An optical-mechanical coupling analysis method for large deformation lens

Abstract

The application discloses a kind of optical-mechanical coupling analysis methods for large deformation lens, first obtain lens initial physical information, by executing equivalent optical surface reconstruction, non-continuous microstructure is converted into three-dimensional curved surface reference;Subsequently, by displacement vector superposition, introduce the geometric nonlinear deformation under service condition;Core analysis link adopts the strategy of MLS and Newton iteration, reconstructs local continuous face type in discrete point cloud and solves accurate intersection point;Finally, the performance evaluation result with 80% energy radius as index is output.The application realizes that no matter how lens is distorted, stretched or becomes non-circular special shape, high-precision face type restoration can be realized, by numerical iteration intersection algorithm, partial derivative is obtained by using analytical derivation, the normal vector second-order continuous smooth at intersection point is guaranteed, local light deflection caused by large deformation can be accurately captured, which is crucial for energy collection system (such as Fresnel lens) to predict focal spot shift.

Description

Technical Field

[0001] This invention belongs to the field of large-aperture lens technology, specifically relating to an optomechanical coupling analysis method for large deformation lenses. Background Technology

[0002] In technologies such as large-scale solar concentrators and space-based solar energy harvesting, large-aperture lenses (such as Fresnel lenses and thin-film lenses) are core energy-collecting components. To achieve system lightweighting and reduce material costs, lenses and their supporting structures are typically designed to be extremely thin. This structural feature results in the system exhibiting significant elastic mechanical properties under its own weight, wind loads, or thermal stress.

[0003] In order to accurately predict energy collection efficiency and focal spot distribution, optomechanical coupling analysis must be performed. That is, mechanical deformation is obtained through finite element analysis (FEA) and then fed back to the optical simulation system for ray tracing.

[0004] Existing optomechanical coupling methods have the following significant drawbacks when dealing with such "lightweight, large-aperture, large-deformation" scenarios: 1) Traditional Zernike polynomials are orthogonal basis functions defined on the unit circle. For large-aperture energy-gathering lenses, when the deformation reaches the millimeter level, the projection area on the lens surface undergoes geometric changes, causing the surface shape to deviate from the initially defined circular domain. At this point, the Zernike polynomial loses its original mathematical orthogonality and cannot accurately represent the deformed surface shape. 2) For complex large deformations at the millimeter level, if polynomial fitting is forcibly used, extremely high-order (even exceeding 100th order) basis functions are often required. This not only leads to a surge in computation but also triggers Runge's phenomenon, where, when constructing high-order polynomial interpolation using equidistant nodes, the interpolation polynomial oscillates violently near the two endpoints of the interval, causing the error to increase with the degree. This generates spurious numerical oscillations at the edge of the fitting region, severely affecting the accuracy of optical tracking. 3) Existing optomechanical analysis software (such as Zemax) often performs analysis based on linear small displacement mapping; for lightweight structures, deformation itself changes the load distribution (such as geometric nonlinearity caused by large displacement). Currently, there is a lack of an analysis method that can efficiently handle the "large structural deformation - optical microstructure offset - optical system performance".

[0005] Therefore, developing an optomechanical coupling analysis method that can faithfully reproduce the effect of millimeter-level deformation on the surface shape of large-aperture lenses with significant elastic characteristics is of great practical significance for improving the design accuracy of energy collection systems. Summary of the Invention

[0006] The purpose of this invention is to address the following problems: 1) the decrease in fitting accuracy caused by lightweight, large-aperture lenses deviating from the domain of traditional polynomials (such as Zernike polynomials) and losing orthogonality under millimeter-level deformation; 2) the insufficient intersection accuracy of traditional mesh mapping methods when dealing with complex deformed surfaces; and 3) the problem that traditional interpolation methods easily lead to discontinuities in normals and large deviations in refraction calculations due to significant local normal deflection caused by large deformation. Therefore, this invention provides an optomechanical coupling analysis method for lenses with large deformation. By introducing the Moving Least Squares (MLS) local reconstruction technique, high-fidelity reconstruction of the surface shape is achieved under arbitrary large displacement and deformation conditions, eliminating numerical fluctuations caused by global fitting. By coupling the Newton-Raphson iterative algorithm with the local MLS surface, continuous local analytical features are constructed on the basis of discrete point clouds, achieving sub-micron-level numerical intersection accuracy and ensuring the reliability of ray tracing results. Real-time extraction of local micro-element normals through analytical differentiation ensures the accuracy of ray propagation direction calculation under large-angle deflection, thereby accurately predicting energy collection efficiency.

[0007] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0008] An optomechanical coupling analysis method for large deformation lenses includes the following steps:

[0009] Step 1: Initial point cloud generation based on equivalent optical surface reconstruction

[0010] For Fresnel lenses with discontinuous microstructures (taking spherical lenses as an example, and the same applies to aspherical lenses), the equivalent radius of curvature is calculated based on the lens's focal length and the material's refractive index. Using the spherical mapping equation Transform the original two-dimensional planar nodes Elevate to a three-dimensional spherical space to construct an initial equivalent optical surface point cloud. .

[0011] Step 2: Discrete point cloud deformation superposition and spatial preprocessing based on geometric nonlinearity

[0012] Obtain the three-dimensional displacement vector data of the lens under load obtained through finite element analysis (FEA). And superimpose it onto the initial equivalent point cloud. Construct the final large deformation point cloud. The point cloud is spatially partitioned using a KD-tree (K-Dimensional Tree) to establish an efficient neighborhood index structure; the average nearest neighbor distance of the point cloud is calculated, and the computational radius of the MLS is dynamically defined accordingly. .

[0013] Step 3: Local Continuous Surface Reconstruction Based on MLS

[0014] For any query point in the ray tracing process ,exist The nearest neighbor set is searched within the range; the Wendland weighting function is used to weight the neighboring points, and a weighted squared functional is constructed using local quadratic polynomial basis functions. By solving the fitting coefficient matrix, the high-order continuous local height value at the point is obtained.

[0015] Step 4: Accurate intersection of rays and point cloud surfaces based on Newton-Raphson iteration

[0016] A coupled model of the ray parameter equation and the MLS local surface equation is established; the zeroth intersection point of the ray and the reference plane is used as the initial iteration value, and the Newton iteration algorithm is used to update the ray parameter vector; in each iteration, the MLS function is called in real time to update the surface height at the current position until the height residual is less than the preset tolerance (e.g., 10). -8 (mm), to achieve submicron level intersection of light rays with millimeter-scale large deformation surfaces.

[0017] Step 5: Real-time correction of local normals based on infinitesimal partial derivatives

[0018] Using the local polynomial coefficients fitted by MLS in step 3, the partial derivatives at the query point can be obtained directly through analytical differentiation. and This method constructs the unit normal vector at that point. It avoids the step error in discrete mesh normal calculations, ensuring that local tilting caused by large displacements and rotations is accurately reflected in the refraction vector calculation.

[0019] Step 6: Solar Source Simulation and Energy Collection Performance Evaluation

[0020] A square root radial mapping algorithm is used to generate uniformly distributed solar light source origins within a circular aperture, and a Gaussian angle distribution is introduced to simulate the solar cone angle. After performing large-scale ray tracing, a two-dimensional grid density statistical model is established at the image plane. After smoothing with Gaussian filtering, the equivalent radius at a normalized light intensity threshold of 0.2 is calculated as the 80% energy radius, thereby quantitatively evaluating the impact of structural elastic characteristics on light-gathering performance.

[0021] Compared with the prior art, the present invention has the following beneficial technical effects:

[0022] 1. Breaking through the geometric limitations of traditional polynomial fitting: This invention adopts meshless reconstruction based on MLS. It does not rely on a global coordinate system or a predefined basis function space. Instead, it dynamically finds neighborhood points near each ray incident point through a KD tree, so as to achieve high-precision surface shape restoration no matter how the lens is twisted, stretched or becomes a non-circular irregular shape.

[0023] 2. A direct intersection mechanism for point clouds based on Newton-Raphson is introduced, and a numerical iterative intersection algorithm is implemented. The ray equation is coupled with the MLS local fitting function, and the Newton method is used for real-time solution.

[0024] 3. By directly obtaining the partial derivatives through analytical differentiation using the local polynomial coefficients fitted by MLS, the normal vector at the intersection point is guaranteed to be second-order continuous and smooth. This can capture the local light deflection caused by large deformation with extreme accuracy, which is crucial for predicting focal spot shift in energy collection systems (such as Fresnel lenses). Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating an embodiment of the optomechanical coupling analysis method for large deformation lenses according to the present invention;

[0026] Figure 2 This is a schematic diagram of the reconstruction of the equivalent optical surface in an embodiment of the present invention;

[0027] Figure 3 This is a schematic diagram of the deformation local reconstruction strategy in an embodiment of the present invention, wherein a) is a global view and b) is a local view;

[0028] Figure 4 This is a schematic diagram illustrating the iterative solution of the ray mirror intersection points in an embodiment of the present invention;

[0029] Figure 5 This is a schematic diagram of energy distribution in an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0031] like Figure 1 As shown, this embodiment provides an optomechanical coupling analysis method for large deformation lenses. First, the initial physical information of the lens is obtained, and the discontinuous microstructure is transformed into a three-dimensional curved surface reference by performing equivalent optical surface reconstruction. Then, geometric nonlinear deformation under service conditions is introduced by superimposing displacement vectors. The core analysis link adopts a strategy combining MLS and Newton iteration to reconstruct the local continuous surface shape in the discrete point cloud and solve for the precise intersection point. Finally, the performance evaluation result is output with 80% energy radius as the index.

[0032] Includes the following steps:

[0033] Step 1: As Figure 2As shown, for Fresnel lenses with discontinuous microstructures (taking spherical mirrors as an example, the same applies to aspherical mirrors), a preprocessing method for reconstructing the equivalent optical surface is first performed, such as... Figure 2 As shown in (a), the initial input node data typically originates from finite element analysis (FEA) software, and it is represented as defined in... Two-dimensional discrete point cloud on a plane ( ); Because the sawtooth microstructure of a Fresnel lens has macroscopic light-gathering properties, in order to enable continuous ray tracing in subsequent steps, this invention increases the spatial dimension of these planar nodes according to their designed focal length and equivalent refractive index. For example... Figure 2 As shown in (b), by applying the spherical mapping equation Each discrete node in the plane The points were recalculated and positioned in a three-dimensional spherical space to construct an initial equivalent optical surface point cloud. The mapped point cloud not only preserves the topological relationships of the original mesh but also endows the lens model with macroscopic optical curvature characteristics. This step is fundamental to achieving high-precision optomechanical mapping of discontinuous microstructure lenses under large deformations, ensuring that the three-dimensional deformation vector is superimposed in step 2 ( When ), the node can be positioned on the correct initial optical envelope.

[0034] Step 2: Based on geometric nonlinear discrete point cloud deformation superposition and spatial preprocessing, obtain the three-dimensional displacement vector data of the lens under load obtained by finite element analysis (FEA). And superimpose it onto the initial equivalent point cloud. Construct the final large deformation point cloud. The point cloud is spatially partitioned using a KD-tree (K-Dimensional Tree) to establish an efficient neighborhood index structure; the average nearest neighbor distance of the point cloud is calculated, and the computational radius of the MLS is dynamically defined accordingly. .

[0035] Step 3: As Figure 3 As shown, to address the problem that discrete point clouds after large deformation lack analytical expressions, a local reconstruction strategy is adopted. First, the estimated intersection points of rays and surfaces are used... Establish a radius of centered at . Within the influence region of e, all neighboring nodes falling within it are retrieved using a KD-tree, such as... Figure 3 The solid black dots are shown in the diagram. Subsequently, the Wendland weighting function is introduced to spatially weight the neighboring nodes, and a highly continuous and smooth micro-element surface within the local region is fitted using quadratic polynomial basis functions, as shown below. Figure 3The medium-sized mesh surface is shown. This infinitesimal surface not only eliminates the "step effect" between discrete points, but more importantly, it allows the precise normal direction at that point to be obtained directly through analytical differentiation. This "follow-up reconstruction" method ensures that regardless of the overall deformation of the lens, the refraction of each incident ray can be calculated on a locally continuous optical surface, thus guaranteeing the numerical stability of optomechanical coupling analysis under high-order deformations.

[0036] Step 4: As Figure 4 As shown, a coupled model of the ray parametric equation and the MLS local surface equation is established; the height residual between the ray and the local reconstruction surface at the current position is calculated, as shown in the figure. Figure 4 As shown by the midpoint line, the ray parameter vector is continuously corrected using the Newton-Raphson iteration, and the results are compared by the iteration points. The trajectory shows that even in areas of large deformation, the algorithm can ensure that the iteration point is always along the direction of the ray vector. Figure 4 (As shown by the dashed line) converges rapidly to the actual physical intersection point. At this point, until the height residual is less than the preset tolerance (e.g., 10). -8 (mm), to achieve submicron level intersection of light rays with millimeter-scale large deformation surfaces.

[0037] Step 5: Real-time correction of local normals based on differential partial derivatives. Using the local polynomial coefficients fitted by MLS in Step 3, the partial derivatives at the query point are directly obtained through analytical differentiation. and This method constructs the unit normal vector at that point. It avoids the step error in discrete mesh normal calculations, ensuring that local tilting caused by large displacements and rotations is accurately reflected in the refraction vector calculation.

[0038] Step 6: As Figure 5 As shown, a square root radial mapping algorithm is used to generate uniformly distributed solar light source starting points within a circular aperture, and a Gaussian angle distribution is introduced to simulate the solar cone angle. After performing large-scale ray tracing, a two-dimensional grid density statistical model is established at the image plane. After smoothing with Gaussian filtering, the equivalent radius at the normalized light intensity threshold of 0.2 is calculated as the 80% energy radius, thereby quantitatively evaluating the impact of structural elastic characteristics on light-gathering performance.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the present invention.

Claims

1. A method for optomechanical coupling analysis of large deformation lenses, characterized in that: Includes the following steps: Step 1: For Fresnel lenses or aspherical mirrors with discontinuous microstructures, calculate the equivalent radius of curvature based on the lens design focal length and material refractive index. Using the spherical mapping equation , original two-dimensional planar nodes Elevate to a three-dimensional spherical space to construct an initial equivalent optical surface point cloud. ; Step 2: Obtain the three-dimensional displacement vector data of the lens under load obtained through finite element analysis. ,Will Superimposed onto the initial equivalent point cloud Construct the final large deformation point cloud. ; A KD-tree is used to spatially partition the point cloud, establishing an efficient neighborhood index structure; the average nearest neighbor distance of the point cloud is calculated, and the calculation radius of the moving least squares method is dynamically defined. ; Step 3: For any query point in the ray tracing process ,exist Search for its nearest neighbor set within the range; use the Wendland weighting function to weight the neighboring points, construct a weighted squared functional using local quadratic polynomial basis functions, and obtain the high-order continuous local height value at the point by solving the fitting coefficient matrix. Step 4: Establish a coupled model of the ray parameter equation and the MLS local surface equation; use the zeroth intersection point of the ray and the reference plane as the initial iteration value, and use the Newton iteration algorithm to update the ray parameter vector; in each iteration, call the MLS function in real time to update the surface height at the current position until the height residual is less than the preset tolerance, so as to realize the intersection of the ray and the millimeter-level large deformation surface. Step 5: Using the local polynomial coefficients fitted by MLS in Step 3, directly obtain the partial derivatives at the query point through analytical differentiation. and Construct the unit normal vector at that point; avoid the step error in the calculation of discrete grid normals, and ensure that the local tilt caused by large displacement and large rotation can be accurately reflected in the calculation of refraction vector; Step 6: Use the square root radial mapping algorithm to generate uniformly distributed solar light source starting points within the circular aperture, and introduce Gaussian angle distribution to simulate the solar cone angle; after performing large-scale ray tracing, establish a two-dimensional grid density statistical model at the image plane, smooth it with Gaussian filtering, and calculate the 80% energy radius to quantitatively evaluate the impact of structural elastic characteristics on light-gathering performance.

2. The optomechanical coupling analysis method for large deformation lenses according to claim 1, characterized in that: Step 1 specifically includes: For Fresnel lenses or aspherical mirrors with discontinuous microstructures, the first step is to perform a reconstruction preprocessing of the equivalent optical surface. The initial input nodal data typically originates from finite element analysis software, i.e., data defined on the surface. A two-dimensional discrete point cloud on a plane, wherein Because the serrated microstructure of a Fresnel lens has macroscopic light-gathering properties, in order to perform continuous ray tracing in subsequent steps, the spatial dimension of these planar nodes is increased according to the focal length and equivalent refractive index of the Fresnel lens; this is achieved by applying the spherical mapping equation. Each discrete node in the plane The points were recalculated and positioned in a three-dimensional spherical space to construct an initial equivalent optical surface point cloud. The mapped point cloud not only preserves the topological relationships of the original mesh, but also endows the lens model with macroscopic optical curvature characteristics, ensuring that step 2, which involves superimposing three-dimensional deformation vectors, is effective. When ), the node can be positioned on the correct initial optical envelope.

3. The optomechanical coupling analysis method for large deformation lenses according to claim 1, characterized in that: Step 3 specifically includes: First, using the estimated intersection point of the light rays and the surface... Establish a radius of centered at . The influence region of e is determined by using a KD tree to retrieve all neighboring nodes falling within the influence region. Subsequently, a Wendland weighting function is introduced to spatially weight the neighboring nodes, and a highly continuous and smooth micro-element surface is fitted using a quadratic polynomial basis function. The micro-element surface eliminates the "step effect" between discrete points, allowing the precise normal direction at that point to be obtained directly through analytical differentiation. This "follow-up reconstruction" method ensures that regardless of the overall deformation of the lens, each incident ray can be refracted on a locally continuous optical surface, guaranteeing the numerical stability of optomechanical coupling analysis under high-order deformation.

4. The optomechanical coupling analysis method for large deformation lenses according to claim 1, characterized in that: Step 4 specifically includes: By calculating the height residual between the ray and the local reconstruction surface at the current position, the ray parameter vector is continuously corrected using Newton-Raphson iteration, and the results are compared at the iteration points. The trajectory shows that even in regions of large deformation, the algorithm can ensure that the iteration points always converge rapidly to the actual physical intersection points along the direction of the ray vector. At this point, until the height residual is less than the preset tolerance, submicron level intersection between the light ray and the millimeter-level large deformation surface is achieved.

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