A fast method for removing scratches from large-diameter optical components

Abstract

The invention relates to the field of optical processing technology, and in particular to a method for quickly removing scratches from a large-caliber optical element. A defect detection unit is mounted on a tool end of a magnetorheological polishing drive unit, point cloud data of scratches on the optical element are extracted by the defect detection unit, a scratch curve is then fitted, a normal vector of the curve is calculated, a small removal function magnetorheological polishing module is used to vertically remove the scratches along the direction of the normal vector to achieve quick removal of the scratches, and finally a large removal function magnetorheological polishing module is used to traverse the entire optical element surface to retain high-precision surface features of the optical element.

Description

Technical Field

[0001] The invention belongs to the technical field of optical processing, and in particular relates to a method for quickly removing scratches from a large-caliber optical element. Background Art

[0002] Large-aperture optical components, with their huge light-collecting area, can increase the resolution of telescopes to an unprecedented level. The manufacturing technology of large-aperture optical components is an important reflection of a country's comprehensive strength. Scratches are inevitably introduced during the manufacturing, transportation, and even use of large-aperture optical components, which will increase the scattering of the imaging optical system and reduce the loss threshold of the laser system, causing great harm. Therefore, once scratches appear in any link of the manufacturing, transportation, and use of large-aperture optical components, they must be eliminated as much as possible.

[0003] Existing scratch removal methods include contact removal methods and non-contact removal methods. Contact removal methods include magnetorheological polishing technology, airbag polishing technology, etc., and non-contact removal methods include HF (hydrogen fluoride) etching technology, plasma etching technology, etc. The traditional contact removal method requires traversing the entire optical component, and the manufacturing cycle is too long. The non-contact removal method will generate reaction products in the process of removing scratches, which will limit the improvement of the laser damage threshold of the optical component. In addition, this non-contact removal technology is currently not available for large diameters, and is limited in removing scratches on large-diameter optical components. Summary of the invention

[0004] In view of this, the present invention aims to provide a method for quickly removing scratches from large-aperture optical elements, by using a defect detection unit carried by a magnetorheological polishing drive unit to extract point cloud data of scratches on the optical element, then fitting the scratch curve, and then calculating the normal vector of the curve, and then using a small removal function magnetorheological polishing module to vertically remove the scratches along the direction of the normal vector to achieve rapid removal of the scratches, and finally using a large removal function magnetorheological polishing module to traverse the entire optical element surface to retain the high-precision surface features of the optical element.

[0005] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0006] A method for quickly removing scratches from a large-aperture optical element comprises the following steps:

[0007] S1: Setting a defect detection unit at the tool end of a magnetorheological polishing driving unit, and setting an optical element for scratches to be detected within a detection range of the defect detection unit;

[0008] S2: Control the defect detection unit to extract the scratch position coordinates on the optical element, and then fit the scratch position coordinates to obtain a scratch curve; calculate the normalized normal vector of each point on the scratch curve;

[0009] S3: replacing the defect detection unit with a small removal function magnetorheological polishing module installed on the tool end of the magnetorheological polishing drive unit; the small removal function magnetorheological polishing module uses the scratch position coordinates obtained in step S2 as the removal position and the normalized normal vector obtained in step S2 as the removal direction to vertically remove the surface scratches of the optical element;

[0010] S4: Replace the magnetorheological polishing module with a small removal function by a magnetorheological polishing module with a large removal function and install it on the tool end of the magnetorheological polishing drive unit; measure the surface error and magnetorheological removal function of the optical element, and calculate the residence time when processing the optical element;

[0011] S5: Control the large removal function magnetorheological polishing module to traverse the entire surface of the optical element and perform full-aperture processing on the optical element.

[0012] Further, step S2 includes the following steps:

[0013] S21: Calculate the distance between adjacent points on each scratch according to the scratch position coordinates, and then obtain the normalized cumulative arc length of each point on each scratch;

[0014] S22: setting the B-spline order of the fitting, and calculating the B-spline control points according to the normalized cumulative arc length of each point on each scratch;

[0015] S23: setting a B-spline node vector, and performing B-spline fitting in combination with the B-spline order and the B-spline control points to obtain a scratch curve of each scratch;

[0016] S24: Calculate the normalized normal vector of each point on the scratch curve.

[0017] Furthermore, in step S21, the distance between adjacent points on each scratch is calculated by the following formula, namely:

[0018] ;

[0019] in, represents the distance between the i-th point and the i-1-th point in the k-th scratch, represents the position coordinates of the i-th point of the k-th scratch, represents the position coordinates of the i-1th point of the kth scratch, , n represents the total number of points on each scratch;

[0020] According to distance Get the cumulative arc length of each point on each scratch :

[0021] ;

[0022] Where j represents the number of points on each scratch;

[0023] The cumulative arc length of each point on each scratch is calculated by the following formula Perform normalization to obtain the normalized cumulative arc length of each point on each scratch :

[0024] .

[0025] Further, in step S22, the normalized cumulative arc length of each point on each scratch is calculated by the following formula: The corresponding fitting position coordinates :

[0026] ;

[0027] in, , m represents the number of B-spline control points, M represents the maximum number of B-spline control points, and p represents the B-spline order. represents the mth B-spline control point when fitting the kth scratch, represents the B-spline basis function of the m-th B-spline control point under the B-spline order p when fitting the k-th scratch;

[0028] The position coordinates of the i-th point of the k-th scratch are calculated by the following formula: The corresponding fitting position coordinates The gap between E:

[0029] ;

[0030] Minimize the above formula to get the B-spline control point when fitting the k-th scratch .

[0031] Further, in step S23, the B-spline node vector u is:

[0032] ;

[0033] At this time, each scratch curve is obtained :

[0034] .

[0035] Further, in step S24, each scratch curve is obtained The derivative of , and each scratch curve is obtained The tangent vector ,Right now:

[0036] ;

[0037] Find the tangent vector of each scratch The derivative of , and each scratch curve is obtained The normal vector ,Right now:

[0038] ;

[0039] Normal vector Normalize to get the normalized normal vector ,Right now:

[0040] .

[0041] Further, in step S4, the surface error E is measured by interferometer. 0 , and the large removal function magnetorheological polishing module is used to process the test piece made of the same material as the optical element to obtain the magnetorheological removal function RF; the residence time T is obtained by the following formula:

[0042] ;

[0043] in, Represents convolution calculation.

[0044] Compared with the prior art, the invention can achieve the following beneficial effects:

[0045] In the method for quickly removing scratches from large-aperture optical components created by the present invention, the point cloud data of scratches on the optical component is extracted by a defect detection unit, and then the scratch curve is fitted, and the normal vector of the curve is calculated. Then, a small removal function magnetorheological polishing module is used to vertically remove the scratches along the direction of the normal vector to achieve quick removal of the scratches. Finally, a large removal function magnetorheological polishing module is used to traverse the entire optical component surface, retaining the high-precision surface features of the optical component and achieving high-precision convergence of the surface shape. Compared with traditional methods, the method proposed by the present invention can shorten the scratch removal cycle, especially when removing scratches on the surface of large-aperture optical components. The method proposed by the present invention has significant advantages in improving the post-processing efficiency of high-power laser optical components and reducing manufacturing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0047] Figure 1 A schematic flow chart of a method for quickly removing scratches from a large-aperture optical element according to an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of the detection and use of the method for quickly removing scratches from a large-aperture optical element according to an embodiment of the present invention;

[0049] Figure 3 A schematic diagram of the motion trajectory of the defect detection unit according to an embodiment of the present invention;

[0050] Figure 4 It is a schematic diagram of vertical removal and parallel removal;

[0051] Figure 5 A schematic diagram of the processing and use of the method for quickly removing scratches from a large-aperture optical element according to an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of vertical scratch removal by a small removal function magnetorheological polishing module according to an embodiment of the present invention.

[0053] Description of reference numerals:

[0054] 1. Magnetorheological polishing drive unit; 2. Defect detection unit; 3. Optical element; 4. Support platform; 5. Small removal function magnetorheological polishing module. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0056] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0057] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0058] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0059] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0060] like Figure 1 As shown, the method for quickly removing scratches from a large-aperture optical element according to an embodiment of the present invention comprises the following steps:

[0061] S1: Figure 2 As shown, the defect detection unit 2 is arranged at the tool end of the magnetorheological polishing driving unit 1, and the optical element 3 to be detected for scratches is placed on the supporting platform 4, and the optical element 3 is within the detection range of the defect detection unit 2, ensuring that the defect detection unit 2 can completely scan the optical element 3. The coordinates of the optical element 3 and the coordinates of the magnetorheological polishing driving unit 1 are unified in a coordinate system, thereby facilitating the extraction and fitting of the position coordinates of the scratches.

[0062] Among them, the magnetorheological polishing drive unit 1 can be a magnetorheological polishing machine tool (such as a conventional CNC machine tool) or a new type of magnetorheological polishing processing equipment such as an industrial robot. In an embodiment of the present invention, the magnetorheological polishing drive unit 1 preferably adopts a robotic arm. The robotic arm has multiple degrees of freedom and can meet the requirements of removing the normal vector of the scratch. The defect detection unit 2 is arranged at the tool end of the robotic arm.

[0063] The defect detection unit 2 in the embodiment of the present invention preferably adopts a high-resolution industrial camera of model MV-CE200-11UM / C, a resolution of 5472×3648, and a pixel size of 2.4μm×2.4μm, which is a device for defect detection on the surface of the optical element 3, and can distinguish scratches with a width of tens of microns. The defect detection unit 2 uses a scattering imaging method to detect defects on the surface of the optical element 3. When the incident light is irradiated on the surface defect, the defect area will produce chaotic scattering. Although the roughness of the reflector surface will also cause a certain degree of scattering, the scattering directionality and intensity of the surface defects are significantly higher in comparison. In the dark field imaging mode, the defect detection unit 2 uses six ring lights for grazing incidence illumination, which can effectively highlight the scattering of the surface defect area. When there are defects on the surface, these areas will show bright scratch morphology in the image captured by the camera. This grazing incidence illumination has the characteristics of high efficiency and is suitable as a rough scanning method to find surface defects. The fine scanning mode of the defect detection unit 2 uses high-power white light for vertical illumination. At surface defects, scattering also occurs, but scratches appear as dark shadows. This type of illumination has a high signal-to-noise ratio and is therefore often used to accurately calculate the size and shape of surface defects.

[0064] Before using the defect detection unit 2 to perform defect detection on the optical element 3, it is necessary to calibrate the defect detection unit 2 using a standard part with known defect information, that is:

[0065] The standard part is placed on the support platform 4, and the magnetorheological polishing driving unit 1 is driven, so that the magnetorheological polishing driving unit 1 drives the defect detection unit 2 to move along the surface of the standard part. At the same time, the defect detection unit 2 performs defect detection on the surface of the standard part to obtain the detected defect position coordinates. . Get the coordinates of the defect location The actual defect position coordinates of the standard part The difference ,Right now:

[0066]

[0067] If the difference If the error range is within the error range, it is considered that the defect detection unit 2 has been calibrated. Otherwise, the defect detection unit 2 needs to be recalibrated. In the embodiment of the present invention, the error range is less than 0.01 mm, that is, , and All are less than 0.01mm.

[0068] S2: Control the defect detection unit 2 to move along the surface of the optical element 3 as follows: Figure 3The scratch position coordinates on the optical element 3 are extracted and then the scratch position coordinates are fitted to obtain the scratch curve. Figure 3 The direction of the blue arrow in the middle is the step direction of the defect detection unit 2, and the direction of the red arrow is the track gauge direction of the motion trajectory of the defect detection unit 2. Then, the normalized normal vector of each point on the scratch curve is calculated.

[0069] The fitting method for the scratch curve in step S2 includes but is not limited to the least square method, the polynomial fitting method and the B-spline fitting method. In the embodiment of the present invention, the B-spline fitting method is preferably used. Step S2 includes the following steps:

[0070] S21: Calculate the distance between adjacent points on each scratch according to the scratch position coordinates, and then obtain the normalized cumulative arc length of each point on each scratch.

[0071] The distance between adjacent points on each scratch is calculated by the following formula:

[0072] ;

[0073] in, represents the distance between the i-th point and the i-1-th point in the k-th scratch, represents the position coordinates of the i-th point of the k-th scratch, represents the position coordinates of the i-1th point of the kth scratch, , n represents the total number of points on each scratch;

[0074] According to distance Get the cumulative arc length of each point on each scratch :

[0075] ;

[0076] Where j represents the number of points on each scratch;

[0077] The cumulative arc length of each point on each scratch is calculated by the following formula Perform normalization to obtain the normalized cumulative arc length of each point on each scratch :

[0078] .

[0079] S22: setting the B-spline order of the fitting, and calculating the B-spline control points according to the normalized cumulative arc length of each point on each scratch.

[0080] The normalized cumulative arc length of each point on each scratch is calculated by the following formula: The corresponding fitting position coordinates :

[0081] ;

[0082] in, , m represents the number of B-spline control points, M represents the maximum number of B-spline control points, that is, there are M+1 B-spline control points, p represents the B-spline order, represents the mth B-spline control point when fitting the kth scratch, represents the B-spline basis function of the m-th B-spline control point at B-spline order p when fitting the k-th scratch.

[0083] The higher the order of B-spline fitting, the smoother the fitting curve will be, but the corresponding calculation will be more complicated. The third-order B-spline is sufficient to fit the scratches on the surface of the optical element 3. Therefore, in the embodiment of the present invention, the third-order B-spline fitting is preferably used, that is, p=3.

[0084] The position coordinates of the i-th point of the k-th scratch are calculated by the following formula: The corresponding fitting position coordinates The gap between E:

[0085] ;

[0086] Use the least squares method to minimize the above formula and get the B-spline control points when fitting the k-th scratch. .

[0087] S23: setting a B-spline node vector, and performing B-spline fitting in combination with the B-spline order and the B-spline control points to obtain a scratch curve of each scratch.

[0088] The selection of the B-spline node vector will affect the shape of the B-spline. Common node vectors are uniformly distributed, but non-uniform node vectors can be used for complex data. In the embodiment of the present invention, uniform node vectors are preferably used to fit scratches. Therefore, for a p-order B-spline and M+1 control points, the B-spline node vector u is:

[0089] ;

[0090] In the above formula, for a B-spline order of p and M+1 control points, the length of the B-spline knot vector u is M+1+p+1 and is uniformly distributed in [0,1]. Taking the third-order B-spline with M=16 as an example, the length of the B-spline knot vector u is 21, and the corresponding B-spline knot vector u is:

[0091] .

[0092] According to the B-spline control points Perform B-spline fitting with the B-spline node vector u to obtain each scratch curve :

[0093] .

[0094] S24: Since the shape of the magnetorheological removal function is non-circularly symmetrical, it has a major axis and a minor axis. It is approximately axisymmetric in the major axis direction and asymmetric in the minor axis direction. If the major axis direction of the magnetorheological removal function is consistent with the normal vector direction of the scratch curve, then the magnetorheological removal function is considered to be perpendicular to the scratch removal, that is, the major axis direction of the magnetorheological removal function is the direction of the magnetorheological removal function. If the major axis direction of the magnetorheological removal function is perpendicular to the normal vector direction of the scratch curve, then the magnetorheological removal function is considered to be parallel to the scratch removal. Vertical removal and parallel removal are as follows: Figure 4 Therefore, in order to determine that the major axis direction of the magnetorheological removal function is the direction of the magnetorheological removal function, that is, the magnetorheological removal function is perpendicular to the scratch removal, it is necessary to solve the normal vector of the scratch parameterization curve.

[0095] First, find each scratch curve The derivative of , and each scratch curve is obtained The tangent vector ,Right now:

[0096] ;

[0097] Find the tangent vector of each scratch The derivative of , and each scratch curve is obtained The normal vector ,Right now:

[0098] ;

[0099] Normal vector Normalize to get the normalized normal vector ,Right now:

[0100] .

[0101] Calculate the normalized normal vector The spatial interval when removing scratches is the same as the spatial interval when removing scratches with magnetorheological fluid, which can reduce the time of normal vector calculation without affecting the removal efficiency.

[0102] S3: The small removal function magnetorheological polishing module 5 replaces the defect detection unit 2 and is installed on the tool end of the magnetorheological polishing drive unit 1, such as Figure 5The small removal function magnetorheological polishing module 5 uses the scratch position coordinates obtained in step S2 as the removal position and the normalized normal vector obtained in step S2 as the removal direction to vertically remove the surface scratches of the optical element 3. The small removal function magnetorheological polishing module 5 removes the scratches in the normal direction of the scratches. Figure 6 As shown, when the scratch on the surface of the optical element 3 is observed to completely disappear under the white light interferometer, it is considered that the scratch has been removed, and step S3 is ended to complete the rapid removal of the scratch.

[0103] In step S3, the magnetorheological polishing structure in the invention patent application with Chinese patent publication number CN113352152A, publication date September 7, 2021, and patent name "A magnetorheological polishing processing system based on a robotic arm" is preferably integrated into a small removal function magnetorheological polishing module 5 in an embodiment of the present invention, and the size of the magnetorheological polishing wheel in the small removal function magnetorheological polishing module 5 is 160mm, and the sizes of the magnetorheological fluid circulation system and supply system in the small removal function magnetorheological polishing module 5 match the 160mm magnetorheological polishing wheel.

[0104] S4: Replace the small removal function magnetorheological polishing module 5 with the large removal function magnetorheological polishing module and install it on the tool end of the magnetorheological polishing drive unit 1. Measure the surface error and magnetorheological removal function of the optical element 3, and calculate the dwell time when processing the optical element 3.

[0105] In the embodiment of the present invention, the surface error E of the optical element 3 is measured by an interferometer. 0 , and the large removal function magnetorheological polishing module is used to process the test piece of the same material as the optical element 3 to obtain the magnetorheological removal function RF. The residence time T is obtained by the following formula:

[0106] ;

[0107] in, The structure of the large removal function magnetorheological polishing module is consistent with that of the small removal function magnetorheological polishing module 5, except that the size of the magnetorheological polishing wheel in the large removal function magnetorheological polishing module is 360 mm, and the size of the magnetorheological fluid circulation system and supply system in the large removal function magnetorheological polishing module matches the 360 ​​mm magnetorheological polishing wheel.

[0108] S5: After the small removal function magnetorheological polishing module 5 completes the polishing operation according to the process of step S3, the scratches have been completely removed. At this time, the large removal function magnetorheological polishing module is controlled to traverse the surface of the entire optical element 3 according to the common method, and the optical element 3 is processed and shaped in full aperture, so as to quickly achieve surface shape convergence and ensure that the high-precision surface shape can be retained after the scratches are quickly removed.

[0109] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0110] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for quickly removing scratches from large-diameter optical components, characterized in that: The following steps are involved: S1: Setting a defect detection unit at a tool end of a magnetorheological polishing driving unit, and setting an optical element for scratches to be detected within a detection range of the defect detection unit; S2: Control the defect detection unit to extract the scratch position coordinates on the optical element, and then fit the scratch position coordinates to obtain a scratch curve; calculate the normalized normal vector of each point on the scratch curve; Step S2 includes the following steps: S21: Calculate the distance between adjacent points on each scratch according to the scratch position coordinates, and then obtain the normalized cumulative arc length of each point on each scratch; S22: setting the B-spline order of the fitting, and calculating the B-spline control points according to the normalized cumulative arc length of each point on each scratch; S23: setting a B-spline node vector, and performing B-spline fitting in combination with the B-spline order and the B-spline control points to obtain a scratch curve of each scratch; S24: Calculate the normalized normal vector of each point on the scratch curve; S3: replacing the defect detection unit with a small removal function magnetorheological polishing module and installing it on the tool end of the magnetorheological polishing drive unit; the small removal function magnetorheological polishing module uses the scratch position coordinates obtained in step S2 as the removal position and the normalized normal vector obtained in step S2 as the removal direction to vertically remove the surface scratches of the optical element; S4: replacing the small removal function magnetorheological polishing module with a large removal function magnetorheological polishing module and installing it on the tool end of the magnetorheological polishing drive unit; measuring the surface error and magnetorheological removal function of the optical element, and calculating the residence time when processing the optical element; S5: Control the large removal function magnetorheological polishing module to traverse the entire surface of the optical element to perform full-aperture processing on the optical element.

2. The method for quickly removing scratches from a large-diameter optical element according to claim 1, characterized in that: In step S21, the distance between adjacent points on each scratch is calculated by the following formula: ； in, represents the distance between the i-th point and the i-1-th point in the k-th scratch, represents the position coordinates of the i-th point of the k-th scratch, represents the position coordinates of the i-1th point of the kth scratch, , n represents the total number of points on each scratch; According to the distance Get the cumulative arc length of each point on each scratch : ； Where j represents the number of points on each scratch; The cumulative arc length of each point on each scratch is calculated by the following formula Perform normalization to obtain the normalized cumulative arc length of each point on each scratch : 。 3. The method for quickly removing scratches from a large-diameter optical element according to claim 2, characterized in that: In step S22, the normalized cumulative arc length of each point on each scratch is calculated by the following formula: The corresponding fitting position coordinates : ； in, , m represents the number of the B-spline control points, there are M+1 B-spline control points in total, p represents the B-spline order, represents the mth B-spline control point when fitting the kth scratch, represents the B-spline basis function of the m-th B-spline control point at the B-spline order p when fitting the k-th scratch; The position coordinates of the i-th point of the k-th scratch are calculated by the following formula: The corresponding fitting position coordinates The gap between E: ； Minimize the above formula to get the B-spline control point when fitting the k-th scratch .

4. The method for quickly removing scratches from a large-diameter optical element according to claim 3, characterized in that: In step S23, the B-spline knot vector u is: ； At this time, each scratch curve is obtained : 。 5. The method for quickly removing scratches from a large-diameter optical element according to claim 4, characterized in that: In step S24, each scratch curve is calculated The derivative of , and each scratch curve is obtained The tangent vector ,Right now: ； Find the tangent vector of each scratch The derivative of , and each scratch curve is obtained The normal vector ,Right now: ； Normal vector Normalize to get the normalized normal vector ,Right now: 。 6. The method for quickly removing scratches from a large-diameter optical element according to claim 5, characterized in that: In step S4, the surface error E0 is measured by an interferometer, and the large removal function magnetorheological polishing module is used to process a test piece made of the same material as the optical element to obtain a magnetorheological removal function RF; the residence time T is obtained by the following formula: ； in, Represents convolution calculation.

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