passes through point B, the rotation angle of Pd around the rotation axis can be calculated. Combine all the rotation angles, and the traversal point corresponding to the smallest rotation angle is the fourth iteration point D; Case 2: Assume that point C and point B are in the same containing plane. The calculation method for this case is the same as that in Case 1, and then the method in Claim 6 is used to calculate the new containing plane.

10. The method for calculating the flatness error of an optical surface based on the minimum zone according to claim 1, wherein, In step S6, it is judged whether the four iterative points A, B, C, and D satisfy the triangle criterion or the cross criterion discrimination criterion. If not, one point is removed according to certain rules, and then it jumps to step S5 to continue the rotation iteration until the four iterative points all satisfy the minimum region discrimination criterion, which is specifically as follows: The discrimination method of the triangle criterion is as follows: When three iterative points are in the same containing plane, the triangle criterion is judged, and the iterative point on the other plane is projected onto this plane. If the projection point is inside the triangle formed by the other three points and includes the sides, then the minimum region triangle criterion is satisfied, otherwise it is not satisfied; The judgment rule for removing invalid iterative points when the triangle criterion is not satisfied is as follows: Assume that the iterative points A, C, and D are all on the upper containing plane, project point B onto the upper containing plane to obtain the projection point B', connect the three points A, C, and D to form a triangle. At this time, point B' is outside the triangle. Select the side of the triangle closest to point B' as the new rotation axis, and at the same time discard the points that are not on the rotation axis. The discrimination method of the cross criterion is as follows: When the four iterative points are distributed in two containing planes in pairs, the cross criterion is judged, and the iterative points are projected onto the same containing plane, and the two points on the same containing plane are respectively connected. If the two formed line segments intersect, then the minimum region cross criterion is satisfied, otherwise it is not satisfied; The judgment rule for removing invalid iterative points when the cross criterion is not satisfied is as follows: Assume that point A and point D are on the upper containing plane, and point B and point C are on the lower containing plane; Project all points onto the upper containing plane or the lower containing plane, and connect the two points on the same containing plane to form two line segments. Since the minimum region cross discrimination criterion is not satisfied, the two line segments do not have an intersection point at this time. Extend the two line segments to obtain the intersection point. According to the position of the intersection point, it can be divided into two cases: a) The intersection point is on one of the line segments, select the straight line where this line segment is located as the rotation axis; b) The intersection points are not on both line segments. In this case, randomly select a straight line as the rotation axis; Finally, discard the iterative points on the other straight line that are farther from the rotation axis.

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