Automatic optimization method of reflective optical system

Abstract

The invention discloses an automatic optimization method of a reflective optical system, and solves the problems that the optimization method of the existing optical system needs a large amount of sample data, the calculation speed is low or the application range is narrow. The front structure and the rear structure are divided, the evaluation surface is added between the front structure and the rear structure, and the original detection surface is combined, so that on one hand, the effect of limiting the whole structure is achieved, and on the other hand, the process of simultaneously optimizing all original mirror surfaces is decomposed into the process of optimizing the front structure and the rear structure independently, and the structure optimization progress is accelerated; in addition, by introducing an optimization mode of firstly reducing the aperture of the primary mirror and then gradually increasing the aperture of the primary mirror, irrelevant parameter changes can be eliminated, and then a large number of parameter combinations with low optical performance can be eliminated in a parameter change space, so that the whole optimization process is more efficient and stable.

Description

Technical Field

[0001] This invention relates to an optimization method for optical systems, and more specifically to an automated optimization method for a reflective optical system. Background Technology

[0002] As the demand for high-resolution observation systems in space continues to increase, the importance of large-aperture reflective space optical systems in defense and commercial remote sensing is also gradually growing. The wide spectral range and absence of chromatic aberration of reflective optical systems make them a superior choice for high-resolution Earth observation systems in space remote sensing and astronomical observation.

[0003] The initial structure of a conventional reflective optical system is based on the third-order aberration theory. The initial parameters that meet the design requirements are solved by simultaneously solving the analytical expressions of the system structural parameters and aberration coefficients. Particle swarm optimization or genetic algorithms are also used to solve for the initial structure of reflective optical systems, but these methods have slow computation and convergence speeds. Another approach involves using large-scale neural networks combined with a large number of similar optical structures to map parameters and obtain the required structural parameters. For example, Côté et al. incorporated fully connected networks (FC) and recurrent neural networks (RNNs) into the automated optical design process. This approach requires a large number of reference optical structures to generate the training dataset and also consumes relatively large computational resources. Xinge Yang et al. introduced the concept of course learning into the design of refractive optical systems, but this method is mainly for small-aperture systems, and issues such as sagittal and accuracy requirements are not prominent. The optimized results cannot be used for large-aperture optical systems, limiting its applicability. Summary of the Invention

[0004] To address the technical problems of existing optical system optimization methods requiring large amounts of sample data, having slow computation speeds, or having narrow applicability, this invention provides an automated optimization method for reflective optical systems.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: An automated optimization method for a reflective optical system, characterized by the following steps: Step 1: Construct a reflective differentiable geometric tracing engine; the reflective differentiable geometric tracing engine includes multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control terms, mirror shape constraints, and principal axis direction imaging accuracy enhancement terms. Step 2: Establish a basic configuration library for reflective optical systems. The basic configuration library includes the basic configurations of various reflective optical systems. The basic configuration includes the number of mirrors and the aperture, spacing, focal length, field of view, curvature of the reflecting surface, and quadratic surface coefficient of each mirror, as well as the position of the detection surface. Step 3: Select the target basic configuration from the basic configuration library, input the target basic configuration into the differentiable geometry tracing engine, and reduce the aperture of the primary reflector in the target basic configuration to K% of its original size (30≤K≤90). The spacing between other reflectors, focal length, field of view, reflective surface curvature, and quadratic surface coefficients will then change accordingly. The following steps are then performed based on the differentiable geometry tracing engine: Step 3.1: Take the primary and secondary mirrors in the target basic configuration as the front structure and the other mirrors as the rear structure, and set an evaluation surface between the front and rear structures; the evaluation surface and the focal plane of the front structure are on the same plane, and the light rays after passing through the front structure can form a light spot on the evaluation surface. Step 3.2: Set up a surface light source between the front structure and the rear structure; the size of the surface light source is consistent with the size of the light spot that can be formed on the evaluation surface, and the emission cone angle of the surface light source is consistent with the convergence angle of the front structure. At the same time, the working end of the surface light source faces the rear structure. Step 3.3: The light emitted from the surface light source is converged onto the detection surface after passing through the rear structure to obtain the first light spot; at the same time, parallel light is incident on the front structure, and the parallel light is converged onto the evaluation surface after passing through the front structure to obtain the second light spot; Step 3.4: Calculate the changes in parameters of each mirror in the next step using the first and second light spots, and simultaneously optimize the multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control conditions, mirror shape constraints, and principal axis direction imaging accuracy enhancement conditions. Step 3.5: Based on the calculated changes in the parameters of each mirror, increase the parameters of each mirror accordingly, and return to step 3.1 until the aperture of the main mirror is changed to 100% of its original value. Then, the mirror shape constraint, focal length deviation control condition, and multi-field RMS imaging quality constraint are optimized to the best state. The mirror parameters corresponding to the best state are the optimal parameters, and the optimization is completed.

[0006] Furthermore, in step 1, the multi-field RMS imaging quality constraint condition for: ; in, Represents the weights of different fields of view. Let be the intersection point of the j-th effective ray in the i-th field of view on the focal plane; Let be the centroid of all intersection points in the i-th field of view; This refers to the amount of light.

[0007] Furthermore, in step 1, the substructure RMS constraint conditions and for: ; in, The number of light rays corresponding to the front structure. The number of lights in the rear structure. At the focal plane of the primary and secondary lenses The intersection of the effective light rays, The centroid of all intersections at the focal planes of the primary and secondary mirrors; For the detection surface at the first The intersection of the effective light rays, Let be the centroid of all intersection points of the probe surface.

[0008] Furthermore, in step 1, the focal length deviation control term condition for: ; in, This represents the actual focal length calculated in the current iteration. This represents the target desired focal length corresponding to the final optimization result.

[0009] Furthermore, in step 1, the mirror shape constraint condition for: ; in, Let r be the set of indices of all the mirror surfaces, where r is the mirror parameter. Let be the sagittal value of the k-th mirror.

[0010] Furthermore, in step 1, the condition for the imaging accuracy enhancement term in the main axis direction... for: ; in, Main axis direction The intersection of the effective light rays on the detection surface, The centroid of all effective ray intersections at the probe surface; This is the minimum acceptable threshold.

[0011] The beneficial effects of this invention are: 1. This invention divides the structure into a front structure and a rear structure, and adds an evaluation surface between them. Combined with the original detection surface, this serves to limit the overall structure and decomposes the original process of optimizing all mirrors simultaneously into separate optimization processes for the front and rear structures. This accelerates the optimization process and improves its stability. Furthermore, by introducing an optimization method that first reduces the primary mirror aperture and then gradually increases it, irrelevant parameter changes can be eliminated. This allows for the elimination of a large number of parameter combinations with low optical performance within the parameter variation space, making the entire optimization process more efficient and stable.

[0012] 2. This invention utilizes the evaluation surface position set between the front and rear structures and the geometric angle relationship under the 0 field of view condition (i.e., the output light cone angle of the surface light source is consistent with the convergence angle of the front structure). This physical structure-driven optimization scheme has strong portability, does not require a large amount of sample data, and only requires a basic configuration similar to the target requirements, making the optimization method simpler and easier to implement, and with high accuracy. At the same time, this method can be transferred to other optical systems in multiple scenarios such as space optics and ground-based observation, and has a wide range of applications. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the reflective optical system in an embodiment of the present invention; Figure 2 This is a comparison diagram of the changes in the aperture of the optical system during the optimization process in this embodiment of the invention; Figure 3 This is a comparison chart of the MTF of the optimization results of the optimization method of the present invention and the optimization method of the Zemax software post-processing under the same optimization objective in the embodiments of the present invention, wherein (a) is a comparison chart of the MTF of the optimization results of the Zemax software and (b) is a comparison chart of the MTF of the optimization results of the present invention.

[0014] The attached figures are labeled as follows: 1-Primary mirror, 2-Secondary mirror, 3-Third mirror, 4-Fourth mirror, 5-Detection surface. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] An automated optimization method for a reflective optical system provided by an embodiment of the present invention includes the following steps: Step 1: Construct a reflective differentiable geometric tracing engine. This reflective differentiable geometric tracing engine includes multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control terms, mirror shape constraints, and principal axis direction imaging accuracy enhancement terms. The introduction of these conditions can improve the accuracy, convergence speed, and flexibility of the automatic optimization method.

[0017] in: Multi-field RMS imaging quality constraints for: ; In the formula, Represents the weights of different fields of view. Let be the intersection point of the j-th effective ray in the i-th field of view on the focal plane; Let be the centroid of all intersection points in the i-th field of view; This refers to the amount of light.

[0018] Substructure RMS constraints and for: ; In the formula, The number of light rays corresponding to the front structure. The number of lights in the rear structure. At the focal plane of the primary and secondary lenses The intersection of the effective light rays, The centroid of all intersections at the focal planes of the primary and secondary mirrors; For the detection surface at the first The intersection of the effective light rays, Let be the centroid of all intersection points of the probe surface.

[0019] Focal length deviation control conditions for: ; In the formula, This represents the actual focal length calculated in the current iteration. This represents the target desired focal length corresponding to the final optimization result.

[0020] Mirror shape constraints for: ; in, Let r be the set of indices of all the mirror surfaces, where r is the mirror parameter. Let be the sagittal value of the k-th mirror.

[0021] Conditions for enhancing imaging accuracy in the main axis direction for: ; In the formula, Main axis direction The intersection of the effective light rays on the detection surface, The centroid of all effective ray intersections at the probe surface; This is the minimum acceptable threshold.

[0022] Step 2: Establish a basic configuration library for reflective optical systems. The basic configuration library includes the basic configurations of various reflective optical systems. The basic configuration includes the number of mirrors and the aperture, spacing, focal length, field of view, curvature of the reflecting surface and quadratic surface coefficient of each mirror, as well as the position of the detection surface. In this embodiment, the basic configuration in the basic configuration library is the initial structure of conventional optical design or conventional different reflective optical systems. In a deep learning framework (such as PyTorch or TensorFlow), the structural parameters of the initial structure, such as the radius of curvature, quadratic surface coefficients, higher-order term coefficients, and inter-mirror distance, are transformed into the corresponding basic configuration function according to the characteristics of reflection tracing. The different task requirements are written into yml files to facilitate parameter optimization and calling. Based on the given detector image plane size, the final focal length requirement and field of view requirement corresponding to the optimization requirements are automatically given.

[0023] Step 3: Select the target basic configuration from the basic configuration library, input the target basic configuration into the differentiable geometry tracing engine, and reduce the aperture of the primary reflector in the target basic configuration to K% of the original size (30≤K≤90). Then the spacing, focal length, field of view, curvature of the reflecting surface, and quadratic surface coefficient of the other reflectors will change accordingly. Specifically, the target basic configuration selected in this embodiment is a reflective optical system including a primary mirror 1, a secondary mirror 2, a third mirror 3, a fourth mirror 4, and a detection surface 5; such as Figure 1 As shown, in the reflective optical system, the primary mirror 1 (i.e., the primary reflector) is a concave quadrature surface mirror with a light-passing hole in its middle; the secondary mirror 2 is located on one side of the reflecting surface of the primary mirror 1 and corresponds to the light-passing hole; the third mirror 3 and the fourth mirror 4 are located on the other side of the primary mirror 1; the detection surface 5 is located between the primary mirror 1 and the third mirror 3 and the fourth mirror 4. A plane reflector is located on one side of the detection surface 5, but this plane reflector only serves to reflect the light path and does not participate in the optimization.

[0024] like Figure 2 As shown, specifically, the aperture of the primary mirror 1 is reduced to 50% of its original size, i.e., K is set to 50, leaving room for optimization as the aperture is gradually increased in the future.

[0025] The following steps are performed based on a differentiable geometric tracing engine: Step 3.1: Take the primary and secondary mirrors in the target basic configuration as the front structure and the other mirrors as the rear structure, and set an evaluation surface between the front and rear structures; the evaluation surface is on the same plane as the focal plane of the front structure, and the light rays after passing through the front structure can form a light spot on the evaluation surface. like Figure 1 As shown, specifically, the primary mirror 1 and secondary mirror 2 are used as the front structure, and the third mirror 3 and fourth mirror 4 are used as the rear structure. An evaluation surface is set between the front structure and the rear structure.

[0026] Step 3.2: Set up a surface light source between the front structure and the rear structure; the size of the surface light source is consistent with the size of the light spot that can be formed on the evaluation surface, and the exit cone angle of the surface light source is consistent with the convergence angle of the front structure. At the same time, the working end of the surface light source faces the rear structure. The light source tracing cone angle of the rear structure is consistent with the cone angle of the front structure system under zero field of view, and the radius of its simulated light cone surface light source is the root mean square radius generated by the tracing of the front structure. In the evaluation function, in addition to the root mean square radii of the front and rear structures, other convergence constraints include focal length constraints, manufacturability mirror shape constraints, principal axis direction enhancement terms, etc.

[0027] Step 3.3: The light emitted from the surface light source is converged onto the detection surface 5 in the target base configuration after being acted upon by the rear structure, thus obtaining the first light spot; at the same time, parallel light is incident on the front structure, and the parallel light is converged onto the evaluation surface after being acted upon by the front structure, thus obtaining the second light spot. The performance of the added evaluation surface and the original detection surface 5 represents the quality of the reflective optical system. By adding functions corresponding to multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control terms, mirror shape constraints, and principal axis imaging accuracy enhancement terms as loss functions, the gradient is automatically calculated in backpropagation using the automatic differentiation mechanism in the differentiable geometric tracing engine, and the parameters are automatically updated. This causes changes in the curvature, spacing, and quadratic surface coefficients of each mirror in the target's basic configuration. These parameter changes bring about new structural parameters. In the next iteration, the performance of the light spots on the new evaluation and detection surfaces triggers a new round of changes in the structural parameters of the reflective optical system until the aperture of the primary mirror is restored to 100%, resulting in reflective optical system structural parameters that meet the new focal length and field of view requirements.

[0028] Step 3.4: Calculate the changes in parameters of each mirror in the next step using the first and second light spots. At the same time, optimize the above-mentioned multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control conditions, mirror shape constraints, and principal axis imaging accuracy enhancement conditions. Backpropagate parameters to influence the iteration of the next aperture through a deep learning automatic differentiation mechanism. Step 3.5: Based on the calculated changes in the parameters of each mirror, change the parameters of each mirror accordingly, and return to step 3.1 until the aperture of the main mirror is changed to 100% of its original value. Then, the mirror shape constraint, focal length deviation control condition, and multi-field RMS imaging quality constraint are optimized to the best state. The parameters of each mirror corresponding to this best state are the optimal parameters. The entire optimization process ends and the structural parameters of the overall reflective optical system are obtained.

[0029] As the primary mirror aperture gradually expands from the initial aperture size to the full aperture, the weights of the central and peripheral fields of view can be flexibly adjusted to obtain results that are closer to the final requirements.

[0030] To verify the effectiveness of the present invention, the above method was tested on an NVIDIA A100 GPU.

[0031] A well-designed four-mirror reflective optical system was selected as the basic configuration and transformed into a basic configuration function. The primary mirror of this optical structure has an aperture of 2200mm, a half field of view of 0.2 degrees, and a focal length of 33333.33mm. The structural parameters of this large-aperture spatial reflection system are shown in the table below:

[0032] After setting the surface order, the detector pixel is set to 16000×16000, corresponding to an image size of 235.8424mm, a half field of view of 0.202657 degrees, and an F-number of 15.15. First, the final optimized target requirement is changed, and the focal length is changed to 31000mm. The image size under the new optimized target is automatically calculated to be 219.2967mm, with a half field of view of 0.202657 degrees and an F-number of 14.0909.

[0033] The initial aperture was set to 50% of the initial configuration. The aperture was then gradually increased until it reached 100%, at which point the iteration process ended. The obstruction rate was set to the ratio of the secondary and primary mirror apertures, i.e., 0.1975. The initial center field of view, 0.7 field of view, and full field of view were weighted at a ratio of 1:1:1. The initial propagation distance was set to 2200 mm.

[0034] The entire optical system is divided into a front structure and a rear structure. Through a differentiable reflected ray tracing process, a conical divergence function of the rear system is created using geometric structural relationships. Separate evaluation requirements for the rear structure are constructed. The root mean square radii of the overall optical system and the separate systems of the front and rear structures are simultaneously added to the evaluation function. Convergence constraints such as focal length constraint, manufacturability mirror shape constraint, and principal axis direction enhancement are added for joint optimization. Among them, the focal length constraint has a larger weight, the weight ratio of the root mean square radius of the front structure and the rear structure is 1:1, and the manufacturability mirror shape constraint sag is set to 25mm. The parameters are backpropagated using PyTorch's automatic differentiation mechanism to influence the iteration of the next aperture. At the same time, functions such as visualization of loss curves and root mean square radius evolution curves are written to facilitate evaluation of optimization results and flexible adjustments. When the optimization process increases from the initial aperture of the aperture stop (e.g., 50% of the basic configuration aperture) to 100% of the full aperture, the entire optimization process ends and the overall structural parameters of the mirror are obtained. The learning rates for the initial iterations of the radius of curvature, spacing, and quadratic surface coefficients are 5e-6, 1, and 8e-3, respectively, with an attenuation coefficient of 0.02 and 400 iterations. When the optimization process is halfway complete, the focal length weight and edge field of view weights are further increased, with the focal length weight doubling and the edge field of view weight doubling. The final structural changes during the optimization process are shown in the comparison diagram below. Figure 2 As shown, with the continuous increase in aperture stop diameter, the initial configuration gradually transforms into the final required structure. Figure 3 The diagram shows a comparison of the optical performance results of the MTF curves of the optimization method (b) of this invention and the optimization algorithm (a) built into Zemax, which are post-processed by Zemax software, under the same optimization target (i.e., the focal length changes from 33333.33mm to 31000mm). It can be seen that the automatic optimization method provided by this invention can enable the reflective optical system to achieve better optical performance.

[0035] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An automated optimization method for a reflective optical system, characterized in that, Includes the following steps: Step 1: Construct a reflective differentiable geometric tracing engine; the reflective differentiable geometric tracing engine includes multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control terms, mirror shape constraints, and principal axis direction imaging accuracy enhancement terms. Step 2: Establish a basic configuration library for reflective optical systems. The basic configuration library includes the basic configurations of various reflective optical systems. The basic configuration includes the number of mirrors and the aperture, spacing, focal length, field of view, curvature of the reflecting surface, and quadratic surface coefficient of each mirror, as well as the position of the detection surface. Step 3: Select the target basic configuration from the basic configuration library, input the target basic configuration into the differentiable geometry tracing engine, and reduce the aperture of the primary reflector in the target basic configuration to K% of its original size (30≤K≤90). The spacing between other reflectors, focal length, field of view, reflective surface curvature, and quadratic surface coefficients will then change accordingly. The following steps are then performed based on the differentiable geometry tracing engine: Step 3.1: Take the primary and secondary mirrors in the target basic configuration as the front structure and the other mirrors as the rear structure, and set an evaluation surface between the front and rear structures; the evaluation surface and the focal plane of the front structure are on the same plane, and the light rays after passing through the front structure can form a light spot on the evaluation surface. Step 3.2: Set up a surface light source between the front structure and the rear structure; the size of the surface light source is consistent with the size of the light spot that can be formed on the evaluation surface, and the emission cone angle of the surface light source is consistent with the convergence angle of the front structure. At the same time, the working end of the surface light source faces the rear structure. Step 3.3: The light emitted from the surface light source is converged onto the detection surface after passing through the rear structure to obtain the first light spot; at the same time, parallel light is incident on the front structure, and the parallel light is converged onto the evaluation surface after passing through the front structure to obtain the second light spot; Step 3.4: Calculate the changes in parameters of each mirror in the next step using the first and second light spots, and simultaneously optimize the multi-field RMS imaging quality constraints, substructure RMS constraints, focal length deviation control conditions, mirror shape constraints, and principal axis direction imaging accuracy enhancement conditions. Step 3.5: Based on the calculated changes in the parameters of each mirror, change the parameters of each mirror accordingly, and return to step 3.1 until the aperture of the main mirror is changed to 100% of its original value. Then, the mirror shape constraint, focal length deviation control condition, and multi-field RMS imaging quality constraint are optimized to the best state. The mirror parameters corresponding to the best state are the optimal parameters, and the optimization is completed.

2. The automated optimization method for a reflective optical system according to claim 1, characterized in that: In step 1, the multi-field RMS imaging quality constraint conditions for: ； in, The weights representing different fields of view. Let be the intersection point of the j-th effective ray in the i-th field of view on the focal plane; Let be the centroid of all intersection points in the i-th field of view; This refers to the amount of light.

3. The automated optimization method for a reflective optical system according to claim 2, characterized in that: In step 1, the substructure RMS constraint conditions and for: ； in, The number of light rays corresponding to the front structure. The number of lights in the rear structure. At the focal plane of the primary and secondary lenses The intersection of the effective light rays, The centroid of all intersections at the focal planes of the primary and secondary mirrors; For the detection surface at the first The intersection of the effective light rays, Let be the centroid of all intersection points of the probe surface.

4. The automated optimization method for a reflective optical system according to claim 3, characterized in that: In step 1, the focal length deviation control term condition for: ； in, This represents the actual focal length calculated in the current iteration. This represents the target desired focal length corresponding to the final optimization result.

5. The automated optimization method for a reflective optical system according to claim 4, characterized in that: In step 1, the mirror shape constraint condition for: ； in, Let r be the set of indices of all the mirror surfaces, where r is the mirror parameter. Let be the sagittal value of the k-th mirror.

6. The automated optimization method for a reflective optical system according to claim 5, characterized in that: In step 1, the condition for the imaging accuracy enhancement term in the main axis direction for: ； in, Main axis direction The intersection of the effective light rays on the detection surface, The centroid of all effective ray intersections at the probe surface; This is the minimum acceptable threshold.

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