A random polishing path planning method for an optical element

Abstract

The application discloses a random polishing path planning method of an optical element, and the polishing surface of the optical element is regarded as a continuous probability space, a large number of randomly distributed sampling points (input vectors) are generated in a target area, and a self-organizing mapping network (SOM) with a one-dimensional closed loop topological structure is used to carry out manifold fitting on the random points. The application solves the technical pain point that the coverage is uneven in the processing of irregular edges in the traditional path, and realizes truly full-aperture high-consistency processing.

Description

Technical Field

[0001] This invention relates to the field of optical element manufacturing, specifically a method for planning random polishing paths for optical elements. Background Technology

[0002] In the manufacturing of high-precision optical components, traditional polishing processes typically employ deterministic motion trajectories such as raster paths, spiral paths, or circular paths. However, these traditional paths exhibit extremely high geometric regularity and periodicity in their spatial distribution, resulting in a constant spatial frequency in the removal trajectory formed by the polishing tool on the component surface. During processing, the repeated superposition of the tool influence function (TIF) causes minute fluctuations in the removal amount to accumulate linearly within a specific frequency band, inducing significant mid-frequency errors (MSFerrors) on the component surface, manifesting as visible "stripes" or "ring-like" textures. Furthermore, the velocity fluctuations at edge turning points of the deterministic path and the constant step size between adjacent trajectories easily lead to sudden characteristic peaks in the frequency domain energy spectrum. This structured surface morphology deterioration not only severely reduces the coherence and imaging quality of the optical system but is also extremely difficult to eliminate using conventional methods in subsequent processes, becoming a core technical bottleneck limiting the improvement of the physical limits of large-aperture, ultra-smooth optical component surfaces. Summary of the Invention

[0003] The purpose of this invention is to provide a method for planning random polishing paths for optical elements, comprising the following steps:

[0004] Step 1. Define according to the polishing precision requirements. There are 10 neuron nodes; these neuron nodes form a one-dimensional closed-loop topology.

[0005] Step 2. Initialize the weight vector for each neuron. ,in ; This represents the x and y coordinates of the initial position of the j-th neuron in the optical element coordinate system;

[0006] Step 3. In the t-th iteration, generate a random input vector. , to characterize the random coordinate points of the location to be processed on the surface of the optical element;

[0007] Step 4. For each random input By competing to find the random input The neuron with the closest geometric distance is selected as the guide point for the current path.

[0008] Step 5. Calculate the current path guide point and the neurons in the neighborhood of the current path guide point to the random input. The intensity of movement;

[0009] Step 6. Based on the current path guide point and the neurons in the neighborhood of the current path guide point, input the random input. The intensity of the movement is used to update the weight vector;

[0010] Step 7. Determine if the iteration termination condition is met. If yes, proceed to step 8; otherwise, let t = t + 1 and return to step 3.

[0011] Step 8. Transform the weight vector sequence Join in index order and let connect and A pseudo-random closed-loop polishing trajectory is generated.

[0012] further, The neurons are arranged on a one-dimensional chain, with the first neuron logically adjacent to the Nth neuron, forming a closed loop.

[0013] Furthermore, generate random input vectors. At that time, the sampling of the position to be processed on the surface of the optical element is carried out in a uniform distribution manner or based on the importance sampling according to the initial error distribution of the element surface shape; the larger the initial error of the element surface shape, the more sampling points are required.

[0014] Furthermore, the current path guidance point is shown below:

[0015]

[0016] in, It is the neuron index that is closest to the random sampling point in Euclidean space.

[0017] Furthermore, the current path guide point, and neurons in its neighborhood, input random input. The intensity of the movement is shown below:

[0018]

[0019] in, The neighborhood radius decays exponentially with the number of iterations; For any number The topological distance between each neuron and the current path guide point.

[0020] Furthermore, any number Each neuron and the current path guide point Topological distance between As shown below:

[0021]

[0022] In the formula, This represents the number of neuron nodes.

[0023] Furthermore, the neighborhood radius, which decays exponentially with the number of iterations, is shown below:

[0024]

[0025] In the formula, The initial neighborhood radius; This is a constant representing the total number of iterations.

[0026] Furthermore, the weights are updated as follows:

[0027]

[0028] in, The learning rate decays over time.

[0029] Furthermore, the learning rate decays over time. As shown below:

[0030]

[0031] in The total number of iterations is a constant; This is the initial learning rate.

[0032] Furthermore, when generating pseudo-random closed-loop polishing trajectories, spline curves or circular interpolation algorithms are used to smooth the discrete points.

[0033] The technical effects of this invention are undeniable, and its beneficial effects are as follows:

[0034] 1) Frequency domain characteristic enhancement: Achieving frequency domain decoherence of the machining trajectory.

[0035] Traditional polishing paths (such as gratings and spirals) exhibit strong energy concentration in the frequency domain, manifested as significant characteristic peaks on the power spectral density (PSD) curve, which is the root cause of intermediate frequency (MSF) errors. This invention utilizes the random sampling driving mechanism of SOM to transform a defined periodic trajectory into a statistically isotropic pseudo-random trajectory. This transforms the polishing removal marks from narrow-band characteristic peaks in the frequency domain into a broadband white noise-like distribution, significantly reducing the peak value of the PSD curve and suppressing the generation of mid-frequency textures (stripes or rings) at their source.

[0036] 2) Kinematic advantages: Zero acceleration mutation control based on closed-loop topology

[0037] Traditional pseudo-random paths (such as Peano curves or random walks) often have numerous sharp turns or fixed start / end points. This invention innovatively introduces closed-loop annular topology constraints. This ensures the path is connected end-to-end and possesses first / second-order continuity, eliminating tool lifting, reversal, and pauses during the polishing process. This not only protects the dynamic lifespan of the machine tool feed system but also corrects local removal deviations caused by sudden changes in motion speed, ensuring precise control of the entire dwell time.

[0038] 3) Geometric adaptability: Self-organizing and adapting morphology across the entire aperture range.

[0039] Optical components often have different aperture sizes (such as circular, rectangular, annular, or even freeform projection surfaces). The SOM algorithm has extremely strong topology preservation and mapping capabilities, and can automatically grow and uniformly fill paths according to arbitrarily complex component boundaries without the need for complex boundary logic judgments. This solves the technical pain point of uneven coverage in the processing of irregular edges in traditional paths, and achieves truly full-aperture high-consistency processing.

[0040] 4) Parameter adjustability: Multi-scale collaborative optimization of path smoothness and uniformity

[0041] By adjusting the neighborhood function radius (σ) and learning rate (η) in the mathematical model, this invention can precisely control the curvature and coverage density of the path. It allows process engineers to dynamically adjust the roughness and smoothness of the path based on the specific distribution of wavefront errors in the optical components. This flexibility enables the invention to both suppress mid-frequency errors through full-field scanning and self-organize the path density based on the initial surface error map, achieving efficient low-frequency surface correction.

[0042] 5) Robustness and low redundancy: Manifold evolution mechanism without self-crossing

[0043] Purely random paths are prone to self-intersections, leading to local over-polishing. The local neighborhood positive feedback mechanism of SOM ensures that the neuron sequence performs its function in spatial evolution. This not only guarantees the statistical randomness of the path but also avoids frequent self-intersections by utilizing topological constraints at the algorithmic level. This greatly reduces the redundancy of the processing path and improves the convergence efficiency. Attached Figure Description

[0044] Figure 1 This is a flowchart of the random polishing path planning method for optical elements according to the present invention;

[0045] Figures 2-4 This is a schematic diagram of the random polishing path planning and generation process of the present invention;

[0046] Figure 5A schematic diagram showing the random polishing path planning for rectangular optical elements adapted to this invention;

[0047] Figure 6 This is a schematic diagram showing the random polishing path planning generated for the circular optical element adapted to this invention. Detailed Implementation

[0048] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0049] Example 1:

[0050] See Figures 1 to 6 A method for planning random polishing paths for optical elements, comprising the following steps:

[0051] Step 1. Define according to the polishing precision requirements. There are 10 neuron nodes; these neuron nodes form a one-dimensional closed-loop topology.

[0052] Step 2. Initialize the weight vector for each neuron. ,in ; This represents the x and y coordinates of the initial position of the j-th neuron in the optical element coordinate system;

[0053] Step 3. In the t-th iteration, generate a random input vector. , to characterize the random coordinate points of the location to be processed on the surface of the optical element;

[0054] Step 4. For each random input By competing to find the random input The neuron with the closest geometric distance is selected as the guide point for the current path.

[0055] Step 5. Calculate the current path guide point and the neurons in the neighborhood of the current path guide point to the random input. The intensity of movement;

[0056] Step 6. Based on the current path guide point and the neurons in the neighborhood of the current path guide point, input the random input. The intensity of the movement is used to update the weight vector;

[0057] Step 7. Determine if the iteration termination condition is met. If yes, proceed to step 8; otherwise, let t = t + 1 and return to step 3.

[0058] Step 8. Transform the weight vector sequence Join in index order and let connect and A pseudo-random closed-loop polishing trajectory is generated.

[0059] Example 2:

[0060] A method for planning random polishing paths for optical elements, with the same technical content as in Embodiment 1, further... The neurons are arranged on a one-dimensional chain, with the first neuron logically adjacent to the Nth neuron, forming a closed loop.

[0061] Example 3:

[0062] A method for planning random polishing paths for optical elements, with the same technical content as any one of embodiments 1-2, further comprising generating random input vectors. At that time, the sampling of the position to be processed on the surface of the optical element is carried out in a uniform distribution manner or based on the importance sampling according to the initial error distribution of the element surface shape; the larger the initial error of the element surface shape, the more sampling points are required.

[0063] For high-precision optical components such as plane mirrors, spherical mirrors, and aspherical mirrors, laser interferometers are generally used for surface shape inspection. The inspection results are usually presented as a two-dimensional surface shape error map. For some aspherical, freeform surfaces, or large-aperture components, surface height data can also be obtained using contact or non-contact profilometers, coordinate measuring machines, laser displacement sensors, etc. For large-aperture optical components, if the aperture is insufficient for a single inspection, a sub-aperture stitching interferometry method can be used. This method stitches together multiple local inspection areas to form a surface shape error map of the complete aperture, and is suitable for large-aperture reflectors, off-axis aspherical surfaces, and other components.

[0064] Example 4:

[0065] A method for planning a random polishing path for an optical element, with the same technical content as any one of embodiments 1-3, further wherein the current path guiding point is as follows:

[0066]

[0067] in, It is the neuron index that is closest to the random sampling point in Euclidean space.

[0068] Example 5:

[0069] A method for planning a random polishing path for an optical element, with the same technical content as any one of embodiments 1-4, further comprising: the current path guiding point, and neurons in the neighborhood of the current path guiding point, feeding random input... The intensity of the movement is shown below:

[0070]

[0071] in, The neighborhood radius decays exponentially with the number of iterations; For any number The topological distance between each neuron and the current path guide point.

[0072] Example 6:

[0073] A method for planning random polishing paths for optical elements, with the same technical content as any one of embodiments 1-5, further wherein any... Each neuron and the current path guide point Topological distance between As shown below:

[0074]

[0075] In the formula, This represents the number of neuron nodes.

[0076] Example 7:

[0077] A method for planning random polishing paths for optical elements, with the same technical content as any one of embodiments 1-6, further wherein the neighborhood radius, which decays exponentially with the number of iterations, is shown below:

[0078]

[0079] In the formula, The initial neighborhood radius; This is a constant representing the total number of iterations.

[0080] Example 8:

[0081] A method for planning random polishing paths for optical elements, with the same technical content as any one of embodiments 1-7, further with the following weight updates:

[0082]

[0083] in, The learning rate decays over time.

[0084] Example 9:

[0085] A method for planning random polishing paths for optical elements, with the same technical content as any one of embodiments 1-8, further comprising a learning rate that decays over time. As shown below:

[0086]

[0087] in The total number of iterations is a constant; This is the initial learning rate.

[0088] Example 10:

[0089] A method for planning a random polishing path for an optical element, with the same technical content as any one of embodiments 1-9, further comprising: when generating a pseudo-random closed-loop polishing trajectory, using a spline curve or circular arc interpolation algorithm to smooth the discrete points.

[0090] Example 11:

[0091] A method for planning a random polishing path for an optical element, with the same technical content as any one of embodiments 1-10, further wherein reaching the iteration termination condition means satisfying any one of the following conditions: reaching the maximum number of iterations, the change in the neuron weight vector being less than a preset threshold, the change in the path length being less than a preset threshold, the path coverage reaching a preset requirement, or the learning rate or neighborhood radius decaying to a preset lower limit.

[0092] Example 12:

[0093] A method for planning random polishing paths for optical components, as described below:

[0094] This invention treats the polished surface of an optical element as a continuous probability space. By generating a large number of randomly distributed sampling points (input vectors) within the target area, a one-dimensional closed-loop topological self-organizing map (SOM) network is used to fit the manifold of these random points.

[0095] Unlike the forced determinism of traditional gratings or spiral paths, the trajectory generated by this scheme breaks the periodicity at the local scale through random sampling, thereby achieving decoherence in the frequency domain; while at the global scale, through the topology preservation property of SOM, a smooth, non-intersecting and end-to-end closed-loop path is constrained to form, thereby meeting the machine tool dynamics requirements and suppressing edge effects.

[0096] This invention employs a single-layer one-dimensional SOM neural network with a ring neighborhood structure:

[0097] 1. Neuron arrangement: N neurons are arranged on a one-dimensional chain, and the first neuron is logically adjacent to the Nth neuron, forming a closed loop.

[0098] 2. Weight Evolution: The weight vector of each neuron This represents the physical position of the polishing tool in the component coordinate system.

[0099] 3. Competitive learning: A point v is randomly sampled from the polished region, attracting the nearest neuron on the circular chain and its neighboring neurons to move towards it.

[0100] 4. Dynamic convergence: As iterations proceed, the learning rate and neighborhood radius gradually decrease, and the disordered neuron loops gradually stretch and smooth out, eventually covering the entire processing surface and forming a pseudo-random closed-loop trajectory.

[0101] The technical solution described in this invention ensures the continuity of the processing through the closed-loop topological constraint of the SOM (Self-Organizing Machine), eliminating the impact caused by motion reversal. Simultaneously, by randomly driving the sampling points, the polishing trajectory achieves statistical isotropy, disrupting the coherent accumulation conditions for mid-frequency errors. Under the same processing conditions, this invention can significantly reduce the peak value of the PSD (Power Spectral Density) characteristic on the surface of optical elements, greatly improving the imaging quality of high-energy laser or deep space exploration systems.

[0102] Example 13:

[0103] A method for planning random polishing paths for optical components, as described below:

[0104] This invention maps discrete random sampling points on the surface of optical elements into continuous, smooth, and self-crossing closed-loop polishing paths by constructing a one-dimensional closed-loop topology self-organizing map (SOM) network. The specific technical steps and mathematical model are as follows:

[0105] Step 1: Network Initialization and Closed-Loop Topology Construction

[0106] First, the network size is set according to the polishing precision requirements, i.e., the network size is defined. There are 100 neurons. The network formed by these nodes has a one-dimensional closed-loop topology, that is, node 1 and node 2. Logically, they are neighbors. Initialize the weight vector for each neuron. ,in Initially, the weight vectors are typically set as a tiny ring distributed around the center of the optical element to give the path an initial topological closure. Specifically, wj(0) refers to the two-dimensional position coordinate vector corresponding to the j-th SOM neuron during initialization. xj and yj represent the abscissa and ordinate of the initial position of the j-th neuron in the optical element coordinate system. The initial weight vectors of all neurons are arranged together to form a tiny ring. Let L be the size of the processing area, and r0 be the initial radius of the small ring, r0 = L / 100. The radius only needs to be small enough; the small ring is essentially a circular line.

[0107] Step 2: Random sampling of the input space

[0108] To break the periodicity of traditional paths, this invention generates pseudo-random input vectors within the region to be polished. In the... In the next iteration, a random input vector is generated. This vector represents a random coordinate point on the surface of the optical element where it needs to be processed. Sampling follows a uniform distribution (or importance sampling based on the distribution of the element's surface shape error). This random driving ensures that the path has broadband characteristics in the frequency domain, thereby suppressing energy accumulation at specific frequencies.

[0109] Step 3: Competition Mechanism and Winning Neuron (BMU) Determination

[0110] For each input random point The network competes to find the neuron that is geometrically closest to it, which serves as the current path guide point, i.e., the winning neuron (Best Matching Unit).

[0111]

[0112] in, It is the neuron index that is closest to the random sampling point in Euclidean space.

[0113] Step 4: Calculate the distance between closed-loop neighborhoods

[0114] This is the core mathematical processing for achieving the "closed-loop" characteristic. Unlike a linear chain, a closed-loop structure requires calculating the shortest logical step length of a neuron on the loop. Calculating any... One neuron and the winning neuron Topological distance between :

[0115]

[0116] This formula ensures that update instructions can be transmitted along the bidirectional shortest path of the ring, guaranteeing the continuity of the path.

[0117] Step 5: Neighborhood Collaborative Update and Smoothness Control

[0118] The winning neuron and its neighboring neurons will all send signals to the sampling point. Movement. The intensity of this movement is controlled by a Gaussian neighborhood function, thus ensuring smooth path deformation. Mathematical expression for the neighborhood function:

[0119]

[0120] in, The neighborhood radius decays exponentially with the number of iterations, ensuring a smooth transition from global macro-level stretching to local fine-tuning. The mathematical expression for weight update is:

[0121]

[0122] in, The learning rate decays over time. This mechanism allows the neuron sequence to self-organize into a closed curve covering the entire field under the "traction" of random points.

[0123] Step 6: Dynamic Convergence and Parameter Decay

[0124] To ensure the path eventually stabilizes and meets the machine tool machining dynamics requirements, the learning rate... and neighborhood radius A specific attenuation strategy must be followed. Attenuation model:

[0125]

[0126] in This is a constant representing the total number of iterations. It is initially relatively large. It is responsible for quickly establishing the path framework, and smaller parameters in the later stages are responsible for eliminating path intersections (Knots) and improving local uniformity.

[0127] Step 7: Closed-loop path generation

[0128] When the iteration ends, the final weight vector sequence will be generated. Join in index order, and Afterwards The discrete points are smoothed using spline curve or circular interpolation algorithms to generate the final pseudo-random closed-loop polishing trajectory.

[0129] The beneficial effects of this invention are as follows:

[0130] Suppressing and eliminating intermediate frequency errors: By utilizing the self-organizing characteristics of the SOM algorithm, the distribution of processing points is transformed from the fixed-frequency accumulation of traditional gratings or spirals into an isotropic distribution similar to white noise. This enables the polishing pressure and removal amount to achieve uniform dispersion in the frequency domain on the component surface, thereby effectively suppressing and eliminating textures (stripes or rings) at specific spatial frequencies.

[0131] Improve the dynamic stability of the machining trajectory: By constructing a one-dimensional closed-loop topology, the movement trajectory of the polishing tool is ensured to be connected end to end throughout the entire machining process. This avoids the frequent tool lifting, reversal, and pauses that occur in traditional paths, effectively reducing the vibration caused by sudden changes in machine tool movement and the local removal deviation caused by dynamic lag.

[0132] Eliminating edge effects and uneven coverage: By leveraging the boundaryless topological characteristics of the SOM closed-loop path, the problem of abrupt coverage changes in the edge region of optical elements in traditional scanning paths is solved, achieving a highly uniform residence time distribution and statistically significant spatial isotropy across the entire aperture range.

[0133] Adaptive optimization of the path: For optical elements with different surface error distributions, this invention aims to utilize the local mapping capability of SOM to achieve self-organized coupling between the processing path density and the surface error distribution, thereby suppressing mid-frequency errors and improving the convergence efficiency of surface accuracy (low-frequency errors).

Claims

1. A method for planning random polishing paths for optical elements, characterized in that, Includes the following steps: Step 1. Define according to the polishing precision requirements. There are 10 neuron nodes; these neuron nodes form a one-dimensional closed-loop topology. Step 2. Initialize the weight vector for each neuron. ,in ; This represents the x and y coordinates of the initial position of the j-th neuron in the optical element coordinate system; Step 3. In the t-th iteration, generate a random input vector. , to characterize the random coordinate points of the location to be processed on the surface of the optical element; Step 4. For each random input By competing to find the random input The neuron with the closest geometric distance is selected as the guide point for the current path. Step 5. Calculate the current path guide point and the neurons in the neighborhood of the current path guide point to the random input. The intensity of movement; Step 6. Based on the current path guide point and the neurons in the neighborhood of the current path guide point, input the random input. The intensity of the movement is used to update the weight vector; Step 7. Determine if the iteration termination condition is met. If yes, proceed to step 8; otherwise, let t = t + 1 and return to step 3. Step 8. Transform the weight vector sequence Join in index order and let connect and A pseudo-random closed-loop polishing trajectory is generated.

2. The method for planning a random polishing path for an optical element according to claim 1, characterized in that, The neurons are arranged on a one-dimensional chain, with the first neuron logically adjacent to the Nth neuron, forming a closed loop.

3. The method for random polishing path planning of an optical element according to claim 1, characterized in that, Generate random input vectors At that time, the sampling of the position to be processed on the surface of the optical element is carried out in a uniform distribution manner or the importance sampling is carried out according to the initial error distribution of the surface shape of the optical element; The greater the surface shape error of the component, the more sampling points are needed.

4. The method for random polishing path planning of an optical element according to claim 1, characterized in that, The current path's guiding point is shown below: in, It is the neuron index that is closest to the random sampling point in Euclidean space.

5. The method for random polishing path planning of an optical element according to claim 1, characterized in that, The current path guide point, and neurons in the neighborhood of the current path guide point, are directed to random input. The intensity of the movement is shown below: in, The neighborhood radius decays exponentially with the number of iterations; For any number The topological distance between each neuron and the current path guide point.

6. The method for random polishing path planning of an optical element according to claim 5, characterized in that, Any number Each neuron and the current path guide point Topological distance between As shown below: In the formula, This represents the number of neuron nodes.

7. The method for random polishing path planning of an optical element according to claim 5, characterized in that, The neighborhood radius, which decays exponentially with the number of iterations, is shown below: In the formula, The initial neighborhood radius; This is a constant representing the total number of iterations.

8. The method for random polishing path planning of an optical element according to claim 5, characterized in that, The weights are updated as follows: in, The learning rate decays over time.

9. The method for random polishing path planning of an optical element according to claim 7, characterized in that, Learning rate decays over time As shown below: in The total number of iterations is a constant; This is the initial learning rate.

10. The method for random polishing path planning of an optical element according to claim 1, characterized in that, When generating pseudo-random closed-loop polishing trajectories, spline curves or circular interpolation algorithms are used to smooth the discrete points.

Images