Conformal ultra-smooth polishing method based on surface shape-velocity mapping

Abstract

The present application relates to the technical field of optical element ultra-precision machining, and particularly to a shape-velocity mapping based shape-preserving ultra-smooth polishing method, which comprises the following steps: obtaining initial surface shape and roughness data of an optical element to be polished; generating a velocity matrix associated with surface shape error distribution based on the initial surface shape data; and controlling a polishing tool to perform polishing according to the velocity matrix and the roughness data.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision machining technology for optical components, and specifically to a conformal ultra-smooth polishing method based on surface shape-velocity mapping. Background Technology

[0002] Modern high-performance optical systems place extremely stringent requirements on the surface accuracy and mid-to-high frequency surface roughness of optical components, with errors controlled at the atomic level across the entire frequency band. With the advent of the post-Moore's Law era, extreme ultraviolet (EUV) lithography projection lenses are a prime example, demanding that the surface error of each optical component from the full aperture to the millimeter scale, the mid-frequency roughness from the millimeter scale to the micrometer scale, and the high-frequency roughness from the micrometer scale to the nanometer scale be controlled within the order of ten picometers, achieving a dimensional accuracy ratio of 10. 9 Such stringent design requirements pose significant challenges to the manufacturing precision of the surface shape of optical components with ultra-high dimensional accuracy and the processing of ultra-smooth surfaces.

[0003] However, in the field of ultra-precision machining of optical components, there exists a "seesaw effect": when a certain machining method improves the accuracy of low-frequency surface features, the roughness of mid-to-high frequencies deteriorates; conversely, when another machining method reduces the roughness of mid-to-high frequencies, the surface features of low frequencies deteriorate. It is impossible to achieve convergence suppression across the entire low, mid, and high frequency bands using only one machining method. Therefore, in the field of modern ultra-precision machining of optical components, multiple machining techniques are often used in an iterative manner. However, this results in slower error convergence across the entire frequency band, reduced machining efficiency, and increased costs.

[0004] Taking ultra-smooth polishing technology as an example, ultra-smooth polishing, also known as smooth polishing, refers to using various types of polishing pads to uniformly or computer-controlledly traverse optical components, achieving a mid-to-high frequency roughness on the order of tens of picometers. However, during the uniform traversal process, due to the shape limitations of the polishing pad, the number of traversals at each point on the optical component is not consistent, with more traversals in the middle and fewer at the edges. After polishing, a deteriorated surface shape with a low center and high edges is formed, such as... Figure 15 , Figure 16 As shown.

[0005] In the 1970s, Itek Corporation in the United States proposed Computer-Controlled Optical Surface (CCOS) technology. This technology uses a deterministic small-particle removal function and an initial surface shape as input. Through deconvolution calculations, it obtains the dwell time of the small particle at each point on the optical surface, thereby achieving convergence of surface shape errors. The removal efficiency of the small particle is theoretically guided by the Preston equation, controlling the removal amount by controlling the relative movement speed and contact pressure between the small particle and the optical element. However, in the ultra-smooth polishing stage, using nanoscale abrasives or abrasive-free processing methods results in extremely low peak and volumetric removal amounts, making it difficult to obtain the removal function. Furthermore, during the polishing process, the removal function becomes uncertain due to the influence of temperature, humidity, pressure fluctuations, and polishing pad wear. The dwell time calculated based on the deterministic polishing assumption becomes inaccurate, leading to "uncertain polishing." Third, when deconvolution is performed between a removal function with extremely low volume removal and the initial surface shape of the optical element, areas with large removal amounts have long dwell times, far exceeding the time required for ultra-smooth polishing. This leads to excessively long processing times, making the polishing slurry more unstable and further increasing uncertainty, creating a vicious cycle. Areas with small removal amounts do not achieve effective ultra-smoothing, resulting in uneven distribution of the ultra-smooth effect. Fourth, for medium to large aperture (meter-level) optical elements, deconvolution calculations are time-consuming and memory-intensive, severely reducing polishing efficiency. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a conformal ultra-smooth polishing method based on surface-velocity mapping, aiming to solve the problems of difficult-to-obtain and easily changing removal functions, large computational load, and low processing efficiency in traditional CCOS.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention discloses a conformal ultra-smooth polishing method based on surface shape-velocity mapping, comprising:

[0009] Obtain the initial surface shape and roughness data of the optical element to be polished;

[0010] Based on the initial surface shape data, a velocity matrix associated with the surface shape error distribution is generated;

[0011] The polishing tool is controlled to perform the polishing process based on the velocity matrix and roughness data.

[0012] Furthermore, the polishing tool is controlled to perform the polishing process based on the speed matrix, specifically including:

[0013] Velocity compensation is applied to the velocity matrix at the edges of the polished area.

[0014] The polishing tool is controlled to perform the polishing process based on the compensated velocity matrix and roughness data.

[0015] Furthermore, the initial surface shape and roughness data of the optical element to be polished are obtained. The specific implementation process includes:

[0016] The initial surface shape data of the optical element to be polished is measured using a laser interferometer or profilometer, and its spatial wavelength range is less than or equal to the effective aperture of the optical element to be polished and greater than 1 mm.

[0017] The mid-frequency roughness of the optical element to be polished was measured using a white light interferometer, with a spatial wavelength range of less than or equal to 1 mm and greater than 1 μm.

[0018] The high-frequency roughness of the optical element to be polished was measured using an atomic force microscope, with a spatial wavelength range of less than or equal to 1 μm and greater than or equal to 10 nm.

[0019] Furthermore, based on the initial surface shape data, a velocity matrix associated with the surface shape error distribution is generated. The specific implementation process includes:

[0020] The initial surface shape data is resampled according to the preset machining step distance;

[0021] Normalization is performed on the resampled surface data to map the sag distribution to the [0,1] interval;

[0022] Based on the normalized surface shape, a velocity matrix is ​​generated according to the linear mapping principle, where the maximum sag is mapped to the preset minimum velocity Vmin, and the minimum sag is mapped to the preset maximum velocity Vmax.

[0023] Furthermore, the normalization process is achieved using the following formula:

[0024] Z norm =[Z rs -min(Z rs )] / [max(Z rs )-min(Z rs )];

[0025] Among them, Z norm For the normalized sag-elevation surface, Z rs For the resampled surface shape, min(Z) rs ) and max(Z rs ) are the minimum and maximum values ​​of the resampled surface, respectively.

[0026] Furthermore, the preset minimum speed Vmin is greater than or equal to 1 mm / s and less than or equal to 2 mm / s, and the preset maximum speed Vmax is greater than or equal to 3 mm / s and less than or equal to 5 mm / s.

[0027] Furthermore, the speed compensation is achieved through the following process:

[0028] Construct a compensation coefficient matrix W(i,j), where the compensation coefficient calculation method for each element is as follows:

[0029] W(i,j) = C, when d(i,j) ≥ L;

[0030] W(i,j) = 1 + (C - 1) * [d(i,j) - L1] / [L - L1], when L1 < d(i,j) < L;

[0031] W(i,j) = 1, when d(i,j) < L1;

[0032] Where, d(i,j) is the minimum distance from the element (i,j) in the speed matrix to the boundary of the polishing area, L1 is the starting distance of linear compensation, L is the complete compensation distance, C is the compensation coefficient, and i and j are positive integers;

[0033] The compensated speed matrix V_comp(i,j) is calculated by the following formula:

[0034] V_comp(i,j) = V(i,j) * W(i,j);

[0035] Where, V(i,j) is the initial speed matrix.

[0036] Furthermore, the polishing process specifically includes:

[0037] Select a polishing disc with a matching diameter according to the size of the area to be polished, and configure a polishing liquid with a predetermined concentration;

[0038] Control the polishing tool to move according to the compensated speed matrix to traverse the surface to be polished;

[0039] Preset the total number of traversals according to the medium and high frequency roughness level of the optical element to be polished.

[0040] Furthermore, the preset total number of traversals adopts an iterative polishing strategy, and the specific implementation process is as follows:

[0041] When the RMS value range of the initial surface shape of the optical element to be polished is greater than or equal to 1 nm and less than or equal to 10 nm, split the total number of traversals into multiple iterative executions, and perform 2 to 3 traversals in a single iteration;

[0042] After one iteration is completed, re-measure the surface shape. If the medium and high frequency roughness does not meet the preset requirements, use the current surface shape as the new initial surface shape, and repeat the conformal ultra-smooth polishing method until the preset requirements are met.

[0043] Furthermore, the polishing disc is a 73# asphalt disc with a diameter of 15% to 20% of the maximum side length of the area to be polished, and the asphalt thickness is greater than or equal to 3 mm and less than or equal to 5 mm; the polishing liquid is a nano-cerium oxide polishing liquid with an average particle diameter of greater than or equal to 100 nm and less than or equal to 200 nm, and a concentration of greater than or equal to 3% and less than or equal to 5%; during the polishing process, the rotation speed of the polishing disc is greater than or equal to 100 RPM and less than or equal to 200 RPM, and the applied pressure is greater than or equal to 5 N and less than or equal to 10 N.

[0044] The conformal ultra-smooth polishing method based on surface shape-velocity mapping described in this invention has the following advantages:

[0045] This invention proposes a direct control strategy based on "surface shape-velocity mapping." Using initial surface shape data, a velocity matrix associated with the surface shape error distribution is generated. Without any deconvolution calculations, the velocity control commands for the polishing tool can be directly and quickly generated from the initial surface shape. This significantly reduces the algorithm's complexity and computational resource requirements, shortens process preparation time, and avoids the risk of convergence failure due to calibration errors in the removal function or model mismatch. Attached Figure Description

[0046] Figure 1 This is one of the schematic diagrams of the conformal ultra-smooth polishing process based on surface shape-velocity mapping of the present invention;

[0047] Figure 2 This is the second schematic diagram of the conformal ultra-smooth polishing process based on surface shape-velocity mapping of the present invention;

[0048] Figure 3 This is the third schematic diagram of the conformal ultra-smooth polishing process based on surface shape-velocity mapping of the present invention;

[0049] Figure 4 This is a schematic diagram of the initial surface shape of the optical element to be polished according to the present invention;

[0050] Figure 5 This is a schematic diagram of the workpiece surface shape after resampling of the optical element to be polished according to the present invention;

[0051] Figure 6 This is a schematic diagram of the normalized resampling surface shape of the optical element to be polished according to the present invention;

[0052] Figure 7 This is a schematic diagram of the velocity mapping of the optical element to be polished according to the present invention;

[0053] Figure 8 This is a schematic diagram of the compensated velocity mapping of the optical element to be polished according to the present invention;

[0054] Figure 9This is a schematic diagram of the surface shape before conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0055] Figure 10 This is a schematic diagram of the surface shape after conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0056] Figure 11 This is a schematic diagram of the mid-frequency roughness before conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0057] Figure 12 This is a schematic diagram of the mid-frequency roughness after conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0058] Figure 13 This is a schematic diagram of high-frequency roughness before conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0059] Figure 14 This is a schematic diagram of high-frequency roughness after conformal ultra-smooth polishing based on surface shape-velocity mapping;

[0060] Figure 15 This is a schematic diagram of the surface shape before traditional ultra-smooth polishing;

[0061] Figure 16 This is a schematic diagram illustrating the deterioration of the surface shape after traditional ultra-smooth polishing. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0063] like Figures 1 to 14 As shown, this invention provides a conformal ultra-smooth polishing method based on surface shape-velocity mapping, comprising:

[0064] Obtain the initial surface shape and roughness data of the optical element to be polished;

[0065] Based on the initial surface shape data, a velocity matrix associated with the surface shape error distribution is generated;

[0066] The polishing tool is controlled to perform the polishing process based on the velocity matrix and roughness data.

[0067] This invention proposes a direct control strategy based on "surface shape-velocity mapping." Using an initial surface shape, a velocity matrix associated with the surface shape error distribution is generated. Without any deconvolution calculations, the velocity control commands for the polishing tool can be directly and quickly generated from the initial surface shape. This significantly reduces the algorithm's complexity and computational resource requirements, shortens process preparation time, and avoids the risk of convergence failure due to calibration errors in the removal function or model mismatch.

[0068] When using a disc polishing tool (such as an asphalt disc), if the disc polishing tool does not exceed the boundary of the workpiece, the number of times the edge of the component is traversed is less and the number of times the middle is traversed is more. This results in less material removal in the edge area of ​​the workpiece than in the center area, forming a deteriorated surface shape of "concave in the middle and high around the edges", which becomes a bottleneck restricting the surface shape convergence accuracy.

[0069] In this regard, such as Figure 2 As shown, this application controls the polishing tool to perform polishing processing based on a speed matrix, specifically including:

[0070] Velocity compensation is applied to the velocity matrix at the edges of the polished area.

[0071] The polishing tool is controlled to perform the polishing process based on the compensated velocity matrix and roughness data.

[0072] By introducing a spatial location-based compensation function, the preset velocity matrix is ​​modified only within the region affected by edge effects. In the central region, the dwell time is reduced by increasing the velocity, thus compensating for the increased material removal caused by excessive traversal.

[0073] Furthermore, the initial surface shape and roughness data of the optical element to be polished are obtained. The specific implementation process includes:

[0074] The initial surface shape data of the optical element to be polished is measured using a laser interferometer or profilometer, and its spatial wavelength range is less than or equal to the effective aperture of the optical element to be polished and greater than 1 mm.

[0075] The mid-frequency roughness of the optical element to be polished was measured using a white light interferometer, with a spatial wavelength range of less than or equal to 1 mm and greater than 1 μm.

[0076] The high-frequency roughness of the optical element to be polished was measured using an atomic force microscope, with a spatial wavelength range of less than or equal to 1 μm and greater than or equal to 10 nm.

[0077] The use of laser interferometers or profilometers to measure the initial surface shape data at the full aperture scale provides high-precision, full-aperture initial data input for subsequent surface shape-velocity mapping, which is the fundamental guarantee for achieving high-precision surface shape convergence.

[0078] By quantitatively monitoring the intermediate frequency error in the spatial wavelength range of less than or equal to 1 mm and greater than 1 μm using a white light interferometer, the process can suppress the ripple in this frequency band in a targeted manner, effectively reducing small-angle scattering caused by intermediate frequency error and improving the imaging contrast of the optical system.

[0079] By measuring the high-frequency roughness in the spatial wavelength range of less than or equal to 1 μm and greater than or equal to 10 nm using atomic force microscopy, the ultra-smooth surface effect pursued by this invention can be accurately characterized and verified, meeting the stringent requirements of high-end optical systems for extremely low scattering loss and high laser damage threshold.

[0080] Furthermore, such as Figure 3 As shown, based on the initial surface shape data, a velocity matrix associated with the surface shape error distribution is generated. The specific implementation process includes:

[0081] The initial surface shape data is resampled according to the preset machining step distance;

[0082] Normalization is performed on the resampled surface data to map the sag distribution to the [0,1] interval;

[0083] Based on the normalized surface shape, a velocity matrix is ​​generated according to the linear mapping principle, where the maximum sag is mapped to the preset minimum velocity Vmin, and the minimum sag is mapped to the preset maximum velocity Vmax.

[0084] The speed mapping strategy of "fast movement at low points and slow movement at high points," where "the point of maximum sag is mapped to Vmin (slow movement) and the point of minimum sag is mapped to Vmax (fast movement)," guarantees conformal convergence. This ensures that: at the "high points" on the normalized resampled surface, where a large amount of material needs to be removed, the speed is reduced to increase dwell time, achieving "more removal"; conversely, at the "low points" on the normalized resampled surface, where material needs to be retained, the speed is increased to reduce dwell time, achieving "less removal."

[0085] Furthermore, the specific resampling process is as follows:

[0086] (1) Define the polishing path and machining step distance: Based on the shape and size of the component to be polished, generate the motion trajectory of the polishing tool (such as a raster path) on the computer. At the same time, set a reasonable machining step distance according to the above principles.

[0087] (2) Generate resampling points: Along the defined polishing path, generate a series of dense and uniform path points P(i,j) at intervals of processing steps. These points are the new locations where surface profile elevation values ​​need to be assigned.

[0088] (3) Data interpolation calculation: For each newly generated path point P(i,j), there is no initial measurement value. Therefore, it is necessary to estimate the sag value Z(i,j) of the point by means of mathematical interpolation algorithm based on the surface data of the original measurement grid points around it.

[0089] Commonly used interpolation algorithms include:

[0090] Bilinear interpolation: It has high computational efficiency and can meet most accuracy requirements.

[0091] Bicubic interpolation: provides smoother and more accurate interpolation results, better preserving the smoothness of the surface shape.

[0092] (4) Output resampled data: Combine all path points P(i,j) and their corresponding interpolated sag values ​​Z(i,j) into a new, regular dataset. This dataset is the resampled surface data, which achieves a one-to-one precise match with the actual polishing path.

[0093] By employing resampling processing, each control point in the polishing process is based on precise surface shape information, achieving digital control. Through rational setting of the machining step distance, effective control and correction of surface shape errors are ensured. While maintaining accuracy, excessive data density is avoided, thus optimizing processing efficiency.

[0094] Furthermore, the normalization process is achieved using the following formula:

[0095] Z norm =[Z rs -min(Z rs )] / [max(Z rs )-min(Z rs )];

[0096] Among them, Z norm For the normalized sag-elevation surface, Z rs For the resampled surface shape, min(Z) rs ) and max(Z rs ) are the minimum and maximum values ​​of the resampled surface, respectively.

[0097] By using a normalization formula, complex surface data is uniformly mapped to the [0,1] interval, establishing a stable and reliable mathematical foundation for subsequent linear velocity mapping and ensuring the accuracy and universality of velocity calculation.

[0098] Furthermore, the preset minimum speed Vmin is greater than or equal to 1 mm / s and less than or equal to 2 mm / s, and the preset maximum speed Vmax is greater than or equal to 3 mm / s and less than or equal to 5 mm / s.

[0099] Furthermore, speed compensation is achieved through the following process:

[0100] Construct the compensation coefficient matrix W(i,j), where the compensation coefficient of each element is calculated as follows:

[0101] W(i,j)=C, when d(i,j)≥L;

[0102] W(i,j)=1+(C - 1)*[d(i,j)-L1] / [L - L1] when L1 < d(i,j) < L;

[0103] W(i,j)=1 when d(i,j) < L1;

[0104] Where, d(i,j) is the minimum distance from the element (i,j) in the velocity matrix to the boundary of the polishing area, L1 is the starting distance of linear compensation, L is the complete compensation distance, C is the compensation coefficient, and i and j are positive integers;

[0105] The compensated velocity matrix V_comp(i,j) is calculated by the following formula:

[0106] V_comp(i,j)=V(i,j)*W(i,j);

[0107] Where, V(i,j) is the initial velocity matrix.

[0108] A specially designed edge velocity compensation model forms a smooth transition velocity field by constructing a distance-based compensation coefficient matrix, effectively avoiding the introduction of new annular errors on the surface shape due to improper compensation. On the basis of shape control, combined with optimized ultra-smooth process parameters, an atomic-level ultra-smooth surface is directly achieved on a high-precision surface shape. Thus, in one process, the effective convergence and optimization of low-frequency, medium-frequency, and high-frequency full-band errors are synchronously realized, solving the "edge effect" problem of disk polishing, increasing the polishing speed in the central area, and compensating for the problem of low edge removal efficiency caused by uneven traversal times of the polishing disk. Through the velocity mapping strategy of "fast walking at low points and slow walking at high points", the "quasi-deterministic" control of the material removal amount is achieved, and the low-frequency surface shape error is actively corrected and converged to extremely high precision.

[0109] Furthermore, the polishing process specifically includes:

[0110] Select a polishing disk with a diameter matching the size of the area to be polished, and configure the polishing liquid with a predetermined concentration;

[0111] Control the polishing tool to move according to the compensated velocity matrix to traverse the surface to be polished;

[0112] Preset the total number of traversals according to the medium-high frequency roughness level of the optical element to be polished.

[0113] Specifically: when the high-frequency roughness RMS is between 1 and 2 nm, the total number of traversals is about 20 - 25 times; when the high-frequency roughness RMS is between 0.5 - 1 nm, the total number of traversals is about 10 - 20 times.

[0114] The core control parameters for ultra-smooth polishing were clarified: the direct correlation between the number of traversals and the roughness at medium and high frequencies was pointed out, providing a key and clear process control dimension for achieving ultra-smooth surfaces.

[0115] Furthermore, the preset total number of traversals adopts an iterative polishing strategy, specifically as follows:

[0116] When the RMS value of the initial surface shape of the optical element to be polished is in the range of 1nm to 10nm, the total number of traversals is divided into multiple iterations, with each iteration performing 2 to 3 traversals.

[0117] After one iteration, the surface shape is remeasured. If the mid-to-high frequency roughness does not meet the preset requirements, the current surface shape is used as the new initial surface shape, and the conformal ultra-smooth polishing method is repeated until the preset requirements are met.

[0118] By employing an iterative strategy of "measurement-calculation-processing-remeasurement," an intelligent feedback closed loop is formed, which can adaptively approach the final processing target, effectively avoiding the risks caused by single-stage over-polishing or under-polishing, and realizing intelligent closed-loop control of the processing process. Especially for high-precision components with small initial surface RMS values ​​(1nm-10nm), the iterative strategy is adopted to greatly improve the success rate of final processing and the stability of surface convergence.

[0119] Furthermore, the polishing disc is a 73# asphalt disc with a diameter of 15% to 20% of the maximum side length of the area to be polished, and the asphalt thickness is greater than or equal to 3 mm and less than or equal to 5 mm; the polishing liquid is a nano-cerium oxide polishing liquid with an average particle diameter of greater than or equal to 100 nm and less than or equal to 200 nm and a concentration of 3% to 5%; during the polishing process, the rotation speed of the polishing disc is greater than or equal to 100 RPM and less than or equal to 200 RPM, and the applied pressure is greater than or equal to 5 N and less than or equal to 10 N.

[0120] The optimal process window for achieving ultra-smooth surfaces is provided: by limiting a series of specific parameters such as asphalt grade, disk size, polishing fluid concentration and particle size, rotation speed and pressure, the optimal process combination for achieving atomically smooth surfaces is determined, ensuring that the method can stably and reliably reproduce the ultra-smooth effect in specific implementation.

[0121] For large optical components with meter-level apertures, traditional CCOS technology suffers from problems such as difficulty in calculating dwell time and uneven ultra-smooth polishing results. This invention, combined with its direct and efficient speed control algorithm, can efficiently maintain or even converge the surface accuracy of large-aperture components while performing ultra-smooth polishing, thereby shortening the ultra-smooth processing cycle of large-aperture optical components from months or even years to weeks, demonstrating significant engineering application value.

[0122] This invention achieves ultra-smooth processing at low cost and high efficiency: Compared with expensive equipment such as ion beams and magnetorheology, this embodiment is based on the classic asphalt polishing process and achieves the same precision processing effect through parameter optimization and algorithm control, which has extremely high cost performance and promotion value.

[0123] The core framework of "surface shape-velocity mapping" and "edge compensation" proposed in this invention is a universal control platform that does not depend on specific polishing physicochemical processes. Therefore, it can not only be combined with classic asphalt polishing, but in other embodiments, after calculating the velocity, the choice of polishing tool is not limited to an asphalt polishing pad; it can also be integrated with emerging ultra-smooth surface preparation technologies such as catalytic reference etching, bio-enzyme-assisted polishing, and hydrodynamic polishing. By simply adjusting the velocity mapping parameters (Vmax, Vmin) and compensation parameters (C, L, L1) according to the removal function characteristics of the specific technology, conformal ultra-smooth polishing can be achieved. This strong universality allows this invention to adapt to the future development of ultra-smooth technologies, possessing a long lifespan and promising application prospects.

[0124] Preferably, the maximum speed Vmax of the polishing disc is set to 5 mm / s, the minimum speed Vmin is set to 2 mm / s, the compensation coefficient C is set to 1.2, the diameter of the asphalt disc is set to 15 mm, the asphalt thickness is set to 4 mm, the asphalt grade is set to 73#, the average diameter of the cerium oxide particles is set to 200 nm, the concentration is set to 5%, the rotation speed of the asphalt disc is set to 150 RPM, the pressure is set to 10 N, and the number of passes is set to 20.

[0125] Based on the above method, experiments were conducted on ULE-7973 glass with an effective diameter of 66mm × 24mm. The surface shape before ultra-smooth polishing was as follows: Figure 9 As shown, the mid-frequency roughness is as follows Figure 11 As shown, high-frequency roughness is as follows Figure 13 As shown, the polished surface shape is as follows Figure 10 As shown, the mid-frequency roughness is as follows Figure 12 As shown, high-frequency roughness is as follows Figure 14 As shown, the roughness at mid-to-high frequencies reached atomic precision, and convergence was achieved across the entire frequency band.

[0126] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A shape-preserving super-smooth polishing method based on a shape-velocity mapping, characterized by, The method comprises the following steps: Obtaining initial surface shape and roughness data of an optical element to be polished; Based on the initial surface shape data, a speed matrix associated with the surface shape error distribution is generated, which includes the following steps: Resampling the initial surface shape data according to a preset machining step distance; Based on the resampled surface shape data, normalization is performed to map the height distribution to the interval [0, 1], wherein the normalization is realized by the following formula: Z norm =[Z rs -min(Z rs )] / [max(Z rs )-min(Z rs )]; wherein Z norm is the normalized height surface, Z rs is the resampled surface, min(Z rs ) and max(Z rs ) are the minimum and maximum values of the resampled surface, respectively. Based on the normalized surface shape, a speed matrix is generated according to the linear mapping principle, wherein the maximum height mapping is the preset minimum speed Vmin, and the minimum height mapping is the preset maximum speed Vmax; According to the speed matrix and the roughness data, the polishing tool is controlled to perform polishing, which includes the following steps: Speed compensation is performed on the edge of the polishing area in the speed matrix, and the speed compensation is realized by the following process: A compensation coefficient matrix W(i,j) is constructed, wherein the compensation coefficient of each element is calculated as follows: W(i,j)=C, when d(i,j)≥L; W(i,j)=1+(C-1)*[d(i,j)-L1] / [L-L1], when L1<d(i,j)<L; W(i,j)=1, when d(i,j)<L1; Where d(i,j) is the minimum distance from element (i,j) in the speed matrix to the boundary of the polishing area, L1 is the linear compensation start distance, L is the full compensation distance, C is the compensation coefficient, and i and j are positive integers; The compensated speed matrix V_comp(i,j) is calculated by the following formula: V_comp(i,j)=V(i,j)*W(i,j); Where V(i,j) is the initial speed matrix; According to the compensated speed matrix and the roughness data, the polishing tool is controlled to perform polishing.

2. The shape-from-appearance based conformality ultra-smooth polishing method according to claim 1, wherein, Obtaining initial surface shape and roughness data of an optical element to be polished, which includes the following steps: The initial surface shape data of the optical element to be polished is measured by a laser interferometer or a profilometer, and the spatial wavelength range is less than or equal to the effective aperture of the optical element to be polished and greater than 1mm; The medium frequency roughness of the optical element to be polished is measured by a white light interferometer, and the spatial wavelength range is less than or equal to 1mm and greater than 1μm; The high frequency roughness of the optical element to be polished is measured by an atomic force microscope, and the spatial wavelength range is less than or equal to 1μm and greater than or equal to 10nm.

3. The shape-from-velocity mapping based conformality ultra-smooth polishing method according to claim 1, wherein, The preset minimum speed Vmin is greater than or equal to 1mm / s and less than or equal to 2mm / s, and the preset maximum speed Vmax is greater than or equal to 3mm / s and less than or equal to 5mm / s.

4. The shape-from-velocity mapping based conformality ultra-smooth polishing method of claim 1, wherein, Polishing, which includes the following steps: According to the size of the polishing area, a polishing disc with matching diameter is selected, and a polishing liquid with a predetermined concentration is configured; The polishing tool is controlled to move according to the compensated speed matrix to traverse the surface to be polished; According to the medium and high frequency roughness level of the optical element to be polished, the total traversal number is preset.

5. The shape-from-velocity mapping based conformality ultra-smooth polishing method according to claim 4, wherein, The preset total traversal number adopts an iterative polishing strategy, and the implementation process is as follows: When the RMS value of the initial surface shape of the optical element to be polished is greater than or equal to 1nm and less than or equal to 10nm, the total traversal number is divided into multiple iterations, and each iteration is performed 2 to 3 times. After one iteration is completed, the surface shape is re-measured, if the medium-high frequency roughness does not reach the preset requirement, the current surface shape is taken as a new initial surface shape, the conformal super-smooth polishing method is repeatedly executed until the preset requirement is reached.

6. The shape-from-velocity mapping based conformality ultra-smooth polishing method according to claim 4, wherein, The polishing disc is a 73# pitch disc, the diameter of which is 15%-20% of the maximum side length of the area to be polished, and the pitch thickness is greater than or equal to 3 mm and less than or equal to 5 mm; the polishing liquid is a nano cerium oxide polishing liquid, the average particle diameter of which is greater than or equal to 100 nm and less than or equal to 200 nm, and the concentration of which is greater than or equal to 3% and less than or equal to 5%; during the polishing process, the rotating speed of the polishing disc is greater than or equal to 100 RPM and less than or equal to 200 RPM, and the applied pressure is greater than or equal to 5 N and less than or equal to 10 N.

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