An Initial Structural Design Method for a Stationary Zoom System Based on Analytical Region Definition

Abstract

A method for designing the initial structure of a stationary zoom system includes the following steps: S1, establishing the basic structure of a classic stationary zoom system, determining the mathematical range of key parameters of the intermediate zoom group, and realizing the partitioning of the solution region and parameter dimensionality reduction; S2, introducing a rear focusing group, and introducing minimum braking constraints for deformable mirrors and realizing continuous zoom and basic aberration constraints based on free space; S3, establishing a nonlinear evaluation function, and obtaining the globally optimal numerical solution within the boundary conditions of the set variables and the analytical region of the structure. This invention solves the problem of not being able to obtain a convergent solution when directly using optical design software for optimization design. By incorporating the telescope structure into the stationary zoom system to reduce the dimensionality of key parameters, the numerical solution of the initial structure is calculated. This process involves a series of equations and constraints describing the stationary zoom system, which can effectively correct aberrations, achieve high zoom efficiency, and maintain a stable image plane at the required magnification.

Description

Technical Field

[0001] This invention relates to the field of photoelectric imaging technology, and in particular to a method for the initial structure of a stationary zoom system. Background Technology

[0002] Zoom systems possess the optical property of adjusting the magnification of the imaged object while maintaining image plane stability. The continuous zoom capability of a zoom system is manifested in its ability to simultaneously achieve wide-field searching at short focal lengths and high-resolution capture at long focal lengths and narrow fields of view, all while maintaining high image quality, and to switch focal lengths as needed. This makes it irreplaceable in fields such as consumer electronics, digital cameras, surveillance cameras, biological detection, astronomical observation, and military reconnaissance.

[0003] A zoom system mainly consists of a zoom group, a compensation group, and a fixed group. Traditional mechanical zoom achieves zooming while maintaining a constant image plane position through the zoom movement of the zoom group lens and the compensation movement of the compensation group. Traditional zoom lenses can be divided into optical compensation and mechanical compensation types. In optical compensation, the moving elements move linearly in the same direction at a constant speed throughout the zoom process, reducing the requirements on the mechanical structure, but image plane compensation can only be achieved at a limited number of positions, limiting the system's zoom effect. Mechanical compensation, through linear or non-linear movement of the zoom group and curvilinear movement of the compensation group, ensures that image plane displacement is fully compensated at subdivided sequence positions during zooming, achieving large zoom ratios, fastest zoom, and good image quality correction under multiple conjugates across the entire zoom range. New zoom systems achieve zoom by introducing unconventional novel optical elements. These elements, acting as variable focal length devices, form elements that realize both zoom and image plane compensation functions. By changing the object-image conjugate position through element surface deformation, a zoom system with fixed element positions is achieved. These stationary zoom systems replace the mechanical structures of traditional zoom systems with variable focal length devices such as electro-wetting liquid lenses, Micro-Optical-Electro-Mechanical-Systems (MOEMS) components, and phase modulators. The introduction of these new zoom devices overcomes the disadvantages of traditional zoom systems, such as limitations in machining precision of mechanical cams, accurate and rapid control of component movement, and overall system size and power consumption. This effectively achieves high-speed and integrated zoom systems while also improving system stability.

[0004] Establishing a mathematical model is one of the effective methods for solving the initial structure of a stationary zoom system. Traditional mathematical models involve establishing a system of differential equations that maintain zero image plane drift under moving components, calculating the initial Gaussian solution for each component of the system using thin lenses, and calculating the structure of the original zoom system based on the aberrations of each component's thick lens using first and second auxiliary rays. However, directly establishing a differential equation model to solve the initial structure still presents a series of challenges. When using deformable lenses to build a stationary zoom system, to achieve object-image conjugation across the entire focal length of the dynamic zoom system and obtain accurate numerical solutions for each component, the zoom capability of the MOMES system must be considered. Due to the limitations of the MOMES system's zoom capability, a complex solution region composed of multiple variables emerges. In direct calculations in the high-dimensional parameter space of the entire system, optimization easily gets trapped in local optimal solutions, making it impossible to obtain a Gaussian initial structure that satisfies the zoom ratio and image plane stability. If the parameter boundary conditions are not chosen appropriately, both analytical and numerical solutions of the system become difficult to obtain, making direct solution impossible and preventing low-order ray tracing.

[0005] Therefore, the main problem in current methods for solving the initial structure of stationary zoom systems is how to find the global optimal solution and optimization direction in a high-dimensional parameter space, and how to select reasonable parameter boundary conditions and optimization methods to overcome the difficulties in selecting local optimal solutions and parameter boundary conditions.

[0006] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] To address the aforementioned problems, this invention proposes a method for designing the initial structure of a stationary zoom system. This method analyzes and obtains the solution region of each key component parameter and the optimal initial structure design to achieve a stable zoom system with high zoom efficiency and aberration balance.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] S1. Construct the basic structure of a classic stationary zoom system, including the configuration of the intermediate zoom group, and determine the mathematical range of key parameters, wherein the boundary conditions of the parameters are defined, which will limit the range of parameter values ​​and provide necessary constraints for the subsequent optimization process.

[0010] S2. Under the basic structure and boundary conditions determined in step S1, a post-focusing group is introduced to further refine the design. Among them, the minimum braking amount constraint of the deformable mirror is introduced, and based on the parameter range of step S1, continuous zoom and basic aberration constraints are established. According to the characteristics of the intermediate zoom group and the post-focusing group, the structural analytical region is determined to guide the subsequent optimization process.

[0011] S3. Establish a nonlinear evaluation function. This function comprehensively considers the known design constraints and performance indicators, and uses a global optimization algorithm to solve the problem within the boundary conditions and structural analytical region determined in steps S1 and S2, so as to obtain the globally optimal numerical solution and complete the initial structural design of the stationary zoom system.

[0012] In some implementation examples, S1 above includes the following steps:

[0013] A1. Determine the initial structural form of the stationary zoom system, introduce a telescope structure into the medium zoom group, and determine the initial structural form based on the system's aberration balance requirements and the aberration balance characteristics of different telescope structures.

[0014] A2. Introduce a fixed lens group φ into the telescope structure. ref Based on the characteristics of different telescope structures, the positive and negative values ​​of the optical power of each group are determined;

[0015] A3. Based on the interrelationship of the magnification of each component of the lens group, determine the solution range of magnification, optical power, and component spacing under different structures;

[0016] A4. Implement block partitioning of the solution region and parameter dimensionality reduction.

[0017] Furthermore, the aberration variation trends of different telescope structures in step A1 above are shown in Table 1:

[0018] Table 1. Aberration trends of telephoto and reverse telephoto structures

[0019]

[0020] In Table 1, W 040 W 131 W 220 W 222 W 311 These represent the third-order spherical aberration, third-order coma, third-order field curvature, third-order astigmatism, and third-order distortion, respectively. h2 represents the height at which the edge rays enter φ2 after passing through the first part φ1 of the telescope structure. c1 represents the height at which the main ray enters φ2 after passing through the first part φ1 of the telescope structure, and c2 represents the radius of curvature of the second part.

[0021] Furthermore, in step A2 above, different telescope structures have different characteristics, therefore the positive and negative values ​​of the optical power of each group are also different, as shown in Table 2:

[0022] Table 2. Positive and negative values ​​of optical power for each component of the telephoto and reverse telephoto structures.

[0023]

[0024]

[0025] In Table 2, φ represents the optical power of the two deformable mirror components in the telescope system. ref This indicates the optical power of a fixed lens group.

[0026] Furthermore, in step A3 above, the relationship between the magnification of each component is as follows:

[0027]

[0028]

[0029] In the above relationship, m2 and m3 represent φ respectively. ref and The magnification of the component, d′1 represents φ ref The distances between the object and d1, d2 represent respectively. and φ ref The distance between and φ ref and The distance between them.

[0030] Furthermore, the above relationship can be expressed as:

[0031] m2=1 / (1-d′1φ ref )

[0032]

[0033]

[0034] Analyzing the range and trends of the variables in the above relationships yields the parameter ranges for different arrangements of the stationary zoom system, as shown in Table 3.

[0035] Table 3. Parameter range of stabilized zoom systems with different arrangements

[0036]

[0037]

[0038] In some implementation examples, S2 above includes the following steps:

[0039] A5. Introduction of post-focusing group φ focus Gaussian bracket method stationary zoom equations are established for the medium zoom group and the compensation group as a whole;

[0040] A6. Based on the Gaussian bracket method, determine the expressions for the focal length and back focal length of the telescope structure optical system, and use them as initial structural constraints;

[0041] A7. Introduce the minimum braking amount constraint for deformable mirrors, and use the range of curvature change of deformable mirrors as the constraint condition to further limit the variable space;

[0042] A8. Based on nodal aberration theory, off-axis aberration control constraints are introduced to obtain the third-order wave aberration coefficients of the zoom system.

[0043] Furthermore, in step A5 above, the specific equations for the Gaussian bracket method with stationary zoom are established as follows:

[0044] The new stationary zoom equation Z is established as follows:

[0045]

[0046] in 1 A4 represents the parameters of the stationary zoom equation, φ1, φ2, φ m φ represents the optical power of the element i = 1, 2, 3, ..., m. focus To compensate for the optical power.

[0047] The equivalent optical power of a stationary zoom system is expressed using a Gaussian constant. Φ The expression is as follows:

[0048]

[0049] Furthermore, in step A6 above, based on the set of equations for the stationary zoom system listed in step A5, the focal length expression of the optical system is obtained as follows:

[0050] A focus =|f′ sys -1 / 1 C4|

[0051] In the formula A focus Let f' be the system focal length, a Gaussian optical parameter. sys Telescope structure focal length, 1 C4 is a Gaussian constant;

[0052] Based on the set of equations for the stationary zoom system listed in step A5, the back intercept expression for the optical system is obtained as follows:

[0053]

[0054] In the formula A image Here, Φ is the back intercept of the Gaussian optical parameters, bfl is the system back intercept, and Φ is the back intercept. T This refers to the optical power of the system at long focal length. Γ The system scaling ratio, and These represent the changes in optical power of the two anamorphic lens components across the entire focal length, expressed as follows:

[0055]

[0056]

[0057] In the formula φ focus For the rear focusing group, the change in optical power of the ΔΦ zoom system across the entire focal length is expressed as ΔΦ=(Φ W -Φ T ); The change in optical power of a zoom system across the entire zoom range is expressed as: d * The expression is 1 B3 is a Gaussian constant, and its expression is:

[0058] Furthermore, in step A7 above, the minimum braking amount constraint for the deformable mirror is introduced as follows:

[0059]

[0060] Furthermore, in step A8 above, the third-order wave aberration of the off-axis system was analyzed based on nodal aberration theory. For deformable mirrors, their structural characteristics are driven by the complex surface shapes of basic spherical, conical, or freeform surfaces. The third-order wave aberration coefficients of a conical surface are expressed as:

[0061]

[0062]

[0063]

[0064] In the formula C 1asph C 1asph C 1asph Let c represent the third-order spherical aberration coefficient, third-order coma coefficient, and third-order astigmatism coefficient of the conical surface, respectively. j (j=1,2,...,m) represents the radius of curvature of the j-th surface, n i (i = 1, 2, ..., m) represents the refractive index of the i-th element, kj (j=1,2,..,m) represents the conic coefficient of the j-th aspherical term, h j (j = 1, 2, ..., m) represents the ray height when the edge ray enters the j-th surface. This represents the ray height when the principal ray enters the j-th surface.

[0065] According to nodal aberration theory, the third-order off-axis wave aberration coefficients of a stationary zoom system consist of spherical and aspherical terms, and the expressions for each wave aberration coefficient are as follows:

[0066] Spherical aberration coefficient:

[0067] Coma coefficient:

[0068] Astigmatism coefficient:

[0069] Field curvature coefficient:

[0070] Distortion coefficient:

[0071] In the above expression, Let be the field displacement vector of the j-th surface, where α j The tilt angle j of the j-th surface th ; These represent the on-axis spherical aberration, coma, astigmatism, field curvature, and distortion coefficients of the surface, respectively. Represents the normalized field vector;

[0072] The minimum braking amount constraint, Gaussian structure constraint, and wave aberration coefficient constraint of the deformable mirror are introduced.

[0073] In some implementation examples, S3 above includes the following steps:

[0074] A9. Establish a nonlinear evaluation function based on the constraints and solution space;

[0075] A10. Use a global optimization algorithm to solve the nonlinear evaluation function to obtain the optimal initial structural design.

[0076] Furthermore, in step A9 above, the nonlinear evaluation function for the optimization problem is established as follows:

[0077]

[0078] In the above equation, the nonlinear evaluation function L consists of a scaled Gaussian structure L1 and a symmetric aberration term L2 in the off-axis system. Where u j h j mj It is the implicit function parameter u in the explicit function L1 j h j , These are implicit function parameters in the explicit function L2;

[0079] The optimization objective is as follows:

[0080]

[0081] Q i and T i It is the constraint range of the corresponding variable, R(Q) i R(Q) is determined by the solution region of the key parameters determined in step S1. i )=|BFL-1 / Φ| Optical power φ i Distance between components d i Surface tilt angle α i Conic coefficient k i And magnification m2, m3 and key parameters It is an implicit function R(Q) i The parameter β is R(Q) i The coefficients of the function; P(T) i () is the constraint on the braking amount of the deformable mirror.

[0082] Furthermore, in step A10 above, after obtaining the nonlinear evaluation functions, the three focal length nonlinear evaluation functions are used as the nonlinear evaluation functions of the overall system of the main function. Under the solution boundary conditions set by the main function, a global optimization algorithm is used to solve the problem. The obtained numerical solution is the optimal solution under the boundary conditions in the global optimization, that is, the initial numerical solution that satisfies the target focal length and zoom ratio.

[0083] Compared with the prior art, the advantages of the present invention are:

[0084] This invention provides a method for designing the initial structure of a stationary zoom system. By establishing the basic structure of a classic stationary zoom system and determining the mathematical range of key parameters, the method performs dimensionality reduction of the parameter space and defines boundary conditions. Then, by introducing a post-focusing group and refining design constraints, this invention not only enhances the zoom capability of the system but also ensures the stability of image quality during zooming. Finally, by establishing a nonlinear evaluation function and applying a global optimization algorithm, this invention can efficiently solve for the globally optimal numerical solution within given boundary conditions and structural analytical regions, thereby obtaining a high-performance initial structure design. This not only improves design efficiency but also optimizes the overall performance of the optical system, especially showing significant advantages in aberration correction, zoom efficiency, and system stability. In the preferred embodiment, this invention introduces a telescope structure into the design of a stationary zoom system, reducing the dimensionality of the solution parameters of high-dimensional parameters to a block analytical subspace. By modeling and analyzing the parameter space, the key parameters affecting system performance are determined, transforming the complex global mathematical problem into a local analytical solution in a specific boundary condition. This improves the convergence and accuracy in the optimization of the initial Gaussian structure of the system, thereby enabling the design of a stationary zoom optical path with a compact system structure, actuable deformable mirrors, and aberration balance. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a flowchart of the initial structural overall design of the stationary zoom system in an embodiment of the present invention;

[0087] Figure 2 This is a detailed flowchart of the initial structural design of the stationary zoom system in an embodiment of the present invention;

[0088] Figure 3 This is a schematic diagram of a typical stationary zoom system structure in an embodiment of the present invention;

[0089] Figure 4 This is a Gaussian structure optical path diagram of the telephoto system in the telescope structure of this embodiment of the invention;

[0090] Figure 5 This is a Gaussian structure optical path diagram of the anti-photograph system in the telescope structure of this invention embodiment;

[0091] Figure 6 This is a Gaussian structure optical path diagram of a stationary zoom system with fixed telephoto and reverse telephoto elements introduced in an embodiment of the present invention;

[0092] Figure 7 This is a schematic diagram of the optical path of the system with the rear focusing group introduced in an embodiment of the present invention;

[0093] Figure 8 This embodiment of the invention demonstrates how to design and implement a short-focal-length optical path diagram for a stationary catadioptric system using this method.

[0094] Figure 9 This embodiment of the invention uses this method to design and implement the focal path diagram in a stationary catadioptric system;

[0095] Figure 10 This embodiment of the invention demonstrates how to design and implement a long-focal-length optical path diagram for a stationary catadioptric system using this method. Detailed Implementation

[0096] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0097] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0098] This invention provides a method for designing the initial structure of a stationary zoom system. Based on a typical stationary zoom structure, this method primarily addresses the problem of convergence in solving key parameters during the initial structure design of stationary zoom systems. By introducing a telescope structure into the mid-zoom group and classifying and discussing the solution regions of key parameters, dimensionality reduction of the solution parameters is achieved. Furthermore, considering Gaussian structure constraints, minimum braking constraints, and wave aberration coefficient constraints during the initial structure design, nonlinear equations are constructed for optimization to obtain the optimal stationary zoom initial structure. This achieves high-speed, integrated, and accurate design of the initial structure of the stationary zoom system, laying a solid structural foundation for further system optimization.

[0099] refer to Figure 1 and Figure 2 The diagram and flowchart are the initial structural design scheme of the stationary zoom system of the present invention, and are described in detail below:

[0100] (1) Step S1: Establish the basic structure of a classic stationary zoom system and determine the solution region of key parameters for the mid-zoom group. This includes the following steps:

[0101] A1. Determine the initial structural form of the stationary zoom system, introduce a telescope structure into the medium zoom group, and determine the initial structural form based on the system's aberration balance requirements and the aberration balance characteristics of different telescope structures.

[0102] A2. Introduce a fixed lens group φ into the telescope structure. ref Based on the characteristics of different telescope structures, the positive and negative values ​​of the optical power of each group are determined;

[0103] A3. Based on the interrelationship of the magnification of each component of the lens group, determine the solution range of magnification, optical power, and component spacing under different structures;

[0104] A4. Implement block partitioning of the solution region and parameter dimensionality reduction.

[0105] Further details for A1-A4 are as follows:

[0106] A1, such as Figure 3 As shown, the initial structural form of the stationary zoom system is determined. The initial structure of the stationary zoom system includes a front zoom group, a middle zoom group, and a rear intercept adjustment group. A telephoto structure is introduced into the middle zoom group. The telephoto structure can be divided into telephoto structure and reverse telephoto structure according to the different optical powers of its components. According to Table 1, the third-order spherical aberration, coma, astigmatism, field curvature, and distortion of the telephoto structure and the reverse telephoto structure have different trends. Based on the different aberration balance requirements of the system, the choice of which telephoto structure to select as the middle zoom group is determined.

[0107] A2. Incorporate a fixed lens assembly into the telescope structure. The telescope structure is as follows: Figure 4 and Figure 5 As shown, a typical telescope structure consists of two groups, front and rear. The front group φ1 is composed of a lens φ 11 ,φ 12 ,...,φ 1η Composed of, the rear group φ2 is composed of lens φ 21 ,φ 22 ,...,φ 2τ composition. Figure 4 It is a telephoto telescope structure, with the front group optical power φ1 being positive and the rear group optical power φ2 being negative; Figure 5 This is a reverse telephoto structure, where the front element's optical power φ1 is negative and the rear element's optical power φ2 is positive. A fixed lens group φ with a defined optical power is introduced between these two elements. ref ,like Figure 6 As shown, the medium zoom group at this time consists of two morphing lens elements. and the fixed lens group φ between the two elements ref Composition. Based on the positive and negative optical focal lengths of each element in the telephoto and reverse telephoto structures, the positive and negative values ​​of each lens group are determined by Table 2;

[0108] A3. Based on the optical power of each group φ ref The signs of the positive and negative values, and the mathematical relationship between the magnifications m2 and m3 of the second and third components, are used to determine the key parameters m2, m3, and m3 from Table 3. The solution region;

[0109] A4. Complete the preliminary determination of the medium zoom structure form and the m2 and m3 components in the telescope structure. Determination of the solution region for key parameters.

[0110] (2) Step S2: Add the post-focusing group and introduce initial Gaussian structure constraints, minimum braking amount constraints for deformable mirrors, and aberration constraints. Specifically, this includes the following steps:

[0111] A5. Introduction of post-focusing group φ focus Establish the Gaussian bracket method fixed zoom equation for the telescope structure;

[0112] A6. Based on the Gaussian bracket method, determine the expressions for the focal length and back focal length of the telescope structure optical system, and use them as initial structural constraints;

[0113] A7. Introduce the minimum braking amount constraint for deformable mirrors, and use the range of curvature change of deformable mirrors as the constraint condition to further limit the variable space;

[0114] A8. Based on nodal aberration theory, off-axis aberration control constraints are introduced to obtain the third-order wave aberration coefficients of the zoom system.

[0115] Further details for A5-A8 are as follows:

[0116] A5, such as Figure 7 As shown, after the introduction of the medium zoom group, the focusing group φ focus The following is the stationary zoom equation established for the telescope structure using the Gaussian bracket method:

[0117] The new stationary zoom equation Z is established as follows:

[0118]

[0119] in 1 A4 represents the parameters of the stationary zoom equation, φ1, φ2, φ m Characterizing the first Component optical power, φ focus This refers to the optical power of the back focusing group.

[0120] The equivalent optical power of a stationary zoom system is expressed using a Gaussian constant. Φ The expression is as follows:

[0121]

[0122] A6. The system focal length and back intercept obtained from the zoom equations determined by the Gaussian bracket method are as follows:

[0123] A focus =|f′sys -1 / 1 C4|

[0124]

[0125] In the formula A focus Let f' be the system focal length, a Gaussian optical parameter. sys Telescope structure focal length, 1 C4 is a Gaussian constant; A image Here, Φ is the back intercept of the Gaussian optical parameters, bfl is the system back intercept, and Φ is the back intercept. T Γ represents the optical power of the system at telephoto zoom, and Γ represents the system scaling ratio. and These represent the changes in optical power of the two anamorphic lens components across the entire focal length, expressed as follows:

[0126]

[0127]

[0128] In the formula φ focus The optical power of the rear focusing group is ΔΦ, which represents the change in optical power of the zoom system across the entire focal length. The expression is ΔΦ = (Φ...) W -Φ T ); The change in optical power of a zoom system across the entire zoom range is expressed as: d * The expression is 1 B3 is a Gaussian constant, and its expression is: The system focal length and back intercept are introduced as initial structural constraints.

[0129] A7. The minimum braking amount constraint for the introduced deformable mirror is determined as follows:

[0130]

[0131] A8. The introduced wave aberration coefficients are determined as follows:

[0132] Spherical aberration coefficient:

[0133] Coma coefficient:

[0134] Astigmatism coefficient:

[0135] Field curvature coefficient:

[0136] Distortion coefficient:

[0137] In the above expression, Let be the field displacement vector of the j-th surface, where α j The tilt angle j of the j-th surface th ; These represent the on-axis spherical aberration, coma, astigmatism, field curvature, and distortion coefficients of the surface, respectively. Let C represent the normalized field vector. 1asph C 1asph C 1asph Let represent the third-order spherical aberration coefficient, third-order coma coefficient, and third-order astigmatism coefficient of the conical surface, respectively, and their expressions are as follows:

[0138]

[0139]

[0140]

[0141] In the formula C 1asph C 1asph C 1asph Let c represent the third-order spherical aberration coefficient, third-order coma coefficient, and third-order astigmatism coefficient of the conical surface, respectively. j (j=1,2,...,m) represents the radius of curvature of the j-th surface, n i (i = 1, 2, ..., m) represents the refractive index of the i-th element, k j (j=1,2,..,m) represents the conic coefficient of the j-th aspherical term, h j (j = 1, 2, ..., m) represents the ray height when the edge ray enters the j-th surface. This represents the ray height when the principal ray enters the j-th surface.

[0142] The magnitude of wavelet aberration coefficients is introduced as a new constraint.

[0143] (3) Step S3: Establish a nonlinear evaluation function to obtain the globally optimal numerical solution within the boundary conditions and structural analytical domain of the variables. This specifically includes the following steps:

[0144] A9. Establish a nonlinear evaluation function based on the constraints and solution space;

[0145] A10. Use a global optimization algorithm to solve the nonlinear evaluation function to obtain the optimal initial structural design.

[0146] Further details for A9-A10 are as follows:

[0147] A9. The nonlinear evaluation function for the optimization problem is established as follows:

[0148]

[0149] In the above equation, the nonlinear evaluation function L consists of a scaled Gaussian structure L1 and a symmetric aberration term L2 in the off-axis system. Where u j h j m j It is the implicit function parameter u in the explicit function L1 j h j , These are implicit function parameters in the explicit function L2;

[0150] The optimization objective is:

[0151]

[0152] Q i and T i It is the constraint range of the corresponding variable, R(Q) i R(Q) is determined by the solution region of the key parameters determined in step S1. i )=|BFL-1 / Φ| Optical power φ i Distance between components d i Surface tilt angle α i Conic coefficient k i And magnification m2, m3 and key parameters It is an implicit function R(Q) i The parameter β is R(Q) i The coefficients of the function; P(T) i () is the constraint on the braking amount of the deformable mirror.

[0153] A10. After obtaining the nonlinear evaluation functions, the three focal length nonlinear evaluation functions are used as the nonlinear evaluation functions of the overall system of the master function. Under the solution boundary conditions set by the master function, a global optimization algorithm is used to solve the problem. The obtained numerical solution is the optimal solution under the boundary conditions in the global optimization, that is, the initial numerical solution that satisfies the target focal length and zoom ratio.

[0154] like Figures 8 to 10 The figures shown are the optical path diagrams for the short-focal-length, medium-focal-length, and long-focal-length zoom structures designed and implemented by the method of the present invention.

[0155] In some embodiments of the present invention: a telescope structure is introduced as the intermediate zoom group of a classic stationary zoom structure, thereby achieving dimensionality reduction of the initial structural parameters of the optical system and determination of the solution region of key parameters. Further explanation is as follows: based on the aberration characteristics and structural requirements of telescope structures of telephoto and reverse telephoto types, the intermediate zoom group of the stationary zoom system is replaced with a telescope structure of the corresponding structure. Based on the relationship between the positive and negative values ​​of the optical power of the telescope structure components and the magnification of the components, the solution space of key parameters is determined, transforming the complex global mathematical problem into a local analytical solution within a specific boundary condition, thus obtaining the initial structure of the stationary zoom system.

[0156] In some embodiments of the present invention, global nonlinear optimization design calculations are achieved by introducing braking amount, structure, key parameter value ranges, and aberration constraints. Further explanation is as follows: A method for solving the optimal initial structure under multiple constraints is proposed. By analyzing and introducing the system's initial structural constraints, deformable mirror braking amount constraints, aberration constraints, and key parameter range limitations, a nonlinear evaluation function is established, and a global optimization algorithm is used to calculate the optimal initial structure.

[0157] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A method for designing the initial structure of a stationary zoom system, characterized in that, Includes the following steps: S1. Construct the basic structure of a classic stationary zoom system, including the configuration of the intermediate zoom group, and determine the mathematical range of key parameters, where the boundary conditions of the parameters are defined. S2. Under the basic structure and boundary conditions determined in step S1, a back focusing group is introduced to further refine the design; among them, the minimum braking amount constraint of the deformable mirror is introduced, and based on the parameter range of step S1, continuous zoom and basic aberration constraints are established; according to the characteristics of the intermediate zoom group and the back focusing group, the structural analytical region is determined. S3. Establish a nonlinear evaluation function. This function comprehensively considers the known design constraints and performance indicators. It adopts a global optimization algorithm to solve the problem within the boundary conditions and structural analytical region determined in steps S1 and S2, so as to obtain the globally optimal numerical solution and complete the initial structural design of the stationary zoom system. S1 includes the following steps: A1. Determine the initial structural form of the stationary zoom system, introduce a telescope structure into the medium zoom group, and determine the initial structural form based on the system's aberration balance requirements and the aberration balance characteristics of different telescope structures. A2. Introduce a fixed lens group into the telescope structure, and determine the positive and negative values ​​of the optical power of each group based on the characteristics of different telescope structures; A3. Based on the interrelationship of the magnification of each component of the lens group, determine the solution range of magnification, optical power, and component spacing under different structures; A4. Implement block partitioning of the solution region and parameter dimensionality reduction; S2 includes the following steps: A5. Introduce the post-focusing group and establish a Gaussian bracket method stationary zoom equation for the medium zoom group and the compensation group as a whole. A6. Based on the Gaussian bracket method, determine the expressions for the focal length and back focal length of the telescope structure optical system, and use them as initial structural constraints; A7. Introduce the minimum braking amount constraint for deformable mirrors, and use the range of curvature change of deformable mirrors as the constraint condition to further limit the variable space; A8. Based on nodal aberration theory, off-axis aberration control constraints are introduced to obtain the third-order wave aberration coefficients of the zoom system.

2. The method for designing the initial structure of a stationary zoom system as described in claim 1, characterized in that, In step A1, the telescope structure introduced by the intermediate zoom group of the stationary zoom system is used to determine the specific form of the telescope structure based on the system's aberration balance requirements and the aberration balance characteristics of different telescope structures.

3. The method for designing the initial structure of a stationary zoom system as described in claim 1, characterized in that, In step A2, the components of the medium zoom group telescope structure are composed of deformable mirrors. Add a fixed lens group φ ref The positive and negative values ​​of the telescope structure are analyzed based on its optical power characteristics.

4. The method for designing the initial structure of a stationary zoom system as described in claim 1, characterized in that, In step A3, the relationship between the magnifications of the various elements of the lens group is as follows: In the above relationship, m2 and m3 represent the fixed component φ, respectively. ref and The magnification of the component, d1' represents φ ref The distances between the object and d1, d2 represent respectively. and φ ref The distance between and φ ref and The distance between them, and the key system parameters m2 and m3 obtained based on this analysis. The solution region is as follows:

5. The method for designing the initial structure of a stationary zoom system as described in claim 1, characterized in that, In step A5, based on the analysis of the central zoom group, the rear focusing group φ of the stationary zoom system is introduced. focus The stationary zoom equations established using the Gaussian bracket method are as follows: The new stationary zoom equation Z is established as follows: in 1 A4 represents the parameters of the stationary zoom equation, φ1, φ2, φ m φ represents the optical power of the element i = 1, 2, 3, ..., m. focus To compensate for the optical power, The equivalent optical power Φ of a stationary zoom system is expressed as a Gaussian constant as follows: In step A6, the expressions for the determined system focal length and back intercept are as follows: A focus =|f′ sys -1 / 1 C4| In the formula A focus Let f' be the system focal length, a Gaussian optical parameter. sys Telescope structure focal length, 1 C4 is a Gaussian constant; A image Here, Φ is the back intercept of the Gaussian optical parameters, bfl is the system back intercept, and Φ is the back intercept. T Γ represents the optical power of the system at telephoto zoom, and Γ represents the system scaling ratio. and These represent the changes in optical power of the two anamorphic lens components across the entire focal length, expressed as follows: In the formula φ focus The optical power of the rear focusing group is ΔΦ, which represents the change in optical power of the zoom system across the entire focal length. The expression is ΔΦ = (Φ...) W -Φ T ); The change in optical power of a zoom system across the entire zoom range is expressed as: d * The expression is 1 B3 is a Gaussian constant, and its expression is: The system focal length and back intercept are introduced as initial structural constraints. In step A7, the minimum braking amount constraint of the deformable mirror is introduced and expressed as follows: In step A8, the off-axis aberration control constraints are as follows: Spherical aberration coefficient: Coma coefficient: Astigmatism coefficient: Field curvature coefficient: Distortion coefficient: In the above expression, Let be the field displacement vector of the j-th surface, where α j Let be the tilt angle of the j-th surface; These represent the on-axis spherical aberration, coma, astigmatism, field curvature, and distortion coefficients of the surface, respectively. Denotes the normalized field vector; where C 1asph C 2asph C 3asph Let represent the third-order spherical aberration coefficient, third-order coma coefficient, and third-order astigmatism coefficient of the conical surface, respectively, and their expressions are as follows: In the formula C 1asph C 2asph C 3asph Let c represent the third-order spherical aberration coefficient, third-order coma coefficient, and third-order astigmatism coefficient of the conical surface, respectively. j (j=1,2,...,m) represents the radius of curvature of the j-th surface, n i (i = 1, 2, ..., m) represents the refractive index of the i-th element, k j (j=1,2,..,m) represents the conic coefficient of the j-th aspherical term, h j (j = 1, 2, ..., m) represents the ray height when the edge ray enters the j-th surface. This represents the ray height when the principal ray enters the j-th surface.

6. The method for designing the initial structure of a stationary zoom system as described in claim 1, characterized in that, S3 includes the following steps: A9. Establish a nonlinear evaluation function based on the constraints and solution space; A10. Use a global optimization algorithm to solve the nonlinear evaluation function to obtain the optimal initial structural design.

7. The method for designing the initial structure of a stationary zoom system as described in claim 6, characterized in that, In step A9, the nonlinear evaluation function is established as follows: In the above equation, the nonlinear evaluation function L consists of a scaled Gaussian structure L1 and a symmetric aberration term L2 in the off-axis system, where u j h j m j It is the implicit function parameter u in the explicit function L1 j h j , These are implicit function parameters in the explicit function L2; The optimization objective is as follows: Q i and T i It is the constraint range of the corresponding variable, R(Q) i R(Q) is determined by the solution region of the key parameters determined in step S1. i )=|BFL-1 / Φ| Optical power φ i Distance between components d i Surface tilt angle α i Conic coefficient k i And magnification m2, m3 and key parameters It is an implicit function R(Q) i The parameter β is R(Q) i The coefficients of the function; P(T) i () is the constraint on the braking amount of the deformable mirror.

8. The method for designing the initial structure of a stationary zoom system as described in claim 6, characterized in that, In step A10, the optimization method using nonlinear functions is as follows: the nonlinear evaluation functions of the three focal lengths are used as the nonlinear evaluation functions of the overall system of the main function, and the global optimization algorithm is used to solve the problem under the solution boundary conditions set by the main function.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method for designing the initial structure of a stationary zoom system as described in any one of claims 1 to 8.

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