A method for generating an optical initial structure based on differentiable ray tracing

Abstract

The application discloses an optical initial structure generation method based on a differentiable ray tracing. The method comprises the following steps: obtaining a first-order structure of an optical system; optimizing the first-order structure of the optical system to obtain an optimized first-order structure of the optical system; obtaining and screening a plurality of processed initial thin lens structures according to the first-order structure of the optical system; sequentially processing each processed initial thin lens structure by using a plurality of methods to obtain a corresponding optimized thin lens structure; and comprehensively processing all the optimized thin lens structures to finally obtain an optimal optical initial structure. The application realizes the beneficial effect of generating an excellent first-order structure of an optical system, brings the advantage of screening an optimal optical initial structure from multiple structures, and achieves the progress of simple operation, higher automation and significant improvement of optical design efficiency.

Description

Technical Field

[0001] This invention belongs to the field of optical imaging design, specifically relating to a method for generating an initial optical structure based on micro-ray tracing. Background Technology

[0002] When optical designers design a lens, they typically rely on commercial software such as ZEMAX or CODEV, undergoing multiple rounds of manual iteration and optimization, heavily depending on their design experience. For more complex optical systems, the quality of the design largely depends on the initial structure chosen. Currently, methods for obtaining the initial structure of an optical system mainly include PWC (Precision Waveform Computation), patent search, and first-order structure generation. However, all three methods have limitations. PWC, based on primary aberration theory, obtains the lens's structural parameters by solving a set of primary aberration equations. It is suitable for simple systems, but still requires optical designers to have a thorough understanding of optical principles and aberration theory for parameter selection. For more complex optical systems, PWC may result in no solution or multiple solutions. Patent search involves selecting lenses with similar initial structures and design requirements from published optical system patents. Optical designers then adjust system parameters based on their design experience to obtain the initial structure. However, for complex lenses with specific design requirements, finding similar patents is difficult, failing to meet diverse design needs and the exploration of novel lens architectures. First-order structure generation is typically based on… Theory, through optimization This allows for the acquisition of a good first-order optical structure. However, in the process of transforming the first-order optical structure into an actual lens structure, designers still rely on existing commercial software and design experience to select and optimize the initial lens. Summary of the Invention

[0003] To address the problems existing in the background technology, this invention provides a method for generating optical initial structures based on differential ray tracing, which solves the problem of the lack of practical, efficient and fast solution methods in the initial design stage of optical imaging systems.

[0004] The technical solution adopted by the optical initial structure generation method of the present invention includes:

[0005] S1. Obtain the first-order structure of the optical system according to the design requirements of the optical system. Then, process the first-order structure of the optical system sequentially using the differentiable paraxial ray tracing method, the automatic differentiation method, and the gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system.

[0006] S2. The optimized first-order structure of the optical system is processed sequentially using the thin lens optical power processing method and the lens shape screening conditions to obtain several processed initial thin lens structures.

[0007] S3. For each processed initial thin lens structure, the differentiable actual ray tracing method, weighted summation, automatic differentiation method and gradient descent-based optimization algorithm are applied sequentially to obtain the optimized thin lens structure.

[0008] S4. Obtain the corresponding evaluation index based on the optimized thin lens structure. Perform weighted summation, screening, and parameter fine-tuning on all the evaluation indexes of the optimized thin lens structures in sequence to obtain the optimal initial optical structure.

[0009] The gradient descent-based optimization algorithms in steps S1 and S4 include stochastic gradient descent, gradient descent with momentum, and gradient descent with adaptive learning rate.

[0010] Step S1 is as follows:

[0011] S11. Obtain the entrance pupil radius and image height of the optical system according to the optical system design requirements, and initialize and construct the first-order structure of the optical system based on the entrance pupil radius and image height.

[0012] The optical system design requirements include operating band, focal length, field of view, operating F-number, number of components, total system length, system back intercept, component spacing, relative illumination at the edge of the field of view, distortion, and full field of view modulation transfer function.

[0013] The optical system design requirements also include processing conditions, which include the net aperture radius of the thin lens, the lower limit of the thickness of the thin lens, and the upper limit of the thickness of the thin lens.

[0014] S12. The first-order structure of the optical system is traced using a differentiable paraxial ray tracing method to obtain the first-order evaluation function.

[0015] S13. The gradient of the parameters in the first-order structure of the optical system is obtained by processing the first-order evaluation function using the automatic differentiation method.

[0016] S14. Based on the gradient of the parameters in the first-order structure of the optical system, the first-order structure of the optical system is optimized using a gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system.

[0017] The first-order evaluation function in step S12 includes one or more of the following: component interval constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint.

[0018] The component spacing constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint are set according to the following formulas:

[0019]

[0020] L bfl =max(T) bfl -d N ,0)

[0021]

[0022]

[0023] Among them, L gap Indicates component interval constraint; L bfl L represents the back intercept constraint of the system. ttl L represents the total system length constraint. SI Indicates the primary spherical aberration constraint; L SII Indicates primary coma constraint; L SIII Indicates primary astigmatism constraint; L SIV Indicates primary field curvature constraint; L SV Indicates primary distortion constraint; L CI Indicates primary positional color difference constraint; L CII Indicates primary magnification color difference constraint; T gap Indicates the lower limit constraint of the component interval; d i Indicates the group interval; i represents the index; N represents the number of groups; T bfl d represents the target back intercept; N T represents the distance from the last element to the image plane. ttl Indicates the total length of the target; y i Φ represents the edge ray height of the i-th element; i Represents the optical power of the i-th element; μ i and Both represent auxiliary optimization variables for the i-th component; Let represent the height of the principal ray of the i-th component; Q represents the Lagrange invariant of the optical system.

[0024] Step S2 is as follows:

[0025] S21. Based on the thin lens optical power processing method, the optimized first-order structure of the optical system is processed to obtain several different initial thin lens structures.

[0026] S22. Based on the lens shape screening criteria, select the initial thin lens structures that meet the lens shape screening criteria from all the initial thin lens structures, and use each initial thin lens structure that meets the lens shape screening criteria as the processed initial thin lens structure.

[0027] The thin lens optical power processing method in step S21 is set according to the following formula:

[0028]

[0029] Where Φ represents the optical power of a single component in the first-order structure of the optical system; c1 represents the front surface curvature of the component mapped to the initial thin lens structure; c2 represents the rear surface curvature of the component mapped to the initial thin lens structure; n represents the refractive index of the component mapped to the initial thin lens structure; and t represents the center thickness of the component mapped to the initial thin lens structure.

[0030] The lens shape screening conditions in step S22 are set according to the following formula:

[0031] edge, t∈[Thi1,Thi2]

[0032] c1,c2∈(-R -1 ,R -1 )

[0033]

[0034] Where edge represents the edge thickness of the initial thin lens structure; t is the center thickness of the initial thin lens structure; Thi1 represents the lower limit of the edge thickness of the initial thin lens structure; Thi2 represents the upper limit of the edge thickness of the initial thin lens structure; c1 represents the curvature of the front surface mapped to the initial thin lens structure; c2 represents the curvature of the rear surface mapped to the initial thin lens structure; R represents the net aperture radius of the initial thin lens structure; R -1 It represents the reciprocal of the net diameter radius.

[0035] Step S3 is as follows:

[0036] S31. For each processed initial thin lens structure, a differentiable actual ray tracing method is used for tracing to obtain several evaluation functions for each processed initial thin lens structure.

[0037] The evaluation functions include the evaluation function for the mean square radius of the dot plot, the evaluation function for the mean square error of the wavefront, the evaluation function for the optical transfer function, the evaluation function for relative illumination, the evaluation function for distortion, the evaluation function for the effective focal length, the evaluation function for the working F number, the evaluation function for the total system length, the evaluation function for the system back intercept, the evaluation function for the air gap, the evaluation function for the thickness of the lens center and edge, the evaluation function for the slope of the lens surface, and the evaluation function for the maximum ray deflection angle.

[0038] S32. For each processed initial thin lens structure, the evaluation functions of all initial thin lens structures are weighted and summed to form the objective function of the initial thin lens structure.

[0039] S33. The objective function of each processed initial thin lens structure is processed using an automatic differentiation method to obtain the gradient of the parameters in the corresponding processed initial thin lens structure.

[0040] The parameters in the processed initial thin lens structure include the curvature, thickness, conic coefficient, glass material, and higher-order aspherical coefficient of each optical surface.

[0041] S34. Based on the gradient of the parameters in the processed initial thin lens structure, the gradient descent-based optimization algorithm is used to optimize each processed initial thin lens structure to obtain the optimized thin lens structure.

[0042] Step S4 is as follows:

[0043] S41. Based on the optimized thin lens structure, obtain several evaluation indicators for each optimized thin lens structure.

[0044] The evaluation metrics include the root mean square radius of the dot plot, optical transfer function, relative illumination, distortion, and total system length.

[0045] S42. Weighted summation of all evaluation indicators for each optimized thin lens structure to obtain a comprehensive evaluation of each optimized thin lens structure.

[0046] S43. Select the optimized thin lens structure with the highest comprehensive evaluation from all optimized thin lens structures, and perform parameter fine-tuning on each parameter of the selected optimized thin lens structure to finally obtain the optimal initial optical structure.

[0047] The innovation of this invention lies in the use of differentiable paraxial ray tracing method, gradient descent-based optimization algorithm, thin lens optical power processing method, lens shape selection conditions, and differentiable actual ray tracing method, which achieves the beneficial effect of generating excellent first-order structures of optical systems. It brings the advantage of obtaining the optimal initial optical structure from multiple sets of structures, and achieves the progress of simple operation, higher degree of automation and significantly improved optical design efficiency.

[0048] The beneficial effects of this invention are:

[0049] 1. This invention utilizes differentiable paraxial ray tracing to automatically generate an excellent first-order structure of an optical system, starting from the design requirements of the optical system and combining primary aberration theory with an optimization algorithm based on gradient descent.

[0050] 2. This invention utilizes a thin lens optical power processing method and lens shape screening conditions to map the first-order optical structure into multiple different optical initial starting points, thereby realizing a large-scale search of optical initial structures from multiple starting points, which is beneficial for discovering new structures.

[0051] 3. This invention utilizes differentiable actual ray tracing, flexibly sets different combinations of evaluation functions and optimization variables, and combines them with gradient descent-based optimization algorithms to optimize multiple sets of differentiated optical structures. Furthermore, it can screen the obtained sets of structures to obtain the optimal initial optical structure. Attached Figure Description

[0052] Figure 1 As described in the embodiments of the present invention picture.

[0053] Figure 2 This is a first-order structural diagram of the optical system in an embodiment of the present invention.

[0054] Figure 3 These are diagrams of several processed initial thin lens structures in embodiments of the present invention.

[0055] Figure 4 This is a diagram of the thin lens structure that receives the highest overall evaluation in this embodiment of the invention.

[0056] Figure 5 This is the optimal initial optical structure diagram in the embodiment of the present invention.

[0057] Figure 6 This is a modulation transfer function diagram of the optimal optical initial structure in this embodiment of the invention.

[0058] Figure 7 This is a relative illumination diagram of the optimal initial optical structure in this embodiment of the invention.

[0059] Figure 8This is a field distortion diagram of the optimal initial optical structure in this embodiment of the invention. Detailed Implementation

[0060] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0061] Example 1

[0062] The optical initial structure generation method of this embodiment includes the following steps:

[0063] S1. Obtain the first-order structure of the optical system according to the design requirements of the optical system. Then, process the first-order structure of the optical system sequentially using the differentiable paraxial ray tracing method, the automatic differentiation method, and the gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system.

[0064] S11. Obtain the entrance pupil radius and image height of the optical system according to the optical system design requirements, and initialize and construct the first-order structure of the optical system based on the entrance pupil radius and image height.

[0065] Optical system design requirements include operating band, focal length, field of view, operating F-number, number of components, total system length, system back intercept, component spacing, relative illumination at the edge of the field of view, distortion, and full field of view modulation transfer function.

[0066] Specifically, the first-order structure of the optical system is characterized by the first-order quantities of each component of the optical system; the first-order quantities of each component include the edge ray height, principal ray height, optical power, and component spacing;

[0067] The design requirements for optical systems also include processing conditions, which include the net aperture radius of the thin lens, the lower limit of the thickness of the thin lens, and the upper limit of the thickness of the thin lens.

[0068] S12. The first-order structure of the optical system is traced using a differentiable paraxial ray tracing method to obtain the first-order evaluation function.

[0069] In practice, the differentiable paraxial ray tracing method is based on Gaussian optics theory and combines it with modern machine learning frameworks such as PyTorch, TensorFlow, or JAX to automatically construct a computational graph during forward paraxial ray tracing and automatically record intermediate variables during the computation process.

[0070] The first-order evaluation function includes one or more of the following constraints: component interval constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint.

[0071] In specific implementation, the first-order evaluation function of this embodiment adopts a weighted sum of component interval constraints, system back intercept constraints, system total length constraints, primary spherical aberration constraints, primary coma constraints, primary astigmatism constraints, primary field curvature constraints, primary distortion constraints, primary positional chromatic aberration constraints, and primary magnification chromatic aberration constraints.

[0072] The component spacing constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint are set according to the following formulas:

[0073]

[0074] L bfl =max(T) bfl -d N ,0)

[0075]

[0076] Among them, L gap Indicates component interval constraint; L bfl L represents the back intercept constraint of the system. ttl L represents the total system length constraint. SI Indicates the primary spherical aberration constraint; L SII Indicates primary coma constraint; L SIII Indicates primary astigmatism constraint; L SIV Indicates primary field curvature constraint; L SV Indicates primary distortion constraint; L CI Indicates primary positional color difference constraint; L CII Indicates primary magnification color difference constraint; T gap Indicates the lower limit constraint of the component interval; d i Indicates the group interval; i represents the index; N represents the number of groups; T bfl d represents the target back intercept; N T represents the distance from the last element to the image plane. ttl Indicates the total length of the target; y i Φ represents the edge ray height of the i-th element; i Represents the optical power of the i-th element; μ i and Both represent auxiliary optimization variables for the i-th component; Let represent the height of the principal ray of the i-th component; Q represents the Lagrange invariant of the optical system.

[0077] In forward differentiable paraxial ray tracing, the relationship between the variables is as follows:

[0078] q i+1 =q i -y i ·φ i

[0079] y i+1 =y i +d i ·q i+1

[0080]

[0081] Where, q i+1 q represents the edge ray aperture angle of the (i+1)th element; i y represents the edge ray aperture angle of the i-th element; i φ represents the edge ray height of the i-th element; i y represents the optical power of the i-th element; i+1 d represents the edge ray height of the (i+1)th element; i This represents the interval between the i-th element and the next element. This represents the principal ray aperture angle of the (i+1)th component; Indicates the principal ray aperture angle of the i-th element; This represents the height of the principal ray of the i-th element; This represents the height of the main ray of the (i+1)th element.

[0082] S13. The gradient of the parameters in the first-order structure of the optical system is obtained by processing the first-order evaluation function using the automatic differentiation method.

[0083] S14. Based on the gradient of the parameters in the first-order structure of the optical system, the first-order structure of the optical system is optimized using a gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system.

[0084] Gradient descent-based optimization algorithms include stochastic gradient descent, gradient descent with momentum, and gradient descent with adaptive learning rate.

[0085] In gradient calculation, the chain rule is applied layer by layer to calculate the gradient of the first-order evaluation function of the optical system with respect to the parameters in the first-order optical structure.

[0086] S2. The optimized first-order structure of the optical system is processed sequentially using the thin lens optical power processing method and the lens shape screening conditions to obtain several processed initial thin lens structures.

[0087] S21. Based on the thin lens optical power processing method, the optimized first-order structure of the optical system is processed to obtain several different initial thin lens structures.

[0088] The optical power processing method for thin lenses is set according to the following formula:

[0089]

[0090] Where Φ represents the optical power of a single component in the first-order structure of the optical system; c1 represents the front surface curvature of the component mapped to the initial thin lens structure; c2 represents the rear surface curvature of the component mapped to the initial thin lens structure; n represents the refractive index of the component mapped to the initial thin lens structure; and t represents the center thickness of the component mapped to the initial thin lens structure.

[0091] By leveraging computing platforms such as GPUs / TPUs, large-scale random sampling of c1 and c2 can be achieved. Then, by substituting c1 and c2, along with the optical power Φ and refractive index n, into the optical power processing formula for thin lenses, large-scale and rapid solutions for the thickness t of thin lenses can be obtained.

[0092] S22. Based on the lens shape screening criteria, select the initial thin lens structures that meet the lens shape screening criteria from all the initial thin lens structures, and use each initial thin lens structure that meets the lens shape screening criteria as the processed initial thin lens structure.

[0093] Lens shape screening criteria are set using the following formula:

[0094] edge, t∈[Thi1,Thi2]

[0095] c1,c2∈(-R -1 ,R -1 )

[0096]

[0097] Where edge represents the edge thickness of the initial thin lens structure; t is the center thickness of the initial thin lens structure; Thi1 represents the lower limit of the edge thickness of the initial thin lens structure; Thi2 represents the upper limit of the edge thickness of the initial thin lens structure; c1 represents the front surface curvature mapped to the initial thin lens structure; c2 represents the rear surface curvature mapped to the initial thin lens structure; R represents the net aperture radius of the initial thin lens structure; R -1 It represents the reciprocal of the net diameter radius.

[0098] S3. For each processed initial thin lens structure, the differentiable actual ray tracing method, weighted summation, automatic differentiation method and gradient descent-based optimization algorithm are applied sequentially to obtain the optimized thin lens structure.

[0099] S31. For each processed initial thin lens structure, a differentiable actual ray tracing method is used for tracing to obtain several evaluation functions for each processed initial thin lens structure.

[0100] Evaluation functions include, but are not limited to, evaluation functions for the mean square radius of the dot plot, wavefront mean square error, optical transfer function, relative illumination, distortion, effective focal length, working F-number, total system length, back intercept, air gap, center and edge thickness of the lens, surface slope of the lens, and maximum ray deflection angle.

[0101] In practice, the mean square radius, mean square error of wavefront, optical transfer function, relative illumination, distortion, effective focal length, working F number, total system length, back intercept, air gap, lens center and edge thickness, lens surface slope and maximum light deflection angle of each processed initial thin lens structure are first obtained, and then the corresponding evaluation function is obtained.

[0102] S32. For each processed initial thin lens structure, the evaluation functions of all initial thin lens structures are weighted and summed to form the objective function of the initial thin lens structure.

[0103] S33. The objective function of each processed initial thin lens structure is processed using an automatic differentiation method to obtain the gradient of the parameters in the corresponding processed initial thin lens structure.

[0104] The parameters in the processed initial thin lens structure include the curvature, thickness, conic coefficient, glass material, and higher-order aspherical coefficients of each optical surface.

[0105] S34. Based on the gradient of the parameters in the processed initial thin lens structure, the gradient descent-based optimization algorithm is used to optimize each processed initial thin lens structure to obtain the optimized thin lens structure.

[0106] Gradient descent-based optimization algorithms include stochastic gradient descent, gradient descent with momentum, and gradient descent with adaptive learning rate.

[0107] Differentiable ray tracing is based on the principle of geometric ray propagation. It alternately calculates the intersection points of the incident ray with the optical surface and the direction cosine of the outgoing ray to establish the propagation path of the light in the actual optical system. During forward ray tracing, a computational graph is automatically constructed and intermediate variables are recorded. This allows the chain rule to be applied layer by layer during gradient calculation to calculate the gradient of the objective function with respect to the parameters of the processed initial thin lens structure.

[0108] S4. Obtain the corresponding evaluation index based on the optimized thin lens structure. Perform weighted summation, screening, and parameter fine-tuning on all the evaluation indexes of the optimized thin lens structures in sequence to obtain the optimal initial optical structure.

[0109] S41. Based on each optimized initial thin lens structure, obtain several evaluation indicators for each optimized initial thin lens structure.

[0110] Evaluation metrics include, but are not limited to, the root mean square radius of the dot plot, optical transfer function, relative illumination, distortion, and total system length.

[0111] S42. Weighted summation of all evaluation indicators for each optimized initial thin lens structure to obtain a comprehensive evaluation of each optimized initial thin lens structure.

[0112] S43. Select the optimized thin lens structure with the highest comprehensive evaluation from all optimized initial thin lens structures, and fine-tune the parameters of each selected optimized thin lens structure to finally obtain the optimal initial optical structure.

[0113] In practice, parameter fine-tuning involves using commercial optical software to fine-tune the parameters of the selected optimized thin lens structure.

[0114] Example 2

[0115] This embodiment designs a rear imaging lens for a mobile phone. This embodiment is implemented using the same method as Embodiment 1.

[0116] The design requirements for the optical system in implementation include:

[0117] Operating band: visible light; focal length: 4.5mm; field of view: 70 degrees; operating F-number: 2.2; number of components: 6 (excluding protective glass); total system length: <5.6mm; system back intercept: >0.5mm (excluding protective glass); component spacing: >0.1mm; relative illumination at the edge of the field of view: >0.4; distortion: <1.5%; and modulation transfer function (MTF) in the optical transfer function: >0.1@350lp / mm.

[0118] During implementation, based on the optical system design requirements, the entrance pupil radius and image height are calculated, and the first-order structure of the optical system is initialized and constructed. The first-order structure of the optical system is characterized by the following formula:

[0119] y1=T efl ·F -1 0.5 = 1.02mm

[0120]

[0121] y img =0mm

[0122] Where y1 represents the edge ray height of the first component; T efl represents the target focal length of the system; F represents the target F-number of the system; θ represents the height of the principal ray on the image plane. FoV Indicates the field of view; Indicates the height of the principal ray of the first component; y img Indicates the height of the light rays at the edge of the image plane;

[0123] In practice, the established first-order evaluation function considers all optical system dimensional constraints and primary aberration constraints, resulting in the following first-order optical evaluation function:

[0124] L = L gap +L ttl +L bfl +L SI +L SII +L SIII +L SIV +L SV +L CI +L CII

[0125] Where L represents the first-order evaluation function; L gap Indicates component interval constraint; L bfl L represents the back intercept constraint of the system. ttl L represents the total system length constraint. SI Indicates the primary spherical aberration constraint; L SII Indicates primary coma constraint; L SIII Indicates primary astigmatism constraint; L SIV Indicates primary field curvature constraint; L SV Indicates primary distortion constraint; L CI Indicates primary positional color difference constraint; L CII This indicates the primary magnification color difference constraint;

[0126] The parameters in the first-order optical structure were optimized using the stochastic gradient descent algorithm. The optimized first-order optical system structure is shown in Table 1. picture( (where y represents the height of the principal ray and y represents the height of the rim ray) and the first-order structure diagram are shown below. Figure 1 and Figure 2 As shown.

[0127] Table 1 First-order structure of the optical system in the embodiment

[0128] Component number i <![CDATA[Φ i / mm -1 ]]> <![CDATA[d i / mm <!-- 9 -->]]> 1 0.1468 0.5589 2 -0.0769 0.6087 3 0.1427 1.0156 4 -0.0458 1.3584 5 0.1362 1.0119 6 -0.0360 0.9199

[0129] Based on the thin lens optical power processing method, the optimized first-order structure of the optical system is processed to obtain several distinct initial thin lens structures. These structures are then selected based on lens shape criteria, such as... Figure 3 The diagram shows several processed initial thin lens structures.

[0130] Based on differentiable ray tracing, the initial thin lens structures after multiple processing steps are optimized. First, an objective function is established. In the initial design stage, evaluation functions are considered for the mean square radius of the dot plot, distortion, effective focal length, working F-number, total system length, back intercept, air gap, lens center and edge thickness, lens surface slope, and maximum ray deflection angle. The final objective function is a weighted sum of the above evaluation functions.

[0131] An adaptive learning rate gradient descent algorithm is used to optimize the parameters of multiple processed initial thin lens structures to obtain an optimized initial thin lens structure. Utilizing computing platforms such as GPUs / TPUs, efficient automatic search and iterative optimization of initial structures starting from a large scale can be achieved. The optimization variables are curvature, thickness, material, and conic coefficients, as well as the coefficients of 4th, 6th, 8th, and 10th order even-order aspherical terms.

[0132] After optimization, corresponding evaluation indicators are obtained based on the optimized thin lens structure. These indicators are then weighted and summed sequentially for each optimized thin lens structure, and the structure with the highest overall evaluation is selected. For example... Figure 4 As shown.

[0133] The thin lens structure with the highest overall evaluation is automatically written into commercial optical design software, and based on this, a flat protective glass is inserted in front of the image. The commercial optical design software is then used to further fine-tune various structural parameters of the system, thereby obtaining the optimal initial optical structure with good image quality, such as... Figure 5 As shown. The lens structure meets the optical system design requirements, with a relative illumination of 0.5 at the edge field of view, a maximum distortion of 1.23%, a system thickness of 5.5mm, and a modulation transfer function (MTF) > 0.15@350lp / mm in the optical transfer function.

[0134] like Figure 6The figure shows the modulation transfer function of the optimal initial optical structure for a mobile phone's rear imaging lens. Figure 7 This is a relative illumination diagram of the optimal initial optical structure for a mobile phone's rear imaging lens. Figure 8 This is a field-of-view distortion diagram for the optimal initial optical structure of a mobile phone's rear imaging lens.

[0135] This invention achieves the beneficial effect of generating excellent first-order structures of optical systems, brings the advantage of selecting the optimal initial optical structure from multiple sets of structures, and achieves progress in simple operation, higher degree of automation and significantly improved optical design efficiency.

[0136] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for generating an initial optical structure based on differentiable ray tracing, characterized in that, The method includes the following steps: S1. Obtain the first-order structure of the optical system according to the design requirements of the optical system. Then, process the first-order structure of the optical system sequentially using the differentiable paraxial ray tracing method, the automatic differentiation method, and the gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system. S2. The optimized first-order structure of the optical system is processed sequentially using the thin lens optical power processing method and the lens shape screening condition to obtain several processed initial thin lens structures. Step S2 is as follows: S21. Based on the thin lens optical power processing method, the optimized first-order structure of the optical system is processed to obtain several different initial thin lens structures. The thin lens optical power processing method in step S21 is set according to the following formula: in, It represents the optical power of a single component in the first-order structure of an optical system; This represents the front surface curvature of the component mapping as the initial thin lens structure; This represents the back surface curvature of the component mapping to the initial thin lens structure; This represents the refractive index of the component mapped to the initial thin lens structure; This indicates that the component is mapped to the center thickness of the initial thin lens structure; S22. Based on the lens shape screening criteria, select the initial thin lens structures that meet the lens shape screening criteria from all the initial thin lens structures, and use each initial thin lens structure that meets the lens shape screening criteria as the processed initial thin lens structure. S3. For each processed initial thin lens structure, the differentiable actual ray tracing method, weighted summation, automatic differentiation method and gradient descent-based optimization algorithm are applied sequentially to obtain the optimized thin lens structure. S4. Obtain the corresponding evaluation index based on the optimized thin lens structure. Perform weighted summation, screening, and parameter fine-tuning on all the evaluation indexes of the optimized thin lens structures in sequence to obtain the optimal initial optical structure.

2. The method for generating an initial optical structure according to claim 1, characterized in that: The gradient descent-based optimization algorithms in steps S1 and S4 include stochastic gradient descent, gradient descent with momentum, and gradient descent with adaptive learning rate.

3. The method for generating an initial optical structure according to claim 1, characterized in that, Step S1 is as follows: S11. Obtain the entrance pupil radius and image height of the optical system according to the optical system design requirements, and initialize and construct the first-order structure of the optical system based on the entrance pupil radius and image height; The optical system design requirements include operating band, focal length, field of view, operating F-number, number of components, total system length, system back intercept, component spacing, relative illumination at the edge of the field of view, distortion, and full field of view modulation transfer function. S12. The first-order structure of the optical system is traced using a differentiable paraxial ray tracing method to obtain the first-order evaluation function; S13. The gradient of the parameters in the first-order structure of the optical system is obtained by processing the first-order evaluation function using the automatic differentiation method. S14. Based on the gradient of the parameters in the first-order structure of the optical system, the first-order structure of the optical system is optimized using a gradient descent-based optimization algorithm to obtain the optimized first-order structure of the optical system.

4. The method for generating an initial optical structure according to claim 3, characterized in that: The first-order evaluation function in step S12 includes one or more of the following: component interval constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint.

5. The method for generating an initial optical structure according to claim 4, characterized in that: The component spacing constraint, system back intercept constraint, system total length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary positional chromatic aberration constraint, and primary magnification chromatic aberration constraint are set according to the following formulas: in, Indicates component interval constraints; This represents the back intercept constraint of the system; Indicates the total length constraint of the system; Indicates the primary spherical difference constraint; This indicates a primary coma constraint; Indicates primary astigmatism constraint; Indicates primary field curvature constraints; Indicates primary distortion constraint; This indicates the primary positional color difference constraint; This indicates the primary magnification color difference constraint; This indicates a lower limit constraint on the component interval; Indicates the component interval; Indicates an index; Indicates the number of components; Indicates the target back intercept; This represents the distance from the last element to the image plane; Indicates the total length of the target; Indicates the edge ray height of the i-th element; Represents the optical power of the i-th element; , , and Both represent auxiliary optimization variables for the i-th component; This represents the height of the principal ray of the i-th element; This represents the Lagrange invariant of the optical system.

6. The method for generating an initial optical structure according to claim 1, characterized in that: The lens shape screening conditions in step S22 are set according to the following formula: in, This indicates the edge thickness of the initial thin lens structure; This represents the center thickness of the initial thin lens structure. This indicates the lower limit of the edge thickness of the initial thin lens structure; This indicates the upper limit of the edge thickness of the initial thin lens structure; This represents the front surface curvature of the component mapping as the initial thin lens structure; This represents the back surface curvature of the component mapping to the initial thin lens structure; This represents the net aperture radius of the initial thin lens structure; It represents the reciprocal of the net diameter radius.

7. The method for generating an initial optical structure according to claim 1, characterized in that, Step S3 is as follows: S31. For each processed initial thin lens structure, a differentiable actual ray tracing method is used for tracing to obtain several evaluation functions for each processed initial thin lens structure. The evaluation functions include the evaluation function for the mean square radius of the dot plot, the evaluation function for the mean square error of the wavefront, the evaluation function for the optical transfer function, the evaluation function for relative illumination, the evaluation function for distortion, the evaluation function for the effective focal length, the evaluation function for the working F number, the evaluation function for the total system length, the evaluation function for the system back intercept, the evaluation function for the air gap, the evaluation function for the thickness of the lens center and edge, the evaluation function for the slope of the lens surface, and the evaluation function for the maximum ray deflection angle. S32. For each processed initial thin lens structure, the evaluation functions of all initial thin lens structures are weighted and summed to obtain the objective function of the initial thin lens structure. S33. The objective function of each processed initial thin lens structure is processed using an automatic differentiation method to obtain the gradient of the parameters in the corresponding processed initial thin lens structure. S34. Based on the gradient of the parameters in the processed initial thin lens structure, the gradient descent-based optimization algorithm is used to optimize each processed initial thin lens structure to obtain the optimized thin lens structure.

8. The method for generating an initial optical structure according to claim 1, characterized in that, Step S4 is as follows: S41. Based on the optimized thin lens structure, obtain several evaluation indicators for each optimized thin lens structure. The evaluation metrics include the root mean square radius of the dot plot, optical transfer function, relative illumination, distortion, and total system length. S42. Weighted summation of all evaluation indicators for each optimized thin lens structure to obtain a comprehensive evaluation of each optimized thin lens structure; S43. Select the optimized thin lens structure with the highest comprehensive evaluation from all optimized thin lens structures, and perform parameter fine-tuning on each parameter of the selected optimized thin lens structure to finally obtain the optimal initial optical structure.

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