Method for determining parameters of grinding tool for accurate grinding and polishing of aspherical mirror

Abstract

The invention provides a method for determining parameters of an accurate grinding and polishing grinding tool for an aspherical mirror. The method comprises the following steps: acquiring a surface shape equation of the aspherical mirror; based on the surface shape equation, calculating the curvature radius of a plurality of points on the aspherical mirror, and taking the curvature radius as a first curvature radius; the curvature radius of the grinding tool is determined according to the minimum value of the first curvature radiuses of the multiple points and serves as a second curvature radius; wherein the second curvature radius is smaller than or equal to the minimum value in the first curvature radiuses; the contact condition of the grinding tool and the aspherical mirror is analyzed, and the polishing pad material type of the grinding tool is selected based on the contact condition. According to the method, the radius of the grinding tool is determined to be not greater than the minimum radius of curvature by calculating the radius of curvature of each point of the aspheric surface, so that the curvature of the grinding tool is matched with the aspheric surface, and interference is avoided during processing; by means of the method, the diameter of the grinding disc can be maximized and is two times of the minimum curvature radius, and the grinding efficiency can be greatly improved; the limitation of traditional experience dependence is broken through, and efficient aspheric surface machining can be guided.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of ultra-precision machining of optical parts, and particularly relates to a method for determining parameters of a non-spherical mirror fine grinding and polishing tool. BACKGROUND

[0002] Non-spherical optical elements play a core role in modern optical systems due to their advantages of "one-time forming" correction of multiple aberrations, and are widely used in fields such as aerospace remote sensing, deep space exploration, high-end microscopes, laser precision machining and the like. Compared with spherical elements, the surface shape of a non-spherical mirror is described by a high-order polynomial (such as a quadratic, cubic or even higher order term), and the curvature radius continuously changes with the position of the aperture, so the geometric characteristics are complex, and high requirements are put forward for the machining precision (especially the surface roughness Ra value and the surface shape precision PV value) and shape consistency. Among them, fine grinding and polishing, as the last key process in the manufacturing of non-spherical mirrors, directly determines the final optical performance, and in this stage, the relative movement between the tool and the workpiece is required to correct the surface shape errors remaining in the previous processes (such as coarse grinding and ultra-precision milling), and to achieve sub-micron or even nanometer level surface quality control. However, the reasonable determination of the tool parameters in the fine grinding and polishing process has always been a bottleneck problem restricting the machining efficiency and quality of non-spherical mirrors.

[0003] The core role of the fine grinding and polishing tool is to gradually converge the workpiece surface error to the target surface shape through a controllable material removal function. To match the complex surface shape of the non-spherical mirror, the tool needs to have the following characteristics: Surface shape adaptability: the curvature distribution of the tool needs to be coordinated with the gradient of the target surface shape of the non-spherical mirror (i.e. the change rate of the curvature radius at each aperture position), so as to avoid "over polishing" or "under polishing" caused by local contact stress concentration; multi-target balance ability: the tool needs to simultaneously satisfy the coordinated optimization of surface shape precision, surface roughness and machining efficiency, and the optimization of a single parameter may lead to the degradation of other indicators.

[0004] At present, the determination of the parameters of the fine grinding and polishing tool for non-spherical mirrors mainly relies on the experience trial and error method, simplified theoretical model and general process template, and there are significant limitations: The experience trial and error method is dominant, and the efficiency is low and the cost is high. In the traditional process, the selection of the curvature radius of the tool is mainly based on the experience of the operator or the historical data of similar parts. For new large-aperture and high-steepness non-spherical mirrors, the trial and error process may need to adjust the parameters multiple times and repeat the machining, resulting in material waste and cycle extension; the simplification of the theoretical model limits the precision. When selecting the curvature radius of the tool for the existing machining of a quadratic surface (such as a hyperboloid or a paraboloid), the traditional formula only considers the vertex curvature matching, but ignores the contact stress distortion caused by the curvature radius gradient in the edge area, which finally leads to the edge "collapse" or the center "bulge" error.

[0005] In view of the above problems, the method for determining the parameters of the fine grinding and polishing tool for aspheric mirrors needs to break through the limitations of traditional experience dependence and build a systematic method that takes into account theoretical accuracy, engineering practicability and multi-objective optimization to support efficient manufacturing of high-precision aspheric optical elements. SUMMARY

[0006] In view of the above defects or deficiencies in the prior art, the present application aims to provide a method for determining the parameters of a fine grinding and polishing tool for an aspheric mirror, comprising the following steps: Obtaining a surface equation of the aspheric mirror; Based on the surface equation, calculating the radii of curvature of a plurality of points on the aspheric mirror as first radii of curvature; Determining the radius of curvature of the tool according to the minimum value of the first radii of curvature of the plurality of points as a second radius of curvature; wherein the second radius of curvature is less than or equal to the minimum value of the first radii of curvature; Analyzing the contact condition of the tool and the aspheric mirror, and selecting the polishing pad material type of the tool based on the contact condition.

[0007] According to the technical scheme provided by the embodiments of the present application, after obtaining the surface equation of the aspheric mirror, the following steps are further included: Calculating the asphericity of the aspheric mirror, which is the deviation between the surface shape of the aspheric mirror and the surface shape of an approximate sphere.

[0008] According to the technical scheme provided by the embodiments of the present application, the calculation of the radii of curvature of a plurality of points on the aspheric mirror based on the surface equation comprises the following steps: If the asphericity is less than or equal to a first preset threshold, then the radii of curvature of a plurality of points on the aspheric mirror are calculated based on the surface equation.

[0009] According to the technical scheme provided by the embodiments of the present application, the surface equation of the aspheric mirror is obtained by the following formula:

[0010] wherein, , is the vertex radius, is the quadratic curve constant, are the coefficients of the fourth, sixth, eighth and tenth order terms, respectively.

[0011] According to the technical scheme provided by the embodiments of the present application, the calculation of the radii of curvature of a plurality of points on the aspheric mirror is specifically calculated by the following formula: ; Where z′ and z′′ are the first and second derivatives of the surface shape equation, respectively.

[0012] According to the technical solution provided in the embodiments of this application, before determining the radius of curvature of the grinding wheel, the following steps are also included: determining the aperture of the grinding wheel, wherein the aperture of the grinding wheel is 1 / 5 to 1 / 4 of the aperture of the aspherical mirror.

[0013] According to the technical solution provided in the embodiments of this application, the analysis of the contact between the grinding wheel and the aspherical mirror includes the following steps: Calculate the offset between the grinding wheel and the aspherical mirror at multiple points, where the offset is the height difference between the spherical surface of the grinding wheel and the surface shape of the aspherical mirror; The expression for the spherical surface of the grinding wheel is: ; Among them, R m X is the second radius of curvature. Pad Let X be the position of a point on the grinding wheel in an aspherical coordinate system. YuanXin and Z YuanXin These are the coordinates of the center of the mold ball.

[0014] According to the technical solution provided in the embodiments of this application, the formula for calculating the offset is: Where z(X_Pad) is the value of the surface equation at X_Pad.

[0015] According to the technical solution provided in the embodiments of this application, the step of selecting the polishing pad material type based on contact conditions includes the following steps: When the maximum value of the offset is less than or equal to the second preset threshold, a polyurethane polishing pad with an elastic deformation not less than the maximum value is selected.

[0016] According to the technical solution provided in the embodiments of this application, the first preset threshold is the surface deviation value corresponding to 0.1% to 0.5% of the aperture of the aspherical mirror.

[0017] Compared with the prior art, the beneficial effects of this application are as follows: This application determines that the radius of the grinding wheel is not greater than the minimum radius of curvature by calculating the radius of curvature at each point of the aspherical surface, thus ensuring the matching of the curvature of the grinding wheel with the aspherical surface and preventing interference during processing; moreover, this method can maximize the diameter of the grinding wheel, which is twice the minimum radius of curvature, thereby greatly improving grinding efficiency; through numerical calculation, it breaks through the limitations of traditional experience-based reliance and can guide the efficient processing of aspherical surfaces. Attached Figure Description

[0018] Fig. 1 A flowchart illustrating the steps of the method for determining the parameters of an aspherical mirror polishing tool provided in this application embodiment; Fig. 2 This is a diagram illustrating the contact analysis between the abrasive tool and the aspherical surface provided in an embodiment of this application. Detailed Implementation

[0019] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] Example 1 As mentioned in the background section, this application proposes a method for determining the parameters of an aspherical mirror fine grinding and polishing abrasive tool to address the problems in the prior art. Figs. 1-2 As shown, it includes the following steps: S1. Obtain the surface shape equation of the aspherical mirror; S2. Based on the surface shape equation, calculate the radius of curvature of multiple points on the aspherical mirror and use them as the first radius of curvature; S3. Determine the radius of curvature of the mold based on the minimum value among the first radii of curvature at multiple points, and use it as the second radius of curvature; wherein the second radius of curvature is less than or equal to the minimum value among the first radii of curvature; S4. Analyze the contact between the abrasive and the aspherical mirror, and select the polishing pad material type of the abrasive based on the contact.

[0022] Specifically, the first step is to obtain the surface shape equation of the aspherical mirror. This equation serves as the baseline for description and is typically determined during the optical design phase, provided as a dataset containing vertex curvature radius, conic constant, and higher-order coefficients. During implementation, operators can input these parameters into specialized optical processing software or numerical calculation programs (such as MATLAB or Python with NumPy) to create a digital model of the mirror.

[0023] Next, the procedure for calculating the radius of curvature at multiple points on the aspherical mirror based on the surface shape equation is implemented. Specifically, a series of discrete points need to be selected radially within the effective aperture of the mirror (e.g., selecting a point every 1 mm from the center to the edge). For each selected point coordinate x, the program will automatically calculate the first derivative z' (slope) and the second derivative z'' (curvature) of the surface shape equation z at that point, and substitute them into the standard differential geometry formula for the radius of curvature r = 1 / |z'' / (1 + z'²)^(3 / 2)| for calculation. The resulting series of radius of curvature values ​​is the "first radius of curvature," which accurately reflects the continuous change of curvature on the complex surface of the aspherical mirror.

[0024] Next, the step of determining the radius of curvature (second radius of curvature) of the grinding wheel based on the minimum first radius of curvature is implemented. The system iterates through all calculated first radius of curvature values ​​and finds the minimum value min(r). According to the core principle of this invention, the radius of curvature R_m of the grinding wheel (i.e., the second radius of curvature) should be set to be less than or equal to this minimum value. For example, R_m can be directly set to min(r). The physical meaning of this rule is to ensure that the curvature of the grinding wheel matches at least the most curved (smallest radius of curvature) area of ​​the mirror surface, thereby geometrically avoiding rigid interference between the grinding wheel and the most curved area when machining other areas. This is the basis for achieving uniform contact across the entire diameter.

[0025] Finally, the steps of analyzing the contact situation and selecting the polishing pad material are implemented. This step is completed through numerical simulation. The system virtually assembles the determined grinding wheel (considered as a spherical cap with radius R_m) with the aspherical mirror model in the software, and calculates the height difference (i.e., offset dev_m) between the grinding wheel surface and other positions on the mirror surface when the vertex of the grinding wheel is tangent to a point on the mirror surface. The distribution of these offsets is analyzed, especially their maximum values. This maximum value directly reflects the amount of elastic deformation required for a good fit between the grinding wheel and the mirror surface. Based on this analysis, the selection of polishing pad material can be scientifically guided: if the maximum offset is very small (e.g., on the micrometer scale), a harder pad material can be selected; if the offset is large (e.g., tens of micrometers), a soft polyurethane or other elastic material with a lower elastic modulus and stronger deformation capacity must be selected to ensure effective surface convergence and avoid scratches.

[0026] The underlying principle of this implementation is to transform the complex machining problem of aspherical mirrors into a numerical optimization problem based on a precise geometric model. Its core is the principle of "most stringent condition matching," which uses the minimum local radius of curvature on the mirror surface to constrain the curvature of the grinding wheel, fundamentally preventing physical interference. Furthermore, through contact mechanics analysis, the geometric deviation is transformed into requirements for the mechanical properties (elasticity) of the grinding wheel material, achieving a collaborative design between geometry and materials.

[0027] This implementation method changes the traditional trial-and-error approach that relies on experience. Its main advantages are: 1) High precision: Based on rigorous mathematical calculations, it ensures optimal matching between the mold substrate parameters and the mirror geometry, improving the control of surface accuracy (PV value) from the source. 2) High efficiency: It avoids repeated grinding and rework caused by improper parameters, significantly shortening the processing cycle. 3) Strong versatility: This process is not dependent on specific types of aspherical surfaces and is equally effective for complex surfaces such as high steepness and off-axis surfaces, providing universal and reliable technical support for the manufacturing of high-end optical components.

[0028] In a preferred embodiment, after obtaining the surface shape equation of the aspherical mirror, the following step is further included: Calculate the asphericity of the aspherical mirror, where the asphericity is the deviation between the surface shape of the aspherical mirror and the surface shape of an approximately spherical surface.

[0029] Specifically, after obtaining the surface shape equation z(x) of the aspherical mirror in the computer software, the program will automatically execute this additional step.

[0030] First, an "approximate sphere" needs to be determined. This approximate sphere is typically the sphere that best approximates the target aspherical surface given a certain aperture. In practice, the most common method is to choose the "best-fit sphere" that has the same height as the aspherical mirror at its vertices and edges. Its radius R_b (approximate spherical radius) can be obtained by substituting the coordinates of the aspherical edge points into the inverse equation of the sphere. Once the approximate spherical radius R_b is determined, its surface shape equation can be expressed. Next, the asphericity is calculated. The asphericity *dev* at each calculation point *x* is defined as the difference between the actual height of the aspheric surface *z(x)* and the approximate height of the sphere *z_sphere(x)*, i.e., *dev(x)* = *z(x)* - *z_sphere(x)*. The program iterates through all pre-selected discrete points, calculating a series of *dev* values. Finally, the overall asphericity of the aspheric mirror is typically characterized by the maximum absolute value of *dev* across all points, *Max|dev|. This value quantifies the degree to which the aspheric mirror deviates from the simplest sphere.

[0031] The principle of this implementation is relative measurement and benchmark comparison. By establishing a simple, well-known geometric benchmark (spherical surface), the characteristics of complex surface shapes (aspherical surfaces) are quantified. Asphericity itself does not directly participate in the core decision-making logic of weight 1, but it provides a macroscopic and intuitive process evaluation index. The main effect of adding this step is to enhance the predictability of process planning and assist decision-making. 1) Rapid assessment of processing difficulty: Asphericity Max|dev| is a very important priori indicator. The larger the value, the more "aspherical" the lens is, usually meaning higher processing difficulty and more process iterations required. This helps process engineers plan resources and time in advance. 2) Process route reference: For lenses with very small asphericity, the processing technology of spherical surfaces can sometimes be partially borrowed, while for lenses with large asphericity, the precise method provided by this invention must be strictly adopted. 3) Result verification: After processing, asphericity can also serve as an auxiliary reference for verifying the processing effect.

[0032] In a preferred embodiment, calculating the radius of curvature of multiple points on the aspherical mirror based on the surface shape equation includes the following steps: If the asphericity is less than or equal to a first preset threshold, then the radius of curvature of multiple points on the aspheric mirror is calculated based on the surface equation.

[0033] Specifically, after obtaining the surface shape equation, the system first calls the above method to calculate the asphericity (usually taking its maximum absolute value Max|dev and comparing it with a pre-set "first preset threshold"). The "first preset threshold" is an empirical value or a process specification value that defines the boundary of "slight asphericity". In practice, this threshold can be set according to factors such as lens diameter and precision requirements. For example, it can be set to a length value corresponding to a fraction of the lens diameter (such as 0.03% to 0.1%), or a fixed small deviation value (such as a few micrometers to tens of micrometers).

[0034] The judgment logic is as follows: If Max|dev ≤ the first preset threshold: This indicates that the aspherical mirror is very close to a sphere, and its "asphericity" is very weak. In this case, the system determines that the accurate calculation method provided by this invention is necessary and efficient, and then executes the subsequent steps of "calculating the radius of curvature at each point".

[0035] This embodiment optimizes the process decision-making to improve the economy and applicability of the method. 1) Avoiding resource waste: For workpieces extremely close to a spherical shape (with extremely small asphericity), blindly adopting complex full-aperture calculations may seem like "using a butcher's knife to kill a chicken". This step determines the value of using this method for such workpieces through judgment, ensuring the universality of the method. At the same time, it can also remind the operator that for truly strong aspherical surfaces, this method must be relied on and cannot be simplified. 2) Enhancing the robustness of the method: It makes the entire determination method not a rigid fixed process, but an intelligent system with preliminary self-judgment ability, capable of adapting to the processing requirements of different types of aspherical workpieces, reflecting the development direction of the intelligence of advanced manufacturing systems.

[0036] In a preferred embodiment, the surface equation of the aspherical mirror is obtained through the following formula:

[0037] Where, , is the vertex radius, is the conic constant, are the coefficients of the fourth-order, sixth-order, eighth-order, and tenth-order higher-order terms respectively.

[0038] Specifically, during implementation, the surface equation is given in a parametric form. The operator or system needs to obtain the following set of optical design parameters: Vertex curvature radius (R0): It represents the curvature radius of the aspherical surface at the optical center point (vertex). Its reciprocal c = 1 / R_0 is called the vertex curvature.

[0039] Conic constant (k): It determines the basic type of the aspherical surface. For example, k = 0 is a spherical surface, -1 < k < 0 is an ellipsoidal surface (the long axis is the optical axis), k = -1 is a parabolic surface, and k < -1 is a hyperbolic surface.

[0040] Higher-order term coefficients (A, B, C, D,...): These coefficients are used to describe the high-order surface shape deviations beyond the quadratic conic curve, enabling the equation to represent more complex aspherical surfaces. A is the fourth-order coefficient, B is the sixth-order coefficient, and so on. For some surface shapes, only A and B may be needed, while for others, C, D, or even higher-order terms may be required.

[0041] In the computer program, this equation is implemented as a function. When the radial coordinate x and the aforementioned parameter set {R0, k, A, B, C, D} are input, the function can calculate the axial height z of the corresponding point. This function is the absolute foundation for all subsequent differential calculations (finding the first and second derivatives to obtain the radius of curvature) and contact analysis (calculating the height difference). For example, when calculating the radius of curvature, the program uses symbolic or numerical differentiation methods to solve for z' and z'' based on this specific equation form.

[0042] In a preferred embodiment, the calculation of the radius of curvature at multiple points on the aspherical mirror is specifically performed using the following formula: ; Where z′ and z′′ are the first and second derivatives of the surface shape equation, respectively.

[0043] Specifically, numerical calculation of derivatives: Based on the surface equation z(x), numerical differentiation methods (such as the central difference method) are used to calculate the first derivative z′ and the second derivative z′′ at that point. For example, the first derivative z′≈[z(xi+h)-z(xi-h)] / (2h), and the second derivative z′′≈[z(xi+h)-2z(xi)+z(xi-h)] / h 2 Where h is a very small step size. For equations in the form of higher-order polynomials, symbolic differentiation can be performed directly to obtain the analytical expressions of z′ and z′′, which can then be substituted into xi for calculation, resulting in higher accuracy.

[0044] Looping Traversal: The system automatically repeats the steps for each point in the point set, eventually obtaining an array of "first radii of curvature" {r(x1), r(x2), ..., r(xn)} that corresponds one-to-one with the point set. This array precisely describes the continuous distribution of the radius of curvature on the aspherical mirror surface.

[0045] In a preferred embodiment, before determining the radius of curvature of the grinding wheel, the step further includes: determining the aperture of the grinding wheel, wherein the aperture of the grinding wheel is 1 / 5 to 1 / 4 of the aperture of the aspherical mirror.

[0046] Specifically, during implementation, after obtaining the curvature radius distribution data of the aspherical mirror through calculation, but before finally determining the curvature radius of the mold (second curvature radius), the operator or automated system needs to first determine the physical dimensions of the mold—diameter Dm.

[0047] The specific implementation is as follows: The effective aperture of the aspherical mirror to be processed, D_workpiece (e.g., 260mm), is known. The diameter Dm of the mold should be determined according to a proportional relationship, i.e., Dm = (1 / 5~1 / 4) × D_workpiece. For example, for a 260mm lens, the mold diameter should be selected between 52mm and 65mm. The implementer can choose a specific value within this range based on the specific processing efficiency requirements and surface convergence accuracy requirements. Generally, choosing a larger value (e.g., 1 / 4) is beneficial for improving processing efficiency, while choosing a smaller value (e.g., 1 / 5) is beneficial for controlling local areas and improving surface convergence accuracy.

[0048] This determination step is typically input through a human-machine interface or automatically set by the system based on a built-in process rule library. Once Dm is determined, it becomes an important boundary condition in subsequent contact analysis, as the analysis scope will be limited to the area covered by the mold diameter.

[0049] In a preferred embodiment, analyzing the contact between the abrasive tool and the aspherical mirror includes the following steps: Calculate the offset between the grinding wheel and the aspherical mirror at multiple points, where the offset is the height difference between the spherical surface of the grinding wheel and the surface shape of the aspherical mirror; The expression for the spherical surface of the grinding wheel is: ; Among them, R m X is the second radius of curvature. Pad Let X be the position of a point on the grinding wheel in an aspherical coordinate system. YuanXin and Z YuanXin These are the coordinates of the center of the mold ball.

[0050] Specifically, the geometric model of the grinding wheel is established: the working surface of the grinding wheel is idealized as a spherical cap. Its geometry is described by the equation of a sphere. To establish this equation, the coordinates (X, Y, X) of the center of the grinding wheel sphere must first be determined. YuanXin Z YuanXin This is achieved by setting a "tangency condition": that is, the vertex of the mold's spherical cap is tangent to a point (Xt, z(Xt)) on the aspherical mirror to be analyzed. According to geometric relationships, the center of the sphere must lie on the normal to that point, and the distance from the point of tangency is Rm. The program will automatically calculate and determine the coordinates of the sphere's center. Define the computational domain: within the range of the mold's diameter Dm, select a series of dense discrete points along the X-axis; the set of these points is the X-axis. Pad Calculate the height difference (offset): For each XPad point, calculate the mold surface height Z. Pad Substituting this into the equation for the sphere, we can calculate the actual height of the mirror z(X). Pad)Substituting this into the aspherical equation yields the result. The difference between the two is the offset devm at that point. This offset array accurately describes the gap distribution between the surface of the mold and the ideal aspherical surface, assuming the mold is a rigid body.

[0051] In a preferred embodiment, the formula for calculating the offset is: Where z(X_Pad) is the value of the surface equation at X_Pad.

[0052] In a preferred embodiment, selecting the polishing pad material type based on contact conditions includes the following steps: When the maximum value of the offset is less than or equal to the second preset threshold, a polyurethane polishing pad with an elastic deformation not less than the maximum value is selected.

[0053] Specifically, key parameters are determined as follows: The system first finds the maximum value `max(devm)` in the offset array. This value represents the maximum amount of elastic deformation that the polishing pad needs to compensate for to achieve the ideal contact state. Simultaneously, a "second preset threshold" is preset in the system or input by the operator. This threshold is a process tolerance, typically a small positive value (e.g., 0.005 mm or 5 micrometers), used to define an "acceptable, near-perfect initial contact state."

[0054] Execution of Judgment Logic: The system performs a judgment: if max(devm) ≤ the second preset threshold, it indicates that the geometric matching degree between the mold substrate and the aspherical mirror is already very high, and the required compensation amount is minimal or within an acceptable tolerance range. Material Selection Decision: When the above conditions are met, the system provides clear material selection guidance: select a polyurethane polishing pad with an elastic deformation not less than max(devm). In practice, this means: Quantitative Material Selection: Process engineers need to consult the technical data of the polyurethane polishing pad (such as its stress-strain curve or the elastic modulus and maximum allowable deformation provided by the manufacturer) and select models whose elastic deformation capacity can cover or exceed the calculated max(devm) value. Advantages of Polyurethane: The decision clearly indicates the selection of "polyurethane" material because polyurethane polishing pads are widely used in optical processing. Their elasticity, wear resistance, and surface properties can be controlled within a wide range through formulation and foaming processes, meeting the needs for deformation compensation from micrometer to sub-millimeter levels. This decision directly guides the workshop in preparing specific consumables, achieving a crucial leap from digital simulation to the physical world.

[0055] In a preferred embodiment, the first preset threshold is the surface deviation value corresponding to 0.1% to 0.5% of the aperture of the aspherical mirror.

[0056] Specifically, the first preset threshold is a length-dimension value used to determine whether the asphericity (Max|dev|) is small enough to confirm the necessity of subsequent fine calculations. The calculation threshold is based on the known effective diameter D of the aspherical lens (e.g., 260mm). The first preset threshold should be set to D × (0.1%~0.5%). That is, the lower limit of the calculation threshold is Thresholdmin = D × 0.001 and the upper limit is Thresholdmax = D × 0.005. Taking a 260mm diameter as an example, this threshold range is approximately 0.26mm to 1.3mm. In practical applications, the engineer can select a specific value within this range based on the actual situation. For example, for applications requiring extremely high precision, a stricter lower limit (e.g., 0.1% × D) can be chosen; for general applications or large-diameter lenses, a value closer to the upper limit (e.g., 0.5% × D) can be chosen to improve the applicability of the method.

[0057] This implementation provides clear process specifications: it offers an industry-acceptable, quantifiable standard for defining "slight asphericity," enabling different operators and factories to have a unified and repeatable judgment criterion when implementing this method, greatly enhancing the standardization and scalability of the method. It also optimizes process efficiency: this optimized range avoids threshold settings that are too stringent (causing all lenses to go through the entire process, reducing efficiency) or too lenient (causing lenses that should use this method to be incorrectly excluded, affecting accuracy). It ensures that subsequent relatively complex calculations are triggered only when the asphericity is "significant" to a certain degree, achieving a reasonable allocation of computational resources and optimization of process efficiency.

[0058] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. The above descriptions are only preferred embodiments of this application. It should be noted that due to the limitations of written expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of this invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of this application.

Claims

1. A method for determining the parameters of an aspherical mirror fine grinding and polishing abrasive, characterized in that, Includes the following steps: Obtain the surface shape equation of an aspherical mirror; Based on the surface shape equation, calculate the radius of curvature of multiple points on the aspherical mirror and use them as the first radius of curvature. The curvature radius of the mold is determined based on the minimum value among the first curvature radii at multiple points, and this value is used as the second curvature radius. Wherein the second radius of curvature is less than or equal to the minimum value among the first radii of curvature; Analyze the contact between the abrasive and the aspherical mirror, and select the polishing pad material type for the abrasive based on the contact condition.

2. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: After obtaining the surface shape equation of the aspherical mirror, the following steps are also included: Calculate the asphericity of the aspherical mirror, where the asphericity is the deviation between the surface shape of the aspherical mirror and the surface shape of an approximately spherical surface.

3. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: The calculation of the radius of curvature at multiple points on the aspherical mirror based on the surface shape equation includes the following steps: If the asphericity is less than or equal to a first preset threshold, then the radius of curvature of multiple points on the aspheric mirror is calculated based on the surface equation.

4. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: The surface shape equation of an aspherical mirror can be obtained using the following formula: in, , The vertex radius, The constant of the quadratic curve, These are the coefficients of the fourth, sixth, eighth, and tenth degree terms, respectively.

5. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: The radius of curvature at multiple points on the aspherical mirror is calculated using the following formula: ； Where z′ and z′′ are the first and second derivatives of the surface shape equation, respectively.

6. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: Before determining the radius of curvature of the grinding wheel, the method further includes the following step: determining the diameter of the grinding wheel, wherein the diameter of the grinding wheel is 1 / 5 to 1 / 4 of the diameter of the aspherical mirror.

7. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 1, characterized in that: The analysis of the contact between the abrasive tool and the aspherical mirror includes the following steps: Calculate the offset between the grinding wheel and the aspherical mirror at multiple points, where the offset is the height difference between the spherical surface of the grinding wheel and the surface shape of the aspherical mirror; The expression for the spherical surface of the grinding wheel is: ； Among them, R m X is the second radius of curvature. Pad Let X be the position of a point on the grinding wheel in an aspherical coordinate system. YuanXin and Z YuanXin These are the coordinates of the center of the mold ball.

8. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 7, characterized in that: The formula for calculating the offset is: Where z(X_Pad) is the value of the surface equation at X_Pad.

9. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 8, characterized in that: The selection of polishing pad material type based on contact conditions includes the following steps: When the maximum value of the offset is less than or equal to the second preset threshold, a polyurethane polishing pad with an elastic deformation not less than the maximum value is selected.

10. The method for determining the parameters of the aspherical mirror fine grinding and polishing abrasive according to claim 3, characterized in that: The first preset threshold is the surface deviation value corresponding to 0.1% to 0.5% of the aperture of the aspherical mirror.

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