Optical initial structure generation method based on micro ray tracing

Abstract

The invention discloses an optical initial structure generation method based on micro ray tracing. The method comprises the steps of firstly obtaining a first-order structure of the optical system, optimizing the first-order structure of the optical system to obtain an optimized first-order structure of the optical system, and obtaining and screening a plurality of processed initial thin lens structures according to the first-order structure of the optical system, and processing each processed initial thin lens structure by adopting a plurality of methods in sequence to obtain corresponding optimized thin lens structures, and carrying out comprehensive processing according to all the optimized thin lens structures to finally obtain an optimal optical initial structure. The beneficial effect of generating the excellent first-order structure of the optical system is achieved, the advantage of screening the optimal optical initial structure from multiple groups of structures is brought, and the progress of being simple in operation, higher in automation degree and capable of remarkably improving the optical design efficiency is achieved.

Description

Technical Field

[0001] The present invention belongs to the field of optical imaging design, and particularly relates to an optical initial structure generation method based on differentiable ray tracing. Background Art

[0002] When an optical designer designs a lens, it is usually necessary to rely on commercial software such as ZEMAX or CODEV, and go through multiple rounds of manual control iteration and optimization, which largely depends on the design experience of the optical designer. For more complex optical systems, the quality of the design results largely depends on the selected initial structure. Currently, the methods for obtaining the initial structure of an optical system mainly include the PWC method, the patent search method, and the first-order structure generation method, but all of these three methods have some defects. The PWC method is based on the primary aberration theory, and obtains the structural parameters of the lens by solving the primary aberration equations. It is suitable for simple systems, but still requires the optical designer to master the optical principle and aberration theory proficiently to select parameters. For more complex optical systems, the PWC method will have no solution or multiple solutions. The patent search method is to select a lens with an initial structure similar to the design requirements according to the publicly available optical system patents, and the optical designer adjusts the system parameters according to the design experience to obtain the initial structure. However, when facing some complex lenses with special design requirements, it is difficult to find similar patents, and it cannot meet the diverse design requirements and the exploration of new lens architectures. The first-order structure generation method is usually based on theory, and obtains a good optical first-order structure by optimizing the figure. However, in the process of converting the optical first-order structure to the actual lens structure, it still depends on the designer to select and optimize the initial lens with the help of existing commercial software and design experience. Summary of the Invention

[0003] In order to solve the problems existing in the background art, the present invention provides an optical initial structure generation method based on differentiable ray tracing, which solves the problem of the lack of practical, efficient and fast solution methods in the initial design stage of an optical imaging system.

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

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

[0006] S2. Sequentially process the optimized first-order structure of the optical system by 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, successively perform processing using the differentiable actual ray tracing method, weighted summation, automatic differentiation method, and the optimization algorithm based on gradient descent to obtain the optimized thin lens structure.

[0008] S4. Obtain the corresponding evaluation indicators according to the optimized thin lens structure, and successively perform weighted summation, screening, and parameter fine-tuning processing based on the evaluation indicators of all optimized thin lens structures to obtain the optimal optical initial structure.

[0009] The optimization algorithm based on gradient descent in step S1 and step S4 includes the stochastic gradient descent algorithm, the gradient descent algorithm combined with momentum, and the gradient descent algorithm with adaptive learning rate.

[0010] Step S1 is specifically 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 the working wavelength band, focal length, field of view, working F-number, number of components, total system length, system back focal length, component spacing, relative illumination at the edge of the field of view, distortion, and modulation transfer function for the full field of view.

[0013] The optical system design requirements also include processing conditions, and the processing conditions 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. Use the differentiable paraxial ray tracing method to trace the first-order structure of the optical system to obtain the first-order evaluation function.

[0015] S13. Use the automatic differentiation method to process the first-order evaluation function to obtain the gradient of the parameters in the first-order structure of the optical system.

[0016] S14. According to the gradient of the parameters in the first-order structure of the optical system, use the optimization algorithm based on gradient descent to optimize the first-order structure of the optical system to obtain the optimized first-order structure of the optical system.

[0017] The first-order evaluation function in step S12 includes one or a combination of multiple of the component spacing constraint, the system back focal length constraint, the total system length constraint, the primary spherical aberration constraint, the primary coma constraint, the primary astigmatism constraint, the primary field curvature constraint, the primary distortion constraint, the primary longitudinal chromatic aberration constraint, and the primary lateral chromatic aberration constraint.

[0018] The 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 axial chromatic aberration constraint, and primary lateral chromatic aberration constraint are set according to the following formulas:

[0019]

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

[0021]

[0022]

[0023] where L gap represents the component interval constraint; L bfl represents the system back intercept constraint; L ttl represents the system total length constraint; L SI represents the primary spherical aberration constraint; L SII represents the primary coma constraint; L SIII represents the primary astigmatism constraint; L SIV represents the primary field curvature constraint; L SV represents the primary distortion constraint; L CI represents the primary axial chromatic aberration constraint; L CII represents the primary lateral chromatic aberration constraint; T gap represents the lower limit constraint of the component interval; d i represents the component interval; i represents the index; N represents the number of components; T bfl represents the target back intercept; d N represents the distance from the last component to the image plane; T ttl represents the target total length; y i represents the marginal ray height of the i-th component; Φ i represents the optical power of the i-th component; μ i and both represent the auxiliary optimization variables of the i-th component; represents the chief ray height of the i-th component; Q represents the Lagrange invariant of the optical system.

[0024] Step S2 is specifically as follows:

[0025] S21. Process the first-order structure of the optimized optical system according to the thin lens optical power processing method to obtain a number of distinct initial thin lens structures.

[0026] S22. Select the initial thin lens structures that meet the lens shape screening criteria from all the initial thin lens structures according to the lens shape screening criteria, and use each of the selected initial thin lens structures that meet 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] Among them, 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 back 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; t represents the central thickness of the component mapped to the initial thin lens structure.

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

[0031] edge,t∈[Thi1,Thi2]

[0032] c1,c2∈(-R -1 ,R -1 )

[0033]

[0034] Among them, edge represents the edge thickness of the initial thin lens structure; t is the central 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 back surface curvature mapped to the initial thin lens structure; R represents the net aperture radius of the initial thin lens structure; R -1 represents the reciprocal of the net aperture radius.

[0035] Step S3 is specifically as follows:

[0036] S31. Perform tracing processing on each processed initial thin lens structure using the differentiable actual ray tracing method, and obtain several evaluation functions of each processed initial thin lens structure respectively.

[0037] The evaluation functions include the evaluation function of the root mean square radius of the spot diagram, the evaluation function of the wavefront root mean square error, the evaluation function of the optical transfer function, the evaluation function of the relative illumination, the evaluation function of the distortion, the evaluation function of the effective focal length, the evaluation function of the working F-number, the evaluation function of the overall system length, the evaluation function of the back intercept of the system, the evaluation function of the air gap, the evaluation function of the center and edge thicknesses of the lenses, the evaluation function of the lens surface slope, and the evaluation function of the maximum ray deflection angle.

[0038] S32. For each processed initial thin lens structure, perform a weighted sum processing on the evaluation functions of all the initial thin lens structures as the objective function of the initial thin lens structure.

[0039] S33. Use the automatic differentiation method to process the objective function of each processed initial thin lens structure to obtain the gradients of the parameters in the corresponding processed initial thin lens structure.

[0040] The parameters in the processed initial thin lens structure include the curvatures, thicknesses, conic coefficients, glass materials, and higher-order aspheric coefficients of each optical surface.

[0041] S34. According to the gradients of the parameters in the processed initial thin lens structure, use an optimization algorithm based on gradient descent to optimize each processed initial thin lens structure to obtain an optimized thin lens structure.

[0042] Step S4 is specifically as follows:

[0043] S41. According to the optimized thin lens structure, obtain several evaluation indicators of each optimized thin lens structure respectively.

[0044] The evaluation indicators include the root mean square radius of the spot diagram, the optical transfer function, the relative illumination, the distortion, and the overall system length.

[0045] S42. Perform a weighted sum on all the evaluation indicators of each optimized thin lens structure to obtain the comprehensive evaluation of each optimized thin lens structure.

[0046] S43. Screen out the optimized thin lens structure with the highest comprehensive evaluation from the comprehensive evaluations of all the optimized thin lens structures, and perform parameter fine-tuning processing on the various parameters of the screened optimized thin lens structure to finally obtain the optimal optical initial structure.

[0047] The innovation of the present invention lies in adopting methods such as differentiable paraxial ray tracing, optimization algorithm based on gradient descent, thin lens power handling method, lens profile screening conditions, differentiable real ray tracing, etc., achieving the beneficial effect of generating an excellent first-order structure of the optical system, bringing the advantage of screening the optimal optical initial structure from multiple groups of structures, and making progress in terms of simple operation, higher automation degree, and significantly improving the optical design efficiency.

[0048] The beneficial effects of the present invention are as follows:

[0049] 1. By using differentiable paraxial ray tracing, the present invention can start from the optical system design requirements, combine the primary aberration theory and the optimization algorithm based on gradient descent, and automatically generate an excellent first-order structure of the optical system.

[0050] 2. By using the thin lens power handling method and the lens profile screening conditions, the present invention maps the first-order optical structure into multiple different optical initial starting points, realizes large-scale search for multiple starting points of the optical initial structure, and is conducive to discovering new structures.

[0051] 3. By using differentiable real ray tracing, the present invention flexibly sets different evaluation function combinations and optimization variables, and combines with the optimization algorithm based on gradient descent to realize the optimization of multiple groups of differential optical structures, and can screen the obtained multiple groups of structures to obtain the optimal optical initial structure. Description of the Drawings

[0052] Figure 1 For the embodiments of the present invention Figure.

[0053] Figure 2 First-order structure diagram of the optical system for the embodiments of the present invention.

[0054] Figure 3 Structural diagrams of several processed initial thin lenses for the embodiments of the present invention.

[0055] Figure 4 Structural diagram of the thin lens with the highest comprehensive evaluation for the embodiments of the present invention.

[0056] Figure 5 Optimal optical initial structure diagram for the embodiments of the present invention.

[0057] Figure 6 Modulation transfer function diagram of the optimal optical initial structure for the embodiments of the present invention.

[0058] Figure 7 Relative illumination diagram of the optimal optical initial structure for the embodiments of the present invention.

[0059] Figure 8This is the field of view distortion diagram of the optimal optical initial structure in the embodiments of the present invention. Detailed implementation manners

[0060] The present invention will be described in more detail below in conjunction with the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also considered within the protection scope of the present invention. The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

[0061] Embodiment 1

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

[0063] S1. Obtain the first-order structure of the optical system according to the optical system design requirements, and process the first-order structure of the optical system successively by using the differentiable paraxial ray tracing method, the automatic differentiation method, and the optimization algorithm based on gradient descent 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] The optical system design requirements include the working wavelength band, focal length, field of view, working F-number, number of components, total system length, system back focal length, component spacing, relative illumination at the edge of the field of view, distortion, and modulation transfer function over the entire field of view.

[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 quantity of each component includes the marginal ray height, chief ray height, optical power, and component spacing;

[0067] The optical system design requirements also include processing conditions, and the processing conditions include the clear 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. Use the differentiable paraxial ray tracing method to trace the first-order structure of the optical system to obtain a first-order evaluation function.

[0069] In specific implementation, the differentiable paraxial ray tracing method starts from Gaussian optical theory, combines modern machine learning frameworks such as PyTorch, TensorFlow, or JAX, and realizes automatically constructing a computational graph during the forward paraxial ray tracing process and automatically recording the intermediate variables during the operation process.

[0070] The first-order evaluation function includes one or a combination of multiple ones among the component interval constraint, the system back intercept constraint, the system total length constraint, the primary spherical aberration constraint, the primary coma constraint, the primary astigmatism constraint, the primary field curvature constraint, the primary distortion constraint, the primary longitudinal chromatic aberration constraint, and the primary lateral chromatic aberration constraint.

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

[0072] The component interval constraint, the system back intercept constraint, the system total length constraint, the primary spherical aberration constraint, the primary coma constraint, the primary astigmatism constraint, the primary field curvature constraint, the primary distortion constraint, the primary longitudinal chromatic aberration constraint, and the primary lateral 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 represents the component interval constraint; L bfl represents the system back intercept constraint; L ttl represents the system total length constraint; L SI represents the primary spherical aberration constraint; L SII represents the primary coma constraint; L SIII represents the primary astigmatism constraint; L SIV represents the primary field curvature constraint; L SV represents the primary distortion constraint; L CI represents the primary longitudinal chromatic aberration constraint; L CII represents the primary lateral chromatic aberration constraint; T gap represents the lower limit constraint of the component interval; d i represents the component interval; i represents the index; N represents the number of components; T bfl represents the target back intercept; d N represents the distance from the last component to the image plane; T ttl represents the target total length; y i represents the marginal ray height of the i-th component; Φ i represents the optical power of the i-th component; μ i and both represent the auxiliary optimization variables of the i-th component; represents the chief ray height of the \(i\)-th component; \(Q\) represents the Lagrange invariant of the optical system.

[0077] In the forward-differentiable paraxial ray tracing, the relationship formulas between various variables are 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] Among them, \(q\) i+1 represents the marginal ray aperture angle of the \((i + 1)\)-th component; \(q\) i represents the marginal ray aperture angle of the \(i\)-th component; \(y\) i represents the marginal ray height of the \(i\)-th component; \(φ\) i represents the optical power of the \(i\)-th component; \(y\) i+1 represents the marginal ray height of the \((i + 1)\)-th component; \(d\) i represents the component interval between the \(i\)-th component and the next component; represents the chief ray aperture angle of the \((i + 1)\)-th component; represents the chief ray aperture angle of the \(i\)-th component; represents the chief ray height of the \(i\)-th component; represents the chief ray height of the \((i + 1)\)-th component.

[0082] S13. Use the automatic differentiation method to process the first-order evaluation function to obtain the gradients of the parameters in the first-order structure of the optical system.

[0083] S14. According to the gradients of the parameters in the first-order structure of the optical system, use the optimization algorithm based on gradient descent to optimize the first-order structure of the optical system to obtain the optimized first-order structure of the optical system.

[0084] The optimization algorithm based on gradient descent includes the stochastic gradient descent algorithm, the gradient descent algorithm with momentum, and the gradient descent algorithm with adaptive learning rate.

[0085] When calculating the gradient, apply the chain rule 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 structure of the optics.

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

[0087] S21. Process the first-order structure of the optimized optical system according to the thin lens power treatment method to obtain several distinct initial thin lens structures.

[0088] The thin lens power treatment method is set according to the following formula:

[0089]

[0090] where Φ represents the 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 central thickness of the component mapped to the initial thin lens structure.

[0091] By leveraging computing platforms such as GPU / TPU, large-scale random sampling of c1 and c2 can be achieved. Then, substituting c1 and c2, as well as the power Φ and refractive index n into the thin lens power treatment formula, large-scale and rapid solution of the thin lens thickness t can be realized.

[0092] S22. Screen out the initial thin lens structures that meet the lens shape screening conditions from all the initial thin lens structures, and regard each initial thin lens structure that meets the lens shape screening conditions as a processed initial thin lens structure.

[0093] The lens shape screening conditions are set according to 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 central 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 represents the reciprocal of the net aperture radius.

[0098] S3. For each processed initial thin lens structure, perform processing using the differentiable actual ray tracing method, weighted summation, automatic differentiation method, and optimization algorithm based on gradient descent in sequence to obtain the optimized thin lens structure.

[0099] S31. Perform ray tracing processing on each processed initial thin lens structure using the differentiable actual ray tracing method to obtain several evaluation functions for each processed initial thin lens structure respectively.

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

[0101] In specific implementation, first obtain the root mean square radius of the spot diagram, the root mean square error of the wavefront, the optical transfer function, the relative illuminance, the distortion, the effective focal length, the working F - number, the total system length, the system back intercept, the air gap, the center and edge thickness of the lens, the lens surface slope, and the maximum ray deflection angle of each processed initial thin lens structure, and then obtain the corresponding evaluation functions.

[0102] S32. For each processed initial thin lens structure, perform weighted summation processing on the evaluation functions of all initial thin lens structures as the objective function of the initial thin lens structure.

[0103] S33. Use the automatic differentiation method to process the objective function of each processed initial thin lens structure 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 high - order aspheric coefficient of each optical surface.

[0105] S34. According to the gradient of the parameters in the processed initial thin lens structure, use the optimization algorithm based on gradient descent to perform optimization processing on each processed initial thin lens structure to obtain the optimized thin lens structure.

[0106] The optimization algorithm based on gradient descent includes the stochastic gradient descent algorithm, the gradient descent algorithm combined with momentum, and the gradient descent algorithm with adaptive learning rate.

[0107] Differentiable physical ray tracing is based on the principle of geometric ray propagation. It alternately calculates the intersection points of incident rays and optical surfaces, as well as the direction cosines of the outgoing rays, thereby establishing the propagation path of rays in an actual optical system. During forward physical ray tracing, a computational graph is automatically constructed, and intermediate variables during the operation are recorded, so that the chain rule can be applied layer by layer during gradient calculation to calculate the gradient of the objective function with respect to the parameters in the processed initial thin lens structure.

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

[0109] S41. According to each optimized initial thin lens structure, obtain several evaluation indicators of each optimized initial thin lens structure respectively.

[0110] The evaluation indicators include, but are not limited to, the root mean square radius of the spot diagram, optical transfer function, relative illuminance, distortion, and system total length.

[0111] S42. Perform weighted summation on all evaluation indicators of each optimized initial thin lens structure to obtain the comprehensive evaluation of each optimized initial thin lens structure.

[0112] S43. Screen out the optimized thin lens structure with the highest comprehensive evaluation from the comprehensive evaluations of all optimized initial thin lens structures, and perform parameter fine-tuning processing on each parameter of the screened optimized thin lens structure to finally obtain the optimal initial optical structure.

[0113] In specific implementation, the parameter fine-tuning processing is to perform parameter fine-tuning on each parameter of the screened optimized thin lens structure through commercial optical software.

[0114] Embodiment 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 optical system design requirements in the implementation include:

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

[0118] In implementation, according to the design requirements of the optical system, 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] Among them, y1 represents the marginal 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; represents the chief ray height of the image plane; θ FoV represents the field of view angle; represents the chief ray height of the first component; y img represents the marginal ray height of the image plane;

[0123] In implementation, the established first-order evaluation function takes into account all the constraints of the optical system's external dimensions and primary aberrations, and the obtained optical first-order evaluation function is:

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

[0125] Among them, L represents the first-order evaluation function; L gap represents the component interval constraint; L bfl represents the system back focal length constraint; L ttl represents the system overall length constraint; L SI represents the primary spherical aberration constraint; L SII represents the primary coma aberration constraint; L SIII represents the primary astigmatism constraint; L SIV represents the primary field curvature constraint; L SV represents the primary distortion constraint; L CI represents the primary longitudinal chromatic aberration constraint; L CII represents the primary lateral chromatic aberration constraint;

[0126] The random gradient descent algorithm is used to optimize the parameters in the first-order structure of the optical system. The optimized first-order structure of the optical system is shown in Table 1, and the corresponding Figure ( where \(h\) represents the chief ray height and \(y\) represents the marginal ray height), and the first-order structure diagrams are respectively as Figure 1 and Figure 2 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] According to the thin lens power treatment method, the first-order structure of the optimized optical system is processed to obtain a number of different initial thin lens structures, and then through lens shape screening conditions, such as Figure 3 shown to obtain a number of processed initial thin lens structures.

[0130] Based on differentiable actual ray tracing, multiple processed initial thin lens structures are optimized. First, an objective function is established. In the initial design stage, consider the evaluation function of the RMS radius of the spot diagram, the evaluation function of distortion, the evaluation function of the effective focal length, the evaluation function of the working F-number, the evaluation function of the total system length, the evaluation function of the back focal length of the system, the evaluation function of the air gap, the evaluation function of the center and edge thickness of the lens, the evaluation function of the lens surface slope, and the evaluation function of the maximum ray deflection angle. The final objective function is the weighted sum of the above evaluation functions.

[0131] The gradient descent algorithm with an adaptive learning rate is used to optimize the parameters in multiple groups of processed initial thin lens structures to obtain the optimized initial thin lens structures. With the help of computing platforms such as GPU / TPU, the automatic search and iterative optimization of the initial structure starting from a large scale can be efficiently realized. The optimization variables are curvature, thickness, material, and conic coefficient, as well as the coefficients of the 4th, 6th, 8th, and 10th even aspheric terms.

[0132] After the optimization is completed, the corresponding evaluation indexes are obtained according to the optimized thin lens structure, and the weighted sum screening is carried out in turn according to the evaluation indexes of all optimized thin lens structures to screen the thin lens structure with the highest comprehensive evaluation, such as Figure 4 shown.

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

[0134] As Figure 6Shown is the modulation transfer function graph of the optimal optical initial structure of the rear imaging lens of a mobile phone. Figure 7 It is the relative illumination graph of the optimal optical initial structure of the rear imaging lens of a mobile phone. Figure 8 It is the field of view distortion graph of the optimal optical initial structure of the rear imaging lens of a mobile phone.

[0135] The present invention realizes the beneficial effect of generating an excellent first-order structure of the optical system, brings the advantage of screening the optimal optical initial structure from multiple groups of structures, and makes progress in terms of simple operation, higher automation degree, and significantly improving the optical design efficiency.

[0136] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the spirit of the present invention and the scope protected by the claims, those of ordinary skill in the art can make many specific transformations in various forms under the inspiration of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. An optical initial structure generation method 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 optical system design requirements, and process the first-order structure of the optical system successively by using the differentiable paraxial ray tracing method, the automatic differentiation method, and the optimization algorithm based on gradient descent to obtain the optimized first-order structure of the optical system; S2. Process the optimized first-order structure of the optical system successively by using the thin lens power treatment method and the lens shape screening conditions to obtain several processed initial thin lens structures; S3. Process each processed initial thin lens structure successively by using the differentiable real ray tracing method, weighted summation, the automatic differentiation method, and the optimization algorithm based on gradient descent to obtain the optimized thin lens structure; S4. Obtain the corresponding evaluation indexes according to the optimized thin lens structure, and perform weighted summation, screening, and parameter fine-tuning processing successively according to the evaluation indexes of all optimized thin lens structures to obtain the optimal optical initial structure.

2. The optical initial structure generation method according to claim 1, characterized in that: The optimization algorithm based on gradient descent in steps S1 and S4 includes the stochastic gradient descent algorithm, the gradient descent algorithm combined with momentum, and the gradient descent algorithm with adaptive learning rate.

3. The method for generating an optical initial structure according to claim 1, wherein Step S1 is specifically: 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 according to the entrance pupil radius and image height; The optical system design requirements include the working wavelength band, focal length, field of view, working F-number, number of components, total system length, system back focal length, component interval, relative illumination of the marginal field of view, distortion, and modulation transfer function of the full field of view; S12. Trace the first-order structure of the optical system by using the differentiable paraxial ray tracing method to obtain the first-order evaluation function; S13. Process the first-order evaluation function by using the automatic differentiation method to obtain the gradient of the parameters in the first-order structure of the optical system; S14. Optimize the first-order structure of the optical system by using the optimization algorithm based on gradient descent according to the gradient of the parameters in the first-order structure of the optical system to obtain the optimized first-order structure of the optical system.

4. The optical initial structure generation method according to claim 3, characterized in that: The first-order evaluation function in step S12 includes one or a combination of more of the component interval constraint, system back focal length constraint, total system length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary longitudinal chromatic aberration constraint, and primary lateral chromatic aberration constraint.

5. The optical initial structure generation method according to claim 4, characterized in that: The component interval constraint, system back focal length constraint, total system length constraint, primary spherical aberration constraint, primary coma constraint, primary astigmatism constraint, primary field curvature constraint, primary distortion constraint, primary longitudinal chromatic aberration constraint, and primary lateral chromatic aberration constraint are set according to the following formulas: L bfl = max(T bfl - d N , 0) Among them, L gap represents the component interval constraint; L bfl represents the system back intercept constraint; L ttl represents the system total length constraint; L SI represents the primary spherical aberration constraint; L SII represents the primary coma aberration constraint; L SIII represents the primary astigmatism constraint; L SIV represents the primary field curvature constraint; L SV represents the primary distortion constraint; L CI represents the primary longitudinal chromatic aberration constraint; L CII represents the primary lateral chromatic aberration constraint; T gap represents the lower limit constraint of the component interval; d i represents the component interval; i represents the index; N represents the number of components; T bfl represents the target back intercept; d N represents the distance from the last component to the image plane; T ttl represents the target total length; y i represents the marginal ray height of the i-th component; Φ i represents the optical power of the i-th component; μ i and both represent the auxiliary optimization variables of the i-th component; represents the chief ray height of the i-th component; Q represents the Lagrange invariant of the optical system.

6. The method for generating an optical initial structure according to claim 1, characterized in that Step S2 is specifically: S21. Process the optimized first-order structure of the optical system according to the thin lens power treatment method to obtain several different initial thin lens structures; S22. Screen out the initial thin lens structures that meet the lens shape screening conditions from all the initial thin lens structures according to the lens shape screening conditions, and use each of the screened initial thin lens structures that meet the lens shape screening conditions as the processed initial thin lens structure.

7. The optical initial structure generation method according to claim 6, wherein: The thin lens optical power processing method in step S21 is set according to the following formula: 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 central thickness of the component mapped to the initial thin lens structure.

8. The optical initial structure generation method according to claim 6, wherein: The lens shape screening conditions in step S22 are set according to the following formula: edge,t∈[Thi1,Thi2] c1, c2 ∈ (-R -1 , R -1 ) Among them, edge represents the edge thickness of the initial thin lens structure; t is the central 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 back surface curvature mapped to the initial thin lens structure; R represents the net aperture radius of the initial thin lens structure; R -1 represents the reciprocal of the net aperture radius.

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

10. The method for generating an optical initial structure according to claim 1, characterized in that, Step S4 is specifically as follows: S41. According to the optimized thin lens structure, obtain several evaluation indicators for each optimized thin lens structure; The evaluation indicators include the root mean square radius of the spot diagram, the optical transfer function, the relative illumination, the distortion, and the total system length; S42. Perform weighted summation on all the evaluation indicators of each optimized thin lens structure to obtain the comprehensive evaluation of each optimized thin lens structure; S43. Screen out the optimized thin lens structure with the highest comprehensive evaluation from the comprehensive evaluations of all the optimized thin lens structures, and perform parameter fine-tuning processing on each parameter of the screened optimized thin lens structure to finally obtain the optimal optical initial structure.

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