Polishing method and apparatus for aspherical elements

Abstract

The present disclosure provides a polishing processing method and device of an aspherical surface element, and relates to the technical field of optical processing. The method comprises the following steps: mapping a plurality of measurement points on a surface of an aspherical surface element to be processed to a first coordinate system with each dwell point as the center, wherein the trajectory direction of the polishing processing trajectory on the corresponding dwell point is the first coordinate system with the coordinate axis as the axis, to obtain a first coordinate; determining the removal efficiency of the reference removal function of each measurement point at each dwell point according to the first coordinate of each measurement point in each first coordinate system and the reference removal function; and determining the dwell time of the dwell point according to the removal efficiency and the material removal amount. The present disclosure considers the time-varying characteristics of the removal function of the non-rotationally symmetric shape distribution, rotates and registers the removal function at each dwell point along the trajectory direction, is closer to the actual polishing processing process, improves the accuracy of the dwell time at each dwell point, improves the accuracy of the material removal model in guiding the actual processing, and further improves the processing precision of the aspherical workpiece.

Description

Technical Field

[0001] This disclosure relates to the field of optical processing technology, and in particular to a polishing method and apparatus for aspherical elements. Background Technology

[0002] Compared to traditional spherical optical systems, aspherical mirrors offer a high degree of freedom. Introducing them into a system can simplify its structure, leading to their increasing adoption in many important optical fields. Before actually fabricating aspherical components, simulations and predictions are necessary to determine if the simulated fabrication accuracy meets requirements.

[0003] In related technologies, the removal function model for aspherical surfaces during simulated processing can be replaced by a single removal function measured on a plane or sphere, and the removal function is treated as constant throughout the processing, with the dwell time at each dwell point predicted. However, in actual processing, the removal function of the grinding and polishing tool exhibits a non-rotationally symmetric distribution during dynamic feeding, and the removal effect of the removal function changes dynamically at different positions, exhibiting time-varying characteristics, which seriously affects the predictive accuracy of the aspherical material removal model. Therefore, how to improve the accuracy of the material removal model in guiding the actual processing of aspherical components is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] This disclosure aims to at least partially address one of the technical problems in the related art.

[0005] Therefore, the first aspect of this disclosure provides a polishing method for aspherical components, comprising:

[0006] Determine multiple dwell points, multiple measurement points, and polishing trajectories on the surface to be processed of the aspherical component;

[0007] Determine the amount of material removed at each of the measurement points;

[0008] Determine the reference removal function for the target polishing equipment to polish the aspherical element;

[0009] The plurality of measurement points are mapped to the first coordinate system corresponding to each of the dwelling points to obtain the first coordinate of each measurement point in each of the first coordinate systems, wherein the first coordinate system is centered on the corresponding dwelling point and the trajectory direction of the polishing process trajectory on the corresponding dwelling point is the coordinate axis;

[0010] Based on the first coordinate of each measurement point in each first coordinate system and the reference removal function, determine the removal efficiency of the reference removal function at each dwelling point for each measurement point;

[0011] A removal function matrix is ​​constructed based on the removal efficiency and the amount of material removed to obtain the residence time corresponding to each residence point;

[0012] The target polishing equipment is controlled to polish the surface to be processed according to the polishing trajectory and the dwell time corresponding to each dwell point.

[0013] A second aspect of this disclosure provides a polishing apparatus for aspherical components, comprising:

[0014] The first determining module is used to determine multiple dwelling points, multiple measuring points, and polishing trajectories on the surface to be processed of the aspherical element;

[0015] The second determining module is used to determine the amount of material removed at each of the measurement points;

[0016] The third determining module is used to determine the reference removal function for the target polishing equipment to polish the aspherical element;

[0017] The first processing module is used to map the plurality of measurement points to a first coordinate system corresponding to each of the dwelling points, and obtain the first coordinate of each measurement point in each of the first coordinate systems, wherein the first coordinate system is centered on the corresponding dwelling point and the trajectory direction of the polishing process trajectory on the corresponding dwelling point is the coordinate axis.

[0018] The fourth determining module is used to determine the removal efficiency of the reference removal function at each dwelling point for each measurement point based on the first coordinate of each measurement point in each first coordinate system and the reference removal function;

[0019] The second processing module is used to construct a removal function matrix based on the removal efficiency and the amount of material removed, so as to obtain the residence time corresponding to each residence point;

[0020] The processing control module is used to control the target polishing equipment to perform polishing processing on the surface to be processed according to the polishing processing trajectory and the dwell time corresponding to each dwell point.

[0021] A third aspect of this disclosure provides an electronic device, including: a processor, and a memory communicatively connected to the processor;

[0022] The memory stores computer-executed instructions;

[0023] The processor executes computer execution instructions stored in the memory to implement the method described in the first aspect above.

[0024] A fourth aspect of this disclosure provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method described in the first aspect above.

[0025] The polishing method for aspherical components disclosed herein takes into account the time-varying characteristics of the removal function with a non-rotationally symmetric distribution. Based on the direction of the polishing trajectory at each dwell point, the coordinates of the measurement points are transformed, and the removal function at each dwell point is rotated and registered with the trajectory direction, which is closer to the actual polishing process. As a result, the dwell time at each dwell point is more accurate, which improves the accuracy of the material removal model in guiding the actual processing, and thus improves the processing accuracy of aspherical workpieces.

[0026] Additional aspects and advantages of this disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this disclosure. Attached Figure Description

[0027] The above and / or additional aspects and advantages of this disclosure will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, in which:

[0028] Figure 1 A schematic flowchart illustrating a polishing method for an aspherical component provided in this embodiment of the present disclosure;

[0029] Figure 2 A schematic diagram of the surface shape error distribution of a surface to be processed, provided for an embodiment of this disclosure;

[0030] Figure 3 This is a schematic diagram illustrating the material removal rate distribution on a surface to be processed, provided as an embodiment of this disclosure.

[0031] Figure 4 This is a schematic diagram of a polishing spot in a magnetorheological polishing technique provided in an embodiment of the present disclosure;

[0032] Figure 5 A schematic diagram of a benchmark removal function provided in an embodiment of this disclosure;

[0033] Figure 6 A schematic diagram of a dwell point and a measuring point on a surface to be processed, provided in an embodiment of this disclosure;

[0034] Figure 7 This is a schematic diagram of a processing procedure when the rotation direction of the polishing wheel is perpendicular to the processing path, provided by an embodiment of the present disclosure.

[0035] Figure 8 This is a schematic diagram illustrating the construction of a removal function matrix according to an embodiment of the present disclosure;

[0036] Figure 9 This is a schematic diagram of the residence time distribution of a surface to be processed, provided by an embodiment of the present disclosure;

[0037] Figure 10 This is a schematic diagram of the residual error distribution on a surface to be processed, provided in an embodiment of the present disclosure.

[0038] Figure 11 A schematic diagram of discrete points of orthogonal projection on a planar element and an aspherical surface provided in an embodiment of this disclosure;

[0039] Figure 12 A schematic diagram illustrating a two-dimensional material removal model and the actual amount of aspherical material removed, provided in an embodiment of this disclosure;

[0040] Figure 13 This is a schematic diagram illustrating the determination of multiple dwelling points and multiple measurement points equidistantly distributed in a neighborhood on a surface to be processed, as provided in an embodiment of this disclosure.

[0041] Figure 14 This is a schematic diagram of a plane passing through two points and perpendicular to the XOY plane, as proposed in an embodiment of this disclosure.

[0042] Figure 15 This is a schematic diagram illustrating a method for determining sampling points according to an embodiment of this disclosure;

[0043] Figure 16 A flowchart illustrating another sampling point planning method with equidistant neighborhood distribution provided in this embodiment of the disclosure;

[0044] Figure 17 This is a schematic diagram of a polishing apparatus for aspherical components provided in this disclosure. Detailed Implementation

[0045] Embodiments of this disclosure are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this disclosure, and should not be construed as limiting this disclosure.

[0046] Specifically, the polishing method and apparatus for aspherical elements according to embodiments of the present disclosure are described below with reference to the accompanying drawings.

[0047] Figure 1 This is a schematic flowchart illustrating a polishing method for an aspherical component provided in an embodiment of this disclosure. Figure 1 As shown, the polishing method for this aspherical element may include:

[0048] Step 101: Determine multiple dwell points, multiple measurement points, and polishing trajectories on the surface to be processed of the aspherical component.

[0049] In this context, the dwell point represents the position where the target polishing equipment stops on the surface to be processed for polishing. The measurement point is used to provide the surface shape error distribution of the surface to be processed, and the dwell time distribution is solved by the material removal amount and material removal efficiency at each measurement point during the simulated processing. The polishing trajectory refers to the spatial path of the target polishing tool on the surface to be processed, covering all dwell points. The aspherical element is a rotationally symmetric aspherical element. Optionally, the number and / or position of the dwell points and measurement points can be the same or different. For example, in some embodiments, the dwell points and measurement points can completely overlap or partially overlap, or there may be no overlapping points between the dwell points and measurement points. This embodiment does not limit this. Optionally, the type of polishing trajectory can be raster scanning, contour following, spiral trajectory, random path, etc., which is not limited in this disclosure.

[0050] Step 102: Determine the amount of material removed at each measurement point.

[0051] In this embodiment of the disclosure, the absolute surface shape of the surface to be processed of the aspherical element can be measured to obtain the absolute surface shape height distribution z(x,y) of the surface to be processed. The surface shape error data of the surface to be processed is determined based on the nominal parameters of the surface to be processed and the absolute surface shape height distribution. The surface shape error data is then processed to obtain the material removal amount at each measurement point.

[0052] Figure 2 This is a schematic diagram of the surface shape error distribution of a surface to be processed, provided in an embodiment of this disclosure. Figure 3 This is a schematic diagram illustrating the material removal distribution on a surface to be processed, provided in an embodiment of this disclosure. In one implementation, the nominal values ​​of the vertex radius of curvature and the quadratic constant of the surface to be processed are R0 and K0, respectively. The deviation between the surface to be processed and the nominal surface, i.e., the surface error e(x,y), is obtained by subtracting the ideal aspherical height under the nominal parameters from the measured absolute surface height z(x,y).

[0053]

[0054] By performing non-negative processing on the surface shape error data, the material removal distribution is obtained:

[0055]

[0056] Step 103: Determine the reference removal function for the target polishing equipment to polish aspherical components.

[0057] In some embodiments of this disclosure, the target polishing device can be a polishing device in controllable flexible optical processing technology, such as small abrasive polishing (the polishing layer uses a flexible polishing adhesive with strong fluidity), magnetorheological polishing (magnetorheological polishing liquid), airbag polishing (changing the shape of the polishing area by air pressure), etc. Figure 4 This is a schematic diagram of a polishing spot in a magnetorheological polishing technique provided in an embodiment of this disclosure. Figure 4 As shown, the removal function of magnetorheological technology exhibits a tail elongation characteristic. Furthermore, for example, in small abrasive polishing, when the polishing tool moves across the workpiece, its removal function also exhibits a certain degree of tail elongation.

[0058] As one implementation method, the polishing process parameters can be set in conjunction with the material removal amount determined for each measurement point in step 102. A planar sample with the same material as the aspherical element to be processed can be taken, and a spot sampling experiment can be performed on it to measure the three-dimensional morphology of the polishing spot and obtain the reference removal function. Figure 5 This is a schematic diagram of a benchmark removal function provided in an embodiment of this disclosure.

[0059] Step 104: Map multiple measurement points to the first coordinate system corresponding to each dwell point to obtain the first coordinate of each measurement point in each first coordinate system.

[0060] In this system, the first coordinate system is centered at the corresponding dwell point, with the direction of the polishing trajectory at that dwell point as the coordinate axis. Coordinate transformation of the measurement points is equivalent to rotating the reference removal function at each dwell point in the coordinate system, aligning it with the direction of the long axis of the polishing spot. Counterclockwise rotation is a positive angle, and clockwise rotation is a negative angle, ensuring that the rotated removal function adapts to the actual polishing direction at each dwell point. This allows for accurate prediction of the removal efficiency of the removal function at different measurement points when applied at the dwell point.

[0061] Figure 6 This is a schematic diagram of a dwell point and a measuring point on a surface to be processed, provided as an embodiment of this disclosure. (See diagram below.) Figure 6 As shown, O(x) i ,y i Let P(x) be a dwell point on the surface to be processed. j ,y j Let be a measurement point on the surface to be processed. In some embodiments of this disclosure, for each measurement point, the coordinate deviation value between the measurement point and each dwell point can be determined separately:

[0062]

[0063] Based on the tangential angle θ at each dwell point of the polishing process trajectory. i Determine the coordinate transformation change of the measurement point relative to each stationary point. Figure 6 The illustrated embodiment is an example. Figure 6 When the direction of the polishing wheel's rotation axis (i.e., the axis around which the polishing wheel rotates during processing) is parallel to the processing path, the coordinate transformation change of the measurement point relative to the dwell point can be referenced by the following formula:

[0064]

[0065] Figure 7 This is a schematic diagram illustrating a machining process where the direction of the polishing wheel's rotation axis is perpendicular to the machining path, as provided in an embodiment of this disclosure. Figure 7 In the case of the embodiment shown, the coordinate transformation change of the measurement point relative to the dwell point can be referred to the following formula:

[0066]

[0067] Based on the coordinate deviation value Δp ij and coordinate transformation change R θ Determine the first coordinate P' of measurement point j in the first coordinate system corresponding to the dwell point i:

[0068] P' = R θ ·Δp ij

[0069] Thus, through coordinate transformation, the first coordinates of each measurement point in each first coordinate system are obtained. Assuming the number of measurement points on the surface to be processed is v, for a certain dwelling point i on the surface to be processed, the v measurement points are mapped to the first coordinate system with the corresponding dwelling point i as the center and the direction of the polishing trajectory on the corresponding dwelling point i as the coordinate axis, thus obtaining the first coordinates of each measurement point.

[0070] Step 105: Based on the first coordinate of each measurement point in each first coordinate system and the reference removal function, determine the removal efficiency of the reference removal function at each dwelling point for each measurement point.

[0071] In one implementation, the baseline removal function obtained in step 103 can be interpolated using P' to calculate the dwell point O(x). i ,y i The removal function of rotation at measurement point P(x) j ,y j The removal efficiency at each point is the removal efficiency of the removal function at each dwell point over all measurement points.

[0072] Step 106: Construct a removal function matrix based on removal efficiency and material removal amount to obtain the residence time corresponding to each residence point.

[0073] Figure 8This is a schematic diagram illustrating the construction of a removal function matrix according to an embodiment of this disclosure. Figure 8 As shown, for measurement point i, it is assumed that the removal function at the four residence points a, b, c, and d has a material removal effect on measurement point i. The material removal efficiency of the removal function at the four residence points a, b, c, and d for point i is written as r. ia r ib r ic r id Write during the 4 o'clock stay. a t b t c t d Then the amount of material removed at measurement point i, δ i It can be represented as:

[0074] δ i =r ia ×t a +r ib ×t b +r ic ×t c +r id ×t d

[0075] Therefore, the amount of material removed at a certain measurement point can be expressed as the sum of the removal efficiencies of the removal functions at all residence points for that measurement point:

[0076]

[0077] Where, δ i r represents the amount of material removed at the i-th measurement point. ij Let t be the removal efficiency of the removal function at residence point j with respect to measurement point i. j Let j be the residence time corresponding to residence point j, and n be the number of residence points on the surface to be processed. Therefore, based on the baseline removal function at each residence point, a removal function matrix is ​​constructed for the removal efficiency and material removal amount at each measurement point:

[0078]

[0079] Based on the amount of material removed at each measurement point determined in step 102 and the removal efficiency of the benchmark removal function at each residence point determined in step 105 for each measurement point, the removal function matrix is ​​simulated and solved to obtain the residence time of the removal function at each residence point. Figure 9 This is a schematic diagram showing the residence time distribution of a surface to be processed, provided as an embodiment of this disclosure.

[0080] Step 107: Control the target polishing equipment to polish the surface to be processed according to the polishing process trajectory and the dwell time corresponding to each dwell point.

[0081] Optionally, in some embodiments of this disclosure, the surface to be processed can be simulated based on the polishing trajectory and the dwell time corresponding to each dwell point to obtain the residual error distribution, thereby confirming whether the dwell time corresponding to each dwell point meets the processing accuracy requirements. When the residual error distribution meets the processing accuracy conditions of the aspherical element, the target polishing equipment is controlled to polish the surface to be processed according to the polishing trajectory and the dwell time corresponding to each dwell point. Figure 10 This is a schematic diagram of the residual error distribution on a surface to be processed, provided as an embodiment of the present disclosure.

[0082] By implementing the embodiments of this disclosure, considering the time-varying characteristics of the removal function with a non-rotationally symmetric distribution, the coordinate transformation of the measurement points is performed based on the direction of the polishing trajectory at each dwell point. The removal function at each dwell point is rotated and registered with the trajectory direction to make it closer to the actual polishing process. As a result, the dwell time at each dwell point is more accurate, which improves the accuracy of the material removal model in guiding the actual processing and thus improves the processing accuracy of the aspherical workpiece in the subsequent processing.

[0083] In related technologies, when establishing a material removal model to simulate the processing, discrete points on the aspherical surface can be sampled by projecting the plane onto the orthogonal axis in a three-dimensional Cartesian coordinate system. Figure 11 This is a schematic diagram of discrete points projected onto a planar element and an aspherical surface, provided as an embodiment of this disclosure. (See diagram below.) Figure 11 As shown, compared to planar elements, the non-developable nature of aspherical surfaces means that their surfaces cannot be discretized into orthogonal equidistant grids. In this case, the spacing between sampling points on the aspherical surface varies significantly with the steepness of the surface. Figure 12 This diagram illustrates a two-dimensional material removal model and the actual amount of aspherical material removed, as provided in an embodiment of this disclosure. Figure 12 (a) is a schematic diagram of a two-dimensional material removal model. The removed areas will overlap stably and will also produce secondary profiles with the same shape. Figure 12 (b) is a schematic diagram of the actual material removal amount on the aspherical surface. The discrete points of the positive axis projection on the aspherical surface will be scattered in areas with high steepness and dense in areas with low steepness. In actual processing, the overlap of the removal function at different positions is different, which will produce secondary profiles of different depths, causing changes in the depth of material removal. Therefore, the prediction results of the material removal model for aspherical surfaces will deviate from the actual processing situation.

[0084] Due to the unique characteristics of aspherical shapes, using a linear two-dimensional material removal model (i.e., representing the material removal amount in two-dimensional space through a linear convolution of the removal function and the residence time) negatively impacts the prediction of material removal from aspherical surfaces and the subsequent actual processing accuracy. Other methods may replace the aspherical model with its best-fit spherical surface to plan residence and measurement points on the aspherical surface. However, this best-fit spherical replacement method still suffers from uneven distribution of sampling points in steep regions, affecting processing accuracy.

[0085] Therefore, in some embodiments of this disclosure, to further improve processing accuracy, multiple sampling points equidistantly distributed in a neighborhood can be determined on the surface to be processed. Then, multiple dwelling points and multiple measurement points equidistantly distributed in a neighborhood are determined from these multiple sampling points. A polishing trajectory is generated based on these multiple dwelling points. By finding uniformly distributed sampling points on a three-dimensional curved surface, this method does not rely on mapping from a plane or sphere to an aspherical surface and adapts to different surface steepness, significantly improving the orthogonal uniformity of sampling points for aspherical components. As an example, in the above-described... Figure 1 Based on the illustrated embodiments, as Figure 13 As shown in the embodiments of this disclosure, the process of determining multiple dwelling points and multiple measurement points equidistantly distributed in a neighborhood on a surface to be processed may include the following steps:

[0086] Step 1301: Taking the vertex of the surface to be processed as the center point, determine multiple first sampling points on the XY direction section of the surface to be processed according to the preset first surface spacing value, wherein the arc length on the surface between adjacent first sampling points on each direction section is the first surface spacing value.

[0087] Among them, the surface arc length between two points refers to the shortest surface arc length between two points on the surface to be processed.

[0088] In this embodiment of the disclosure, the vertex of the aspherical surface can be taken as the center point P. 00 Taking this point as the intersection of the aspherical meridians in the x and y directions, we find the point with respect to P. 00 Using equidistant circles centered on a point on the surface, multiple equidistant first sampling points are determined on the XY direction cross-sections (i.e., the X-direction cross-section and the Y-direction cross-section) of the surface to be processed. Optionally, the number of first sampling points on the X-direction cross-section and the number of first sampling points on the Y-direction cross-section can be the same or different. The equidistant circle on the surface is defined as follows: for a point on the surface to be processed, the set of points equidistant from that point on the curved surface is taken as the equidistant circle on the surface of that point.

[0089] In one possible implementation, multiple equidistant first sampling points on the XY direction cross section of the surface to be processed can be determined by the following steps S1-S5:

[0090] S1: Assume that the vertex P of the surface to be processed on the aspherical element F(x,y,z) is connected to the surface to be processed. 00 The point P is the point whose arc length is l formed by (x0, y0, z0). ij (x x ,y y ,z z ).

[0091] Where F(x,y,z) is the expression for the surface to be processed obtained by fitting the three-dimensional point cloud, and z z The z-axis can be obtained through the F(x,y,z) equation. z (x x ,y y ) represents, and then uses the unknown quantity x x y y The expression for P 00 P ij And a plane G(x,y,z) perpendicular to the XOY plane, such as Figure 14 As shown.

[0092] S2: Confirmed P 00 (x0,y0,z0) and P ij (x x ,y y ,z z ), and contains an unknown quantity x x y y Space curve equation:

[0093]

[0094] S3: Let P 00 (x0,y0,z0) and P ij (x x ,y y ,z z Let ) represent the two endpoints of curve Γ, and let l represent the curve Γ at point P. 00 and P ij Given the arc length between two points (i.e., the spacing value on the first surface in step 1301), the tangent vector of any point P(x,y,z) on curve Γ is:

[0095]

[0096] make Then the tangent vector Angle with the XOY plane The cosine is:

[0097]

[0098] S4: Let Γ be the intersection of the projection cylinder H(x,y)=0 of the space curve Γ onto the XOY plane and the XOY plane. XY , then Γ XY The equation can be expressed as:

[0099]

[0100] S5: On the rectangular coordinate plane XOY, passing through P 00 and P ij The coordinates of the two endpoints are (x0, y0) and (x...). x ,y y From the arc length formula of a plane curve, the arc length between two points on the plane can be written in definite integral form:

[0101]

[0102] Therefore, P 00 (x0,y0,z0) and P ij (x x ,y y ,z z The arc length l on the surface between two points is represented by an upper limit and the integrand contains an unknown x. x The definite integral form. Based on the given spacing value l1 on the first surface, x can be obtained. x The value of is obtained, which yields a set of points that form the same arc length as the given point, thus obtaining equidistant circles on the surface of the given point. Through the above steps S1-S5, multiple equidistant circles on the surface to be processed can be obtained, with the shortest arc length between a point on each equidistant circle and the vertex of the surface to be processed being an integer multiple of the spacing value on the first surface.

[0103] Figure 15 This is a schematic diagram illustrating a method for determining sampling points according to an embodiment of this disclosure. Figure 15 As shown in (a), equidistant circles (C1, C2, C3, ..., C6) are determined on multiple faces of the surface to be processed. K Then, the intersections of the equidistant circles on multiple surfaces with the XY direction intercepts on the rectangular coordinate plane XOY are taken as the first sampling points P of the equidistant distribution. i，0 and P 0，j .

[0104] Step 1302: Divide the first sampling points with equal arc lengths on the surface between them and the center point into a group to obtain K groups of first sampling points.

[0105] Among them, L k =k*l1,L kLet l1 be the arc length on the surface between the first sampling point and the center point of the kth group, l1 be the spacing value on the first surface, K be a positive integer, and k be a positive integer less than or equal to K.

[0106] Taking the method of finding equidistant circles on the surface in step 1301 as an example, the intersection points of the same equidistant circle on the surface centered at the vertex of the surface to be processed and the intercepts in the x and y directions are divided into the same group of first sampling points. As an example, for the intersection point P of the equidistant circle C1 with arc length l1 on the surface between the vertex of the surface to be processed and the intercepts in the XY directions... -1，0 P 1，0 P 0，-1 P 0，1 As the first sampling point of the first group; for the intersection point P of the equidistant circle C2 on the surface with the shortest arc length of 2*l1 between it and the vertex of the surface to be processed, and the intercept in the XY direction. -2，0 P 2，0 P 0，-2 P 0，2 As the first sampling point of the second group, the first sampling points of the other groups follow the same pattern, which will not be elaborated here.

[0107] Step 1303: Taking each first sampling point in the first sampling point of the first group as the center, determine the equidistant circle on the surface corresponding to each first sampling point in the first group based on the spacing value on the first surface.

[0108] In this context, the arc length on the surface between a point on an equidistant circle and its corresponding first sampling point is the distance value on the first surface. For details on how to construct the corresponding equidistant circle on the surface centered on the first sampling point, please refer to the description in step 1301.

[0109] Step 1304: Take the intersection of the equidistant circles on the surface corresponding to the first sampling point of the first group as the second sampling point of the first group.

[0110] like Figure 15 As shown in (b), the intersection point P between the equidistant circles on the surface corresponding to the first sampling point of the first group is... -1，-1 P -1，1 P 1，-1 P 1，1 As the second sampling point in the first group, the arc length on the surface between each second sampling point and its adjacent first sampling point is the spacing value on the first surface. Let P... 1，1 For example, P 1，1 That is, P 1，0 and P 0，1 The equidistant points in the public neighborhood.

[0111] Step 1305: For the K-1 group of first sampling points other than the first sampling point of the first group in the K group, take the first sampling point of the k group and the second sampling point of the k-1 group as the center, and determine the equidistant circle on the surface corresponding to the first sampling point of the k group and the equidistant circle on the surface corresponding to the second sampling point of the k-1 group based on the spacing value on the first surface.

[0112] Step 1306: The intersection point between the equidistant circles on the surface corresponding to the first sampling point of the k-th group and the second sampling point of the (k-1)-th group is taken as the second sampling point of the k-th group.

[0113] like Figure 15 As shown in (c), taking the first sampling point of the second group as an example, and taking the second sampling point P of the first group respectively... -1，-1 P -1，1 P 1，-1 P 1，1 and the first sampling point P of the second group -2，0 P 2，0 P 0，-2 P 0，2 Determine equidistant circles on the surface centered on the point, and use the intersection of these equidistant circles as the second sampling point of the second group. Figure 15 (c) only shows a portion of points P in the second sampling point of the second group. 1，2 and P 2，1 The second sampling points of group K-1, excluding the second sampling points of group 1, are obtained on the surface to be processed through steps 1305 and 1306.

[0114] Step 1307: The vertices of the surface to be processed, the first sampling point of group K, and the second sampling point of group K are used as sampling points.

[0115] Among them, all neighboring sampling points on the surface to be processed are equidistant, such as Figure 15 As shown in (d).

[0116] Step 1308: Determine multiple measurement points in the sampling points based on the pre-set spacing on the second surface.

[0117] Optionally, all sampling points can be used as measurement points, meaning the spacing on the first surface and the spacing on the second surface are equal. Alternatively, some equidistant neighborhood points can be selected from the sampling points based on the spacing on the second surface, meaning the spacing on the first surface is greater than the spacing on the second surface.

[0118] Step 1309: Determine multiple dwelling points in the sampling points based on the pre-set spacing on the third surface.

[0119] Similarly, in some embodiments of this disclosure, all sampling points can be used as dwell points, meaning the spacing on the first surface and the spacing on the third surface are equal. Alternatively, based on the spacing on the second surface, some equidistant neighborhood points can be selected from the sampling points as dwell points, meaning the spacing on the first surface is greater than the spacing on the third surface.

[0120] Therefore, through steps 1301-1309, uniformly distributed dwell points and measurement points can be found on the three-dimensional curved surface, independent of the mapping from a plane or sphere to an aspherical surface, significantly improving the orthogonal uniformity of sampling points of aspherical components, and applicable to the processing of aspherical components with different surface steepness. The method for determining multiple dwell points and multiple measurement points equidistantly distributed in the neighborhood on the surface to be processed in this embodiment can be applied to this disclosure. Figure 1 In the polishing method of the aspherical components shown, based on the time-varying characteristics of the removal function with non-rotational symmetry distribution, by selecting uniformly distributed dwell points and measurement points, the simulated processing process can be made closer to the actual processing scenario, further improving the accuracy of the material removal model in guiding actual processing.

[0121] Figure 16 This flowchart illustrates another method for planning sampling points with equidistant neighborhood distribution, provided by an embodiment of this disclosure. It determines sampling points with equidistant neighborhood distribution in a portion of the surface to be processed. By performing symmetrical and splicing processing on the sampling points in this region, the sampling points on the surface to be processed are obtained, thereby saving computational power. Figure 16 As shown, the method includes:

[0122] Step 1: Input initial surface profile data such as aspherical aperture and surface parameters, and specify a suitable sampling point arc length S (i.e., Figure 1 In the embodiment, the spacing value l1 on the first surface and the initial sampling point P 00 (i.e., the vertices of the surface to be processed). Obtain P 00 A set of points with equal arc lengths along the x and y transects of the aspherical surface is denoted as {Q}. i0} and {Q 0j}(i=1,2,...,p)(j=1,2,...,q).

[0123] Step 2: Using the vertex of the surface to be processed as the center, divide the surface into four equally sized sector surfaces based on the x and y direction intercepts. Take the sector surface formed by the positive x and y direction intercepts as the target sector region. Find equidistant points on the surface of the target sector region and take P. 00 The two points Q that are closest in the positive x and y directions 10 and Q 01 The initial P 10 and P 01 point.

[0124] Step 3: Obtain P 10 and P 01 equidistant circles {Set_01} and {Set_10} on the plane of these two points, and calculate the closest element P in the two point sets {Set_01} and {Set_10} 11_nm , P 11_nm is the n-th sampling point in the m-th group on the y-direction transect, and P 11_nm is used as P when searching for the next sampling point 01 .

[0125] Step 4: Determine whether n<p holds; if yes, continue sampling in the m-th row, use Q n+10 as P when searching for the next sampling point 10 , and return to Step 3.

[0126] Step 5: When n<p does not hold, the sampling of the m-th row is ended, and determine whether m<q holds; if yes, set Q n 0 as P 11_nm (n=2, 3,..., p), use Q 0m+1 as the starting P for the next group 01 , and repeat Step 3. If m<q does not hold, the sampling process on this quadrant is ended.

[0127] Step 6: Perform symmetric splicing processing on the sampling points in the target sector area to obtain all sampling points on the surface to be processed.

[0128] Figure 17 is a schematic diagram of a polishing device for an aspherical element provided by the present disclosure. As Figure 17 shows, the polishing device for an aspherical element may include: a first determination module 1701, a second determination module 1702, a third determination module 1703, a first processing module 1704, a fourth determination module 1705, a second processing module 1706, and a processing control module 1707.

[0129] wherein, the first determination module 1701 is configured to determine a plurality of dwelling points, a plurality of measurement points and a polishing processing trajectory on the surface to be processed of the aspherical element.

[0130] the second determination module 1702 is configured to determine the material removal amount of each measurement point.

[0131] the third determination module 1703 is configured to determine the reference removal function for polishing the aspherical element by the target polishing equipment.

[0132] The first processing module 1704 is used to map multiple measurement points to the first coordinate system corresponding to each dwell point, and obtain the first coordinate of each measurement point in each first coordinate system. The first coordinate system is centered on the corresponding dwell point and the direction of the polishing process trajectory on the corresponding dwell point is the coordinate axis.

[0133] The fourth determining module 1705 is used to determine the removal efficiency of the reference removal function at each dwelling point for each measurement point based on the first coordinate of each measurement point in each first coordinate system and the reference removal function.

[0134] The second processing module 1706 is used to construct a removal function matrix based on the removal efficiency and the amount of material removed, so as to obtain the residence time corresponding to each residence point.

[0135] The processing control module 1707 is used to control the target polishing equipment to polish the surface to be processed according to the polishing processing trajectory and the dwell time corresponding to each dwell point.

[0136] In some embodiments of this disclosure, the first determining module 1701 is specifically used to: determine a plurality of dwelling points and a plurality of measurement points that are equally distributed in the neighborhood on the surface to be processed; and generate a polishing processing trajectory based on the plurality of dwelling points.

[0137] In some embodiments of this disclosure, the first determining module 1701 is specifically used to: determine multiple first sampling points on the XY direction cross-section of the surface to be processed, taking the vertex of the surface to be processed as the center point, according to a pre-set first surface spacing value, wherein the surface arc length between adjacent first sampling points on each direction cross-section is the first surface spacing value; divide the multiple first sampling points into groups of first sampling points with surface arc lengths equal to the center point, to obtain K groups of first sampling points, wherein L k =k*l1,L kLet l1 be the arc length on the surface between the first sampling point and the center point in the k-th group, l1 be the spacing value on the first surface, K be a positive integer, and k be a positive integer less than or equal to K; taking each first sampling point in the first group as the center, determine the equidistant circle on the surface corresponding to each first sampling point in the first group based on the spacing value on the first surface, and the arc length on the surface between the point on the equidistant circle and the corresponding first sampling point is the spacing value on the first surface; take the intersection point between the equidistant circles on the surface corresponding to the first sampling points in the first group as the second sampling point in the first group; for the K-1 groups of first sampling points other than the first sampling points in the first group, ... A sampling point is formed by taking the first sampling point of the k-th group and the second sampling point of the (k-1)-th group as the center, and determining the equidistant circles on the surface corresponding to the first sampling point of the k-th group and the second sampling point of the (k-1)-th group based on the spacing value on the first surface; the intersection point between the equidistant circles on the surface corresponding to the first sampling point of the k-th group and the second sampling point of the (k-1)-th group is taken as the second sampling point of the k-th group; the vertex of the surface to be processed, the first sampling point of the K-th group, and the second sampling point of the K-th group are taken as sampling points; multiple measurement points are determined in the sampling points based on the pre-set spacing on the second surface; multiple dwelling points are determined in the sampling points based on the pre-set spacing on the third surface.

[0138] In some embodiments of this disclosure, the first processing module 1704 is specifically used to: for each measurement point, determine the coordinate deviation value between the measurement point and each dwelling point; determine the coordinate transformation change of the measurement point relative to each dwelling point according to the tangential angle of the polishing process trajectory at each dwelling point; and determine the first coordinate of the measurement point in each first coordinate system according to the coordinate deviation value and the coordinate transformation change.

[0139] In some embodiments of this disclosure, the processing control module 1707 is specifically used to: simulate the processing of the surface to be processed based on the polishing processing trajectory and the dwell time corresponding to each dwell point to obtain the residual error distribution; and, in response to the residual error distribution satisfying the processing accuracy conditions of the aspherical element, control the target polishing equipment to perform polishing processing on the surface to be processed according to the polishing processing trajectory and the dwell time corresponding to each dwell point.

[0140] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0141] To implement the above embodiments, this disclosure also proposes an electronic device, including: a processor and a memory communicatively connected to the processor; the memory stores computer execution instructions; the processor executes the computer execution instructions stored in the memory to implement the method provided in the foregoing embodiments.

[0142] To implement the above embodiments, this disclosure also proposes a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the methods provided in the foregoing embodiments.

[0143] To implement the above embodiments, this disclosure also proposes a computer program product, including a computer program that, when executed by a processor, implements the methods provided in the foregoing embodiments.

[0144] In the foregoing descriptions of the embodiments, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0145] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this disclosure, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0146] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of this disclosure includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of this disclosure pertain.

[0147] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0148] It should be understood that various parts of this disclosure can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0149] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0150] Furthermore, the functional units in the various embodiments of this disclosure can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0151] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of the present disclosure have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present disclosure. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present disclosure.

Claims

1. A polishing method for aspherical components, characterized in that, Includes the following steps: Determine multiple dwell points, multiple measurement points, and polishing trajectories on the surface to be processed of the aspherical component; Determine the amount of material removed at each of the measurement points; Determine the reference removal function for the target polishing equipment to polish the aspherical element; The plurality of measurement points are mapped to the first coordinate system corresponding to each of the dwelling points to obtain the first coordinate of each measurement point in each of the first coordinate systems, wherein the first coordinate system is centered on the corresponding dwelling point and the trajectory direction of the polishing process trajectory on the corresponding dwelling point is the coordinate axis; Based on the first coordinate of each measurement point in each first coordinate system and the reference removal function, determine the removal efficiency of the reference removal function at each dwelling point for each measurement point; A removal function matrix is ​​constructed based on the removal efficiency and the amount of material removed to obtain the residence time corresponding to each residence point; The target polishing equipment is controlled to polish the surface to be processed according to the polishing trajectory and the dwell time corresponding to each dwell point.

2. The method according to claim 1, characterized in that, The determination of multiple dwelling points, multiple measurement points, and polishing trajectories on the surface to be processed of the aspherical element includes: On the surface to be processed, a plurality of dwelling points and a plurality of measurement points are determined in a neighborhood with equal spacing. The polishing trajectory is generated based on the multiple dwell points.

3. The method according to claim 2, characterized in that, The process of determining the plurality of dwelling points and the plurality of measurement points that are equidistantly distributed in a neighborhood on the surface to be processed includes: Taking the vertex of the surface to be processed as the center point, multiple first sampling points on the XY direction section of the surface to be processed are determined according to the preset first surface spacing value, wherein the arc length on the surface between adjacent first sampling points on each direction section is the first surface spacing value. The first sampling points with equal arc lengths on the surface between the plurality of first sampling points and the center point are divided into groups to obtain K groups of first sampling points, where L k =k*l1,L k Let l1 be the arc length on the surface between the first sampling point in the k-th group and the center point, l1 be the spacing value on the first surface, K be a positive integer, and k be a positive integer less than or equal to K; Taking each first sampling point in the first group of first sampling points as the center, an equidistant circle on the surface corresponding to each first sampling point in the first group of first sampling points is determined based on the spacing value on the first surface. The arc length on the surface between the point on the equidistant circle and the corresponding first sampling point is the spacing value on the first surface. The intersection of the equidistant circles on the surface corresponding to the first sampling point of the first group is taken as the second sampling point of the first group; For the K-1 groups of first sampling points other than the first group of first sampling points in the K groups, take the first group of first sampling points and the second group of second sampling points in the k-1 groups as the centers, and determine the equidistant circles on the surface corresponding to the first group of first sampling points and the equidistant circles on the surface corresponding to the second group of second sampling points in the k-1 groups based on the spacing value on the first surface. The intersection point between the equidistant circles on the surface corresponding to the first sampling point of the kth group and the second sampling point of the (k-1)th group is taken as the second sampling point of the kth group. The vertices of the surface to be processed, the K groups of first sampling points, and the K groups of second sampling points are used as sampling points; The plurality of measurement points are determined in the sampling points based on the pre-set spacing on the second surface; The plurality of dwell points are determined in the sampling points based on the pre-set spacing on the third surface.

4. The method according to claim 1, characterized in that, The step of mapping the plurality of measurement points to the first coordinate system corresponding to each of the dwelling points, to obtain the first coordinate of each measurement point in each of the first coordinate systems, includes: For each measurement point, determine the coordinate deviation value between the measurement point and each dwelling point; Based on the tangential angle of the polishing trajectory at each of the dwell points, determine the coordinate transformation change of the measurement point relative to each of the dwell points; Based on the coordinate deviation value and the coordinate transformation change, the first coordinate of the measurement point in each of the first coordinate systems is determined.

5. The method according to claim 1, characterized in that, The step of controlling the target polishing device to polish the surface to be processed according to the polishing trajectory and the dwell time corresponding to each dwell point includes: Based on the polishing trajectory and the dwell time corresponding to each dwell point, the surface to be processed is simulated to obtain the residual error distribution; In response to the residual error distribution satisfying the machining accuracy condition of the aspherical element, the target polishing equipment is controlled to polish the surface to be processed according to the polishing trajectory and the dwell time corresponding to each dwell point.

6. A polishing apparatus for aspherical components, characterized in that, include: The first determining module is used to determine multiple dwelling points, multiple measuring points, and polishing trajectories on the surface to be processed of the aspherical element; The second determining module is used to determine the amount of material removed at each of the measurement points; The third determining module is used to determine the reference removal function for the target polishing equipment to polish the aspherical element; The first processing module is used to map the plurality of measurement points to a first coordinate system corresponding to each of the dwelling points, and obtain the first coordinate of each measurement point in each of the first coordinate systems, wherein the first coordinate system is centered on the corresponding dwelling point and the trajectory direction of the polishing process trajectory on the corresponding dwelling point is the coordinate axis. The fourth determining module is used to determine the removal efficiency of the reference removal function at each dwelling point for each measurement point based on the first coordinate of each measurement point in each first coordinate system and the reference removal function; The second processing module is used to construct a removal function matrix based on the removal efficiency and the amount of material removed, so as to obtain the residence time corresponding to each residence point; The processing control module is used to control the target polishing equipment to perform polishing processing on the surface to be processed according to the polishing processing trajectory and the dwell time corresponding to each dwell point.

7. The apparatus according to claim 6, characterized in that, The first determining module is specifically used for: On the surface to be processed, a plurality of dwelling points and a plurality of measurement points are determined in a neighborhood with equal spacing. The polishing trajectory is generated based on the multiple dwell points.

8. The apparatus according to claim 7, characterized in that, The first determining module is specifically used for: Taking the vertex of the surface to be processed as the center point, multiple first sampling points on the XY direction section of the surface to be processed are determined according to the preset first surface spacing value, wherein the arc length on the surface between adjacent first sampling points on each direction section is the first surface spacing value. The first sampling points with equal arc lengths on the surface between the plurality of first sampling points and the center point are divided into groups to obtain K groups of first sampling points, where L k =k*l1,L k Let l1 be the arc length on the surface between the first sampling point in the k-th group and the center point, l1 be the spacing value on the first surface, K be a positive integer, and k be a positive integer less than or equal to K; Taking each first sampling point in the first group of first sampling points as the center, an equidistant circle on the surface corresponding to each first sampling point in the first group of first sampling points is determined based on the spacing value on the first surface. The arc length on the surface between the point on the equidistant circle and the corresponding first sampling point is the spacing value on the first surface. The intersection of the equidistant circles on the surface corresponding to the first sampling point of the first group is taken as the second sampling point of the first group; For the K-1 groups of first sampling points other than the first group of first sampling points in the K groups, take the first group of first sampling points and the second group of second sampling points in the k-1 groups as the centers, and determine the equidistant circles on the surface corresponding to the first group of first sampling points and the equidistant circles on the surface corresponding to the second group of second sampling points in the k-1 groups based on the spacing value on the first surface. The intersection point between the equidistant circles on the surface corresponding to the first sampling point of the kth group and the second sampling point of the (k-1)th group is taken as the second sampling point of the kth group. The vertices of the surface to be processed, the K groups of first sampling points, and the K groups of second sampling points are used as sampling points; The plurality of measurement points are determined in the sampling points based on the pre-set spacing on the second surface; The plurality of dwell points are determined in the sampling points based on the pre-set spacing on the third surface.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the method as described in any one of claims 1-5.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-5.

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