A method for optimizing the surface of an optical lens or mirror

Abstract

The application discloses a surface optimization method of an optical lens or mirror, and comprises the following steps: given a unit light direction, a target image and a receiving plane, using an original grid to represent a surface of an optical lens or mirror to be optimized; establishing an optimization problem according to a position alignment degree, a light flux variation degree, a smooth degree of the original grid and an obstacle term, and obtaining a deformed grid; recalculating positions of all basic geometric units in the receiving plane in the deformed grid, and obtaining an image after superposition and rendering; establishing an optimization problem according to an image difference between a rendered image and the target image, an image gradient difference, an image boundary exceeding penalty term, a smooth degree of the deformed grid and the obstacle term, and obtaining a second deformed grid; gradually encrypting the grid until a last iteration stop of a highest resolution is achieved, and obtaining a final optimized grid. The above method can optimize a surface shape of an optical lens or mirror according to light source information, a receiving plane position and a target image.

Description

Technical Field

[0001] This invention relates to the field of optical lens or mirror technology, and more particularly to a surface optimization method for an optical lens or mirror. Background Technology

[0002] When the refractive (or reflective) surface of an optical device is uneven, the refracted (or reflected) light rays will form an uneven light field, a phenomenon known as caustics. However, controlling caustics to form a specific light field by designing the surface shape of an optical device is very difficult because slight changes in the refractive (or reflective) surface can cause significant changes in the direction of refraction (or reflection). This process typically requires extensive calculations and the use of ray tracing or other techniques to simulate light passing through a lens (or mirror). The design of optical lenses (or mirrors) has significant theoretical and practical value in many fields such as optoelectronic detection, optical processing, medicine, and architecture.

[0003] Existing methods for designing caustic lenses (or mirrors) typically require first determining auxiliary features such as the normal field or visibility map, and then reconstructing the surface of the optical device based on these features. However, current methods cannot guarantee extremely high accuracy in generating the light field. First, these methods do not directly consider the difference between the caustic light field generated by the reconstructed surface and the target light field, so errors gradually accumulate when calculating auxiliary features and reconstructing the surface. Furthermore, many methods use triangular meshes to represent the surface of the optical device, but use the normal of the vertices of the triangles for refraction, which does not conform to the use of the normal of triangular faces for refraction in the real physical world, further increasing the error. Finally, these methods only require the simulation results to be close to the target, ignoring the difficulties that may arise in actual manufacturing. Summary of the Invention

[0004] The purpose of this invention is to provide a surface optimization method for optical lenses or mirrors. This method can control the beam direction and light intensity distribution in a specified area, and optimize the surface shape of the optical lens or mirror based on light source information, receiving plane position and target image, so that the light emitted from the light source can present the target image on the receiving plane after passing through the lens or mirror, thereby improving the accuracy of optical devices.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for surface optimization of an optical lens or mirror, the method comprising:

[0007] Step 1: Specify the unit illumination direction target image And the receiving plane p, using the original grid M0 to represent the surface of the optical lens or mirror to be optimized;

[0008] Step 2: Calculate the position t′ of each basic geometric element t in the original mesh M0 on the receiving plane p using the laws of refraction or reflection, and then calculate the center position of t′. target image Treating it as a continuous probability distribution μ, calculate the center location. The semi-discrete optimal transmission problem between μ and y is solved to obtain the optimized position.

[0009] Step 3, according to and Alignment level E align The degree of change in luminous flux Φ carried by the basic geometric unit t, E flux The smoothness E of the original mesh M0 smooth and obstacle item E barr An optimization problem is established, and the deformed mesh M1 is obtained through optimization.

[0010] Step 4: Recalculate the positions t′ of all basic geometric elements t on the receiving plane p in the deformed mesh M1, and then overlay and render them to obtain the image g;

[0011] Step 5: Compare the image g obtained in Step 4 with the target image. Image differences E img Image gradient difference E grad Penalty term E for exceeding image boundaries bdr The smoothness E of the deformed mesh M1 smooth and obstacle item E barr An optimization problem is established, and the mesh M2 after secondary deformation is obtained through optimization.

[0012] Step 6: Replace the original mesh M0 with the second-deformed mesh M2, and perform several iterations of M0-M1-M2. By using a coarse-to-fine strategy, the mesh is gradually refined until the final iteration with the highest resolution is reached, resulting in the final optimized mesh. This refers to the surface of an optimized optical lens or mirror.

[0013] As can be seen from the technical solution provided by the present invention, the above method can control the beam direction and light intensity distribution in a specified area, optimize the surface shape of the optical lens or mirror according to the light source information, the position of the receiving plane and the target image, so that the light emitted from the light source can present the target image on the receiving plane after passing through the lens or mirror, thereby improving the accuracy of the optical device. Attached Figure Description

[0014] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic diagram of the surface optimization method for an optical lens or reflector provided in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of the optical path of the lens system described in an embodiment of the present invention;

[0017] Figure 3 This is a schematic diagram of the optical path of the reflector system described in an embodiment of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments, and do not constitute a limitation of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0019] like Figure 1 The diagram shown is a schematic flowchart of a surface optimization method for an optical lens or mirror provided in an embodiment of the present invention. The method includes:

[0020] Step 1: Specify the unit illumination direction target image And the receiving plane p, using the original grid M0 to represent the surface of the optical lens or mirror to be optimized;

[0021] Step 2: Calculate the position t′ of each basic geometric element t in the original mesh M0 on the receiving plane p using the laws of refraction or reflection, and then calculate the center position of t′. target image Treating it as a continuous probability distribution μ, calculate the center location. The semi-discrete optimal transmission problem between μ and y is solved to obtain the optimized position.

[0022] In this step, such as Figure 2 The diagram shown is an optical path schematic of the lens system according to an embodiment of the present invention. Figure 3 The diagram shown is an optical path schematic of the mirror system according to an embodiment of the present invention. Figure 2 It includes a light source with known light emission characteristics, a lens, and a receiving plane; Figure 3 It includes a light source with known light-emitting characteristics, a mirror, and a receiving plane. Light emitted from the light source is refracted by the lens or reflected by the mirror in sequence, and finally reaches the receiving plane, where it forms a pattern.

[0023] First, the direction of the emitted light is determined using the laws of refraction or reflection, as shown by the following formula.

[0024]

[0025] Here, η is the refractive index of the lens; if it is a reflecting mirror, then η = 1. It is the unit surface normal of the basic geometric unit t; Unit illumination direction;

[0026] The intersection of the outgoing ray and the receiving plane p gives the position t′ of the intersection point. The average value of all vertices in t′ is the center position.

[0027] Central position The semi-discrete optimal transport problem between μ and μ is equivalent to solving its dual problem, i.e., optimizing the convex energy function:

[0028]

[0029] here, Represents the energy function; This represents the weight vector to be optimized, which is the variable in the optimization problem; These are the coordinates of the point being integrated; This represents the integral over this position; Indicating the target image The light intensity (pixel brightness) at the location; n t Represents the number of basic geometric units t; It is the i-th cell in the weighted Vinograph, that is:

[0030]

[0031] After optimization, with For each cell, calculate the weights. The weighted center is denoted as

[0032] Step 3, according to and Alignment level E align The degree of change in luminous flux Φ carried by the basic geometric unit t, E flux The smoothness E of the original mesh M0 smooth and obstacle item Ebarr An optimization problem is established, and the deformed mesh M1 is obtained through optimization.

[0033] In this step, and Alignment level E align Determined by the following formula:

[0034]

[0035] n t Represents the number of basic geometric units t;

[0036] The degree of change in luminous flux Φ carried by the basic geometric unit t is E flux Determined by the following formula:

[0037]

[0038] This represents the luminous flux carried by the basic geometric unit t before optimization.

[0039] Obstacle E barr It consists of the following two parts:

[0040]

[0041] Here P(t) i ) indicates that t i Projected onto the receiving plane;

[0042] Represents the directed area;

[0043]

[0044] This is a piecewise function used to prevent triangle flipping;

[0045] ∈2>∈1>0 are two constant thresholds;

[0046] f tir (t i f is also a piecewise function, used to prevent total internal reflection. tir (t i It is determined by the following formula:

[0047]

[0048] Here, η is the refractive index of the lens; if it is a reflecting mirror, then η = 1. It is the i-th basic geometric unit t i The unit surface normal; The unit of illumination direction;

[0049] Smoothness E of the original mesh M0 smooth It consists of the following three parts:

[0050] E smooth =E face +τ1E edge +τ2E lap

[0051] Among them, E face E represents the average curvature of the surface. edge E represents the curvature of the edge. lap τ1 and T2 are the Laplace smoothing terms at the vertices; τ1 and T2 are constant parameters.

[0052] First, let the basic geometric unit t be defined. i The geometric center is Constructing auxiliary variables This represents its second fundamental form, with the mean curvature denoted as H. i =(a i +b i ) / 2, a i b i c i The introduced optimization variables; defined as:

[0053]

[0054] Here A i Indicates t i The area;

[0055] Next set It is t i A set of orthogonal bases, in which These are two orthogonal basis functions; for each adjacent surface t j ,set up Then the Weingarten matrix should be... Mapped to consider:

[0056]

[0057] δ(t i , t j ) is used to measure the second basic type M i Below, t i and t j Continuity between them;

[0058] For each adjacent edge e ij Define h(e) ij )=δ(t i , t j )+δ(t j, t i ), and thus define Eedge as:

[0059]

[0060] ε i Represents all adjacent edges e ij The set of; here Ψ v It is the Welsch function, defined as:

[0061] v is a user-defined constant parameter;

[0062] Finally E lap Determined by the following formula:

[0063]

[0064] Here P U This represents the projection of the domain U of the height field; Let j represent the set of all internal vertices j; Let represent the set of adjacent points of vertex j;

[0065] The final optimization problem is expressed as:

[0066] minγ1E align +γ2E flux +γ3E smooth +γ4E barr ,

[0067] Wherein, γ1, ..., γ4 are user-defined constant parameters.

[0068] Step 4: Recalculate the positions t′ of all basic geometric elements t on the receiving plane p in the deformed mesh M1, and then overlay and render them to obtain the image g;

[0069] In this step, the intersection area of ​​t′ with each pixel grid is calculated, and the luminous flux carried by t′ is distributed into each pixel grid according to the intersection area. Finally, the luminous flux of each pixel grid is superimposed, and then gamma inverse correction is performed to obtain the superimposed rendered image g, represented as:

[0070]

[0071] The Area(.) function represents area; pixel j This represents the j-th pixel.

[0072] Step 5: Compare the image g obtained in Step 4 with the target image. Image differences E img Image gradient difference E gradPenalty term E for exceeding image boundaries bdr The smoothness E of the deformed mesh M1 smooth and obstacle item E barr An optimization problem is established, and the mesh M2 after secondary deformation is obtained through optimization.

[0073] In this step, the smoothness E of the deformed mesh M1 smooth and obstacle item E barr Same as the definition in step 3;

[0074] Rendered image g and target image Image differences E img Determined by the following formula:

[0075]

[0076] n p Number of images;

[0077] Image gradient difference E grad Determined by the following formula:

[0078]

[0079] Among them, G x，y and These represent the rendered image g and the target image, respectively. The gradient matrix; the subscript F denotes the Frobenius norm of the matrix, or simply the F-norm;

[0080] Penalty term E for exceeding image boundaries bdr Determined by the following formula:

[0081]

[0082] here It is t′ i The number of vertices, t′ i It is the position of the i-th basic geometric unit on the receiving plane p; It is the k-th vertex of the basic geometric unit; Indicates the distance within the imaging area The nearest point;

[0083] The final optimization problem is expressed as:

[0084] minλ1E img +λ2E grad +λ3E bdr +λ4E smooth +λ5E barr ,

[0085] Where λ1, ..., λ5 are user-defined constant parameters.

[0086] Step 6: Replace the original mesh M0 with the second-deformed mesh M2, and perform several iterations of M0-M1-M2. By using a coarse-to-fine strategy, the mesh is gradually refined until the final iteration with the highest resolution is reached, resulting in the final optimized mesh. This refers to the surface of an optimized optical lens or mirror.

[0087] This application introduces a piecewise smoothness constraint E during the geometric optimization process. smooth This allows for the design of surfaces that are easy to process and enables the manufacture of optical devices that accurately reproduce target images.

[0088] It is worth noting that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0089] In summary, the method described in the embodiments of the present invention has the following advantages:

[0090] 1) This application proposes an accurate differentiable rendering model based on light flux, which does not require complex ray tracing sampling;

[0091] 2) This application directly drives the optimization of the optical device surface by the difference between the rendering result and the target image, and introduces a smoothness constraint that facilitates processing and manufacturing, thereby enabling the manufacture of optical devices that accurately reproduce the target image.

[0092] 3) This application adopts an iterative, surface-based optimal transmission initialization strategy, which helps to avoid local minima and achieve effective optimization;

[0093] 4) This application can be used to design art installations, LCD backlight panels, color sorter light sources, medical equipment, lighting fixtures, etc., and has important theoretical significance and practical application value in many fields such as optoelectronic detection, optical processing, medicine, and architecture.

[0094] Furthermore, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware, and the corresponding program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0095] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for surface optimization of an optical lens or mirror, characterized in that, The method includes: Step 1: Specify the unit illumination direction target image And the receiving plane p, using the original grid M0 to represent the surface of the optical lens or mirror to be optimized; Step 2: Calculate the position t′ of each basic geometric element t in the original mesh M0 on the receiving plane p using the laws of refraction or reflection, and then calculate the center position of t′. target image Treating it as a continuous probability distribution μ, calculate the center location. The semi-discrete optimal transmission problem between μ and y is solved to obtain the optimized position. Step 3, according to and Alignment level E align The degree of change in luminous flux Φ carried by the basic geometric unit t, E flux The smoothness E of the original mesh M0 smooth and obstacle item E barr An optimization problem is established, and the deformed mesh M1 is obtained through optimization. in, and Alignment level E align Determined by the following formula: n t Represents the number of basic geometric units t; The degree of change in luminous flux Φ carried by the basic geometric unit t is E flux Determined by the following formula: This represents the luminous flux carried by the basic geometric unit t before optimization. Obstacle E barr It consists of the following two parts: Here P(t) i ) indicates that t i Projected onto the receiving plane; Represents the directed area; This is a piecewise function used to prevent triangle flipping; ∈2>∈1>0 are two constant thresholds; f tir (t i f is also a piecewise function, used to prevent total internal reflection. tir (t i It is determined by the following formula: Here, η is the refractive index of the lens; if it is a reflecting mirror, then η = 1. It is the i-th basic geometric unit t i The unit surface normal; The unit of illumination direction; Smoothness E of the original mesh M0 smooth It consists of the following three parts: E smooth =E face +τ1E edge +τ2E lap Among them, E face E represents the average curvature of the surface. edge E represents the curvature of the edge. lap τ1 and τ2 are the Laplace smoothing terms at the vertices; τ1 and τ2 are constant parameters. First, let the basic geometric unit t be defined. i The geometric center is Constructing auxiliary variables This represents its second fundamental form, with the mean curvature denoted as H. i =(a i +b i ) / 2, a i b i c i The introduced optimization variables; defined as: Here A i Indicates t i The area; Next set It is t i A set of orthogonal bases, in which These are two orthogonal basis functions; for each adjacent surface t j ,set up Then the Weingarten matrix should be... Mapped to consider: δ(t i ,t j ) is used to measure the second basic type M i Below, t i and t j Continuity between them; For each adjacent edge e ij Define h(e) ij )=δ(t i ,t j )+δ(t j ,t i ), and then define E edge for: ε I Represents all adjacent edges e ij The set of; here Ψ v It is the Welsch function, defined as: v is a user-defined constant parameter; Finally E lap Determined by the following formula: Here P U This represents the projection of the domain U of the height field; Let j represent the set of all internal vertices j; Let represent the set of adjacent points of vertex j; The final optimization problem is expressed as: min γ1E align +γ2E flux +γ3E smooth +γ4E barr , Where γ1,…,γ4 are user-defined constant parameters; Step 4: Recalculate the positions t′ of all basic geometric elements t on the receiving plane p in the deformed mesh M1, and then overlay and render them to obtain the image g; Step 5: Compare the image g obtained in Step 4 with the target image. Image differences E img Image gradient difference E grad Penalty term E for exceeding image boundaries bdr The smoothness E of the deformed mesh M1 smooth and obstacle item E barr An optimization problem is established, and the mesh M2 after secondary deformation is obtained through optimization. Step 6: Replace the original mesh M0 with the second-deformed mesh M2, and perform several iterations of M0-M1-M2. By using a coarse-to-fine strategy, the mesh is gradually refined until the final iteration with the highest resolution is reached, resulting in the final optimized mesh. This refers to the surface of an optimized optical lens or mirror.

2. The surface optimization method for an optical lens or mirror according to claim 1, characterized in that, In step 2, the direction of the emitted light is first determined using the laws of refraction or reflection by the following formula. Here, η is the refractive index of the lens; if it is a reflecting mirror, then η = 1. It is the unit surface normal of the basic geometric unit t; Unit illumination direction; The intersection of the outgoing ray and the receiving plane p gives the position t′ of the intersection point. The average value of all vertices in t′ is the center position. Central position The semi-discrete optimal transport problem between μ and μ is equivalent to solving its dual problem, i.e., optimizing the convex energy function: here, Represents the energy function; This represents the weight vector to be optimized, which is the variable in the optimization problem; These are the coordinates of the point being integrated; This represents the integral over this position; Indicating the target image The light intensity at the location; n t Represents the number of basic geometric units t; It is the i-th cell in the weighted Vinograph, that is: After optimization, with For each cell, calculate the weights. The weighted center is denoted as 3. The surface optimization method for an optical lens or mirror according to claim 1, characterized in that, In step 4, the intersection area of ​​t′ with each pixel grid is calculated, and the luminous flux carried by t′ is distributed into each pixel grid according to the intersection area. Finally, all the luminous flux of each pixel grid is superimposed, and then gamma inverse correction is performed to obtain the superimposed rendered image g, represented as: The Area(·) function represents area; pixel j This represents the j-th pixel.

4. The surface optimization method for an optical lens or mirror according to claim 1, characterized in that, In step 5, the smoothness E of the deformed mesh M1 is... smooth and obstacle item E barr Same as the definition in step 3; Rendered image g and target image Image differences E img Determined by the following formula: n p Number of images; Image gradient difference E grad Determined by the following formula: Among them, G x，y and These represent the rendered image g and the target image, respectively. The gradient matrix; the subscript F denotes the Frobenius norm of the matrix, or simply the F-norm; Penalty term E for exceeding image boundaries bdr Determined by the following formula: here It is t′ i The number of vertices; t′ i It is the position of the i-th basic geometric unit on the receiving plane p; It is the k-th vertex of the basic geometric unit; Indicates the distance within the imaging area The nearest point; The final optimization problem is expressed as: min λ1E img +λ2E grad +λ3E bdr +λ4E smooth +λ5E barr , Where λ1, ..., λ5 are user-defined constant parameters.

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