An optical system design method based on super lens seidel aberration

Abstract

The present application relates to the technical field of optical design, and provides a kind of optical system design method based on super-structured lens Seidel aberration, optical system design method based on super-structured lens Seidel aberration includes: determining the Seidel aberration function of super-structured surface;Wherein Seidel aberration function includes spherical aberration coefficient, coma coefficient and astigmatism coefficient;According to Seidel aberration function, determine the objective function;According to the objective function, optimization processing is carried out, and optimization processing result is obtained;According to optimization processing result, the structure parameter of target optical system is determined.Through the above mode, the calculation system of super-structured lens Seidel aberration is established, and the Seidel aberration of super-structured lens calculated by the system can be directly linearly superimposed with the Seidel aberration of traditional catadioptric system, which provides a theoretical basis for the design of composite optical system, and finally realizes the aberration collaborative design of super-structured lens and traditional optical system.

Description

Technical Field

[0001] This invention relates to the field of optical design technology, and in particular to an optical system design method based on the Seidel aberration of metalenses. Background Technology

[0002] Metalenses, as a novel type of planar optical device, possess advantages such as ultra-thinness and lightweight design, demonstrating significant application value in driving the miniaturization of imaging systems. However, current metalens design relies excessively on optimization algorithms, lacking a systematic aberration theory as guidance. Particularly when integrating with traditional catadioptric optical systems, the lack of a unified aberration theory framework hinders the coordinated design of the entire system.

[0003] Furthermore, under current technological conditions, a complete Seidel aberration system for metalenses has not yet been established, making it difficult for metalenses and traditional optical systems to achieve effective linkage and coordination in terms of aberrations. Summary of the Invention

[0004] This invention provides an optical system design method based on metalens Seidel aberration, which solves the technical problem that the design of metalenses in the prior art lacks a unified architecture and cannot be effectively linked with the design of traditional optical systems.

[0005] This invention provides a method for designing an optical system based on the Seidel aberration of a metalens, comprising: determining the Seidel aberration function of the metaface; wherein the Seidel aberration function includes spherical aberration coefficient, coma coefficient, and astigmatism coefficient; determining a target function based on the Seidel aberration function; performing optimization processing based on the target function to obtain an optimization result; and determining the structural parameters of the target optical system based on the optimization result.

[0006] Spherical aberration coefficient Represented as:

[0007] ,

[0008] or, ;

[0009] Coma coefficient Represented as:

[0010] ,

[0011] or, ;

[0012] Astigmatism coefficient Represented as:

[0013] ,

[0014] or, ;

[0015] in, This represents the refractive index of the medium to the left of the metasurface with index i. This represents the refractive index of the medium to the left of the metasurface with index i+1; This represents the angle of incidence between the first paraxial ray and the metasurface with index i; This represents the incident height of the first paraxial ray with the metasurface of index i; This represents the angle between the first paraxial ray and the exit angle of the metasurface with index i; This represents the angle of incidence between the second paraxial ray and the metasurface with index i; This represents the incident height of the second paraxial ray with the metasurface of index i; This represents the angle between the second paraxial ray and the exit angle of the metasurface with index i; the first paraxial ray is the edge ray, and the second paraxial ray is the principal ray; This represents the image-side focal length of the metasurface with index i. Indicates the dominant wavelength of the incident light; This represents the additional phase term of order four or higher for the metasurface with index i.

[0016] According to the present invention, an optical system design method based on metalens Seidel aberration is provided, wherein the Seidel aberration function further includes field curvature coefficient and distortion coefficient;

[0017] Field curvature coefficient Represented as: ;

[0018] distortion coefficient Represented as:

[0019] ,

[0020] or, .

[0021] According to the present invention, an optical system design method based on metalens Seidel aberration is provided, wherein the Seidel aberration function further includes positional chromatic aberration coefficient and magnification chromatic aberration coefficient;

[0022] Position color difference coefficient Represented as:

[0023] ,

[0024] or, ;

[0025] Color difference coefficient Represented as:

[0026] ,

[0027] or, ;

[0028] in, This represents the difference in refractive index of the medium on the left side of the metasurface after a change in wavelength. This represents the difference in refractive index of the medium to the right of the metasurface with serial number i after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference in refractive index of the medium on the left side of the metasurface with serial number i+1 after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference between the image-side focal length and the dominant wavelength image-side focal length of the metasurface with serial number i at the wavelength under study.

[0029] The optical system design method based on metalens Seidel aberration provided by the present invention further includes: when the target optical system includes a metaface and other optical surfaces besides the metaface, determining the first type of Seidel aberration function of the metaface and the second type of Seidel aberration function of the other optical surfaces respectively; determining a hybrid objective function based on the first type of Seidel aberration function and the second type of Seidel aberration function; optimizing the hybrid objective function to obtain a hybrid optimization result; and determining the structural parameters of the target optical system based on the hybrid optimization result.

[0030] According to the present invention, an optical system design method based on metalens Seidel aberration is provided, which determines the first type of Seidel aberration function of the metalens and the second type of Seidel aberration function of other optical surfaces, including: determining the corresponding Seidel aberration function according to the type of each surface in the target optical system; if the i-th surface in the target optical system is determined to be a metalens, then the first type of Seidel aberration function of the i-th surface is determined according to a first method; if the i-th surface in the target optical system is determined to be another optical surface, then the second type of Seidel aberration function of the i-th surface is determined according to a second method.

[0031] The present invention provides an optical system design method based on metalens Seidel aberration, which combines objective functions. Represented as:

[0032] ;

[0033] in, The function is about An increasing function or 0; The correlation spherical aberration coefficients are obtained based on the spherical aberration coefficients in the first-type Seidel aberration function and the spherical aberration coefficients in the second-type Seidel aberration function.

[0034] The function is about An increasing function or 0; The coma coefficients are obtained based on the coma coefficients in the first type of Seidel aberration function and the coma coefficients in the second type of Seidel aberration function;

[0035] The function is about An increasing function or 0; The correlation astigmatism coefficient is obtained based on the astigmatism coefficient in the first type Seidel aberration function and the astigmatism coefficient in the second type Seidel aberration function;

[0036] The function is about An increasing function or 0; The relevant field curvature coefficients are obtained based on the field curvature coefficients in the first type of Seidel aberration function and the field curvature coefficients in the second type of Seidel aberration function;

[0037] The function is about An increasing function or 0; The relevant distortion coefficients are obtained based on the distortion coefficients in the first type Seidel aberration function and the distortion coefficients in the second type Seidel aberration function;

[0038] The function is about An increasing function or 0; The relevant positional chromatic aberration coefficients are obtained based on the positional chromatic aberration coefficients in the first type of Seidel aberration function and the positional chromatic aberration coefficients in the second type of Seidel aberration function;

[0039] The function is about An increasing function or 0; The correlation chromatic aberration coefficient is obtained based on the chromatic aberration coefficients in the first type of Seidel aberration function and the chromatic aberration coefficients in the second type of Seidel aberration function.

[0040] The present invention provides an optical system design method based on metalens Seidel aberration. ; ; ;

[0041] ; ; ;

[0042] ;

[0043] Where m represents the total number of metasurfaces and other optical surfaces in the target optical system;

[0044] It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i.

[0045] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements any of the above-described optical system design methods based on meta-lens Seidel aberration.

[0046] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the above-described optical system design methods based on metalens Seidel aberration.

[0047] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements any of the above-described optical system design methods based on metalens Seidel aberration.

[0048] This invention provides an optical system design method based on the Seidel aberration of a metalens. The method includes: determining the Seidel aberration function of the metasurface; wherein the Seidel aberration function includes spherical aberration coefficient, coma coefficient, astigmatism coefficient, field curvature coefficient, distortion coefficient, positional chromatic aberration coefficient, and magnification chromatic aberration coefficient; determining a target function based on the Seidel aberration function; performing optimization processing based on the target function to obtain an optimization result; and determining the structural parameters of the target optical system based on the optimization result. Through the above method, this invention establishes a calculation system for the Seidel aberration of a metalens. The Seidel aberration of the metalens calculated by this system can be directly linearly superimposed with the Seidel aberration of a traditional catadioptric system. This characteristic provides a theoretical basis for the design of composite optical systems, ultimately realizing the collaborative design of aberrations between metalenses and traditional optical systems. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is one of the flowcharts illustrating the optical system design method based on metalens Seidel aberration provided in this embodiment of the invention.

[0051] Figure 2 This is a schematic diagram illustrating the basic concept of an optical system provided in an embodiment of the present invention.

[0052] Figure 3 This is the second flowchart illustrating the optical system design method based on metalens Seidel aberration provided in this embodiment of the invention.

[0053] Figure 4 This is a schematic diagram of the structure of the hybrid optical system provided in an embodiment of the present invention.

[0054] Figure 5 This is a schematic diagram of the physical structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0056] In the description of the embodiments of the present invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of the present invention. In addition, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0057] In embodiments of the present invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0058] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0059] This invention provides an optical system design method based on metalens Seidel aberration, establishes a complete metalens aberration calculation system, and realizes aberration co-design with traditional optical systems.

[0060] Please see Figure 1 , Figure 1 This is one of the flowcharts illustrating the optical system design method based on Seidel aberration of a metalens provided in this embodiment of the invention. In this embodiment, the optical system design method based on Seidel aberration of a metalens may include steps S110 to S140, each step being as follows:

[0061] S110: Determine the Seidel aberration function of the metasurface.

[0062] S120: Determine the objective function based on the Seidel aberration function.

[0063] S130: Perform optimization processing based on the objective function to obtain the optimization result.

[0064] S140: Determine the structural parameters of the target optical system based on the optimization results.

[0065] Metalenses are novel optical elements that utilize nanostructures to achieve wavefront modulation. Compared to traditional lenses, metalenses offer smaller size, lighter weight, and more flexible optical performance design. The optical surfaces of metalenses include metasurfaces.

[0066] Seidel's aberration function can quantify the light deviation in an optical system based on metalenses, and is used to evaluate the imaging performance of the optical system. Therefore, based on Seidel's aberration function, the objective function of the target optical system can be set, and by optimizing the objective function, the structural parameters of the target optical system can be determined.

[0067] In this embodiment, the Seidel aberration function may include spherical aberration coefficient, coma coefficient, and astigmatism coefficient.

[0068] Specifically, the coefficient of spherical aberration It can be represented as:

[0069] ,

[0070] or, .

[0071] Coma coefficient It can be represented as:

[0072] ,

[0073] or, .

[0074] Astigmatism coefficient It can be represented as:

[0075] ,

[0076] or, .

[0077] in, This represents the refractive index of the medium to the left of the metasurface with index i. This represents the refractive index of the medium to the left of the metasurface with index i+1; This represents the angle of incidence between the first paraxial ray and the metasurface with index i; This represents the incident height of the first paraxial ray with the metasurface of index i; This represents the angle between the first paraxial ray and the exit angle of the metasurface with index i; This represents the angle of incidence between the second paraxial ray and the metasurface with index i; This represents the incident height of the second paraxial ray with the metasurface of index i; This represents the angle between the second paraxial ray and the exit angle of the metasurface with index i; This represents the image-side focal length of the metasurface with index i. Indicates the dominant wavelength of the incident light; This represents the additional phase term of order four or higher for the metasurface with index i.

[0078] The first paraxial ray is the edge ray, which is defined as a ray emanating from an on-axis object point and passing through the edge of the entrance pupil of the optical system; the second paraxial ray is the principal ray, which is defined as a ray emanating from an off-axis field of view point and passing through the center of the entrance pupil of the optical system.

[0079] In some embodiments, the Seidel aberration function may further include field curvature coefficients and distortion coefficients;

[0080] Field curvature coefficient It can be represented as: ;

[0081] distortion coefficient It can be represented as:

[0082] ,

[0083] or, .

[0084] In some embodiments, the Seidel aberration function may further include positional chromatic aberration coefficients and magnification chromatic aberration coefficients;

[0085] Position color difference coefficient It can be represented as:

[0086] ,

[0087] or, ;

[0088] Color difference coefficient It can be represented as:

[0089] ,

[0090] or, ;

[0091] in, This represents the difference in refractive index of the medium on the left side of the metasurface after a change in wavelength. This represents the difference in refractive index of the medium to the right of the metasurface with serial number i after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference in refractive index of the medium on the left side of the metasurface with serial number i+1 after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference between the image-side focal length and the dominant wavelength image-side focal length of the metasurface with serial number i at the wavelength under study.

[0092] In this embodiment, the metalens aberration theory under different optical notation systems is fully described by Seidel aberration, which ensures the consistency and universality of the theory under different notation systems and effectively enhances the practical value of the present invention in the field of optical design.

[0093] Please see Figure 2 , Figure 2 This is a schematic diagram illustrating the basic concept of an optical system provided in an embodiment of the present invention.

[0094] The optical path of an optical system involves the object, image, sphere i, sphere i+1, and aperture. The parameters involved include the segment along the optical axis, the segment perpendicular to the optical axis, the angle between the ray and the optical axis, the angle between the optical axis and the normal, the angle between the ray and the normal, and surface spacing, etc.

[0095] The optical notation system in this embodiment includes a first notation system and a second notation system. The definitions and positive / negative values ​​of the axial segment, perpendicular segment, and surface spacing are the same in both the first and second notation systems. Specifically:

[0096] (1) Along the axis segment: including object distance , , Taking the vertex of the interface as the origin, if the direction from the origin to the intersection of the ray and the optical axis, or from the origin to the center of the sphere, is the same as the direction of ray propagation, the value is positive; otherwise, it is negative. The direction of ray propagation is defined as from left to right.

[0097] (2) Perpendicular axis segment: including , , , Those above the optical axis are positive, and those below are negative.

[0098] (3) Surface spacing: including From the vertex of the front surface to the vertex of the back surface, the direction is positive if it is the same as the direction of the light ray, and negative if it is opposite. In a purely refractive system, the surface spacing is always positive.

[0099] In the first and second notation systems, the definitions of the angles between the ray and the optic axis, the angle between the optic axis and the normal, and the angle between the ray and the normal are the same, but the positive and negative values ​​are different. Specifically:

[0100] (4) The angle between the ray and the optical axis: including , , , Starting from the optical axis, rotate from the acute angle direction to the ray or normal.

[0101] In the first symbol system, clockwise rotation results in a negative symbol, and counterclockwise rotation results in a positive symbol.

[0102] In the second symbol system, clockwise rotation results in a positive symbol, and counterclockwise rotation results in a negative symbol.

[0103] (5) Angle between the optical axis and the normal: Starting from the optical axis, rotate from the acute angle direction to the ray or the normal.

[0104] In the first symbol system, clockwise rotation results in a negative symbol, and counterclockwise rotation results in a positive symbol.

[0105] In the second symbol system, clockwise rotation results in a positive symbol, and counterclockwise rotation results in a negative symbol.

[0106] (6) Angle between ray and normal: including and Starting from the normal, rotate from the acute angle direction to the ray.

[0107] In the first symbol system, clockwise rotation results in a negative symbol, and counterclockwise rotation results in a positive symbol.

[0108] In the second symbol system, clockwise rotation results in a positive symbol, and counterclockwise rotation results in a negative symbol.

[0109] Based on this, for optical systems under the first symbol system, the positive value includes , , , , Negative values ​​include , , , , , , , , The seven types of Seidel aberrations (spherical aberration, coma, astigmatism, field curvature, distortion, positional chromatic aberration, and magnification chromatic aberration) are represented as follows:

[0110] ;

[0111] ;

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] .

[0117] For optical systems in the second notation system, positive values ​​include , , Negative values ​​include , , , , , , , , , , The seven types of Seidel aberrations (spherical aberration, coma, astigmatism, field curvature, distortion, positional chromatic aberration, and magnification chromatic aberration) are represented as follows:

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] ;

[0124] .

[0125] In this invention, the first paraxial ray is an edge ray, defined as a ray emanating from an on-axis object point and passing through the edge point of the entrance pupil of the optical system. The incident angle and incident height of this ray with the i-th optical surface are denoted by u. i and h i The angle between the ray and the i-th optical surface is represented by u. i 'express.

[0126] The second paraxial ray is the principal ray, defined as the ray emitted from the off-axis field of view and passing through the center of the entrance pupil of the optical system. The angle of incidence and the incident height of this ray with the optical surface are respectively... and The angle between the ray and the i-th optical surface is represented by... 'express.

[0127] n i n represents the refractive index of the medium to the left of the optical surface with index i. i ' represents the refractive index of the medium to the right of the optical surface numbered i, n i+1 dn represents the refractive index of the medium to the left of the optical surface with index i+1. i This represents the difference in refractive index of the medium on the left side of the optical surface with serial number i after wavelength change; dn i ' represents the difference in refractive index of the medium to the right of optical surface i after the wavelength changes from the dominant wavelength to the dispersive wavelength; dn i+1 This represents the difference in refractive index of the medium on the left side of the optical surface with serial number i+1 after the wavelength changes from the dominant wavelength to the dispersive wavelength; d i r represents the distance between the vertex of the optical surface with index i and the vertex of the optical surface with index i+1; i c represents the radius of curvature of the sphere with index i. i k represents the curvature of the sphere or plane with index i; i f represents the conic coefficient of the sphere with index i; i df represents the image-side focal length of the metalens with serial number i; i denoted by λ, the difference between the image-side focal length and the principal wavelength image-side focal length of the metalens with serial number i at the wavelength of dispersion under study; where λ represents the principal wavelength of the incident light and ΔΦ represents the additional phase term of the metasurface at the fourth order or higher.

[0128] Metasurface phase design follows the following form:

[0129] .

[0130] Where j is any positive integer and i is any integer greater than 3.

[0131] Traditional catadioptric surfaces are designed according to the following form:

[0132] .

[0133] (m) represents the coefficient corresponding to the m-th power of the additional phase of the metalens with index i; This represents the distance between the position of the studied Фi on the superlens and the center of the superlens; The conic coefficient represents the conicity of a conventional catadioptric surface; The sag represents the physical meaning of the projection of the line connecting the position under study on the aspherical surface and the vertex of the subsurface onto the optical axis. It is positive when it is closer to the image side and negative when it is closer to the object side.

[0134] This invention confirms that the correlation between Seidel aberrations and wave aberrations of metasurfaces is completely consistent with the Seidel aberrations of traditional catadioptric optical systems, and can be converted using the same substitution method. Specifically, wave aberration coefficients include: spherical aberration coefficient, coma coefficient, astigmatism coefficient, Petzval field curvature coefficient, distortion coefficient, axial chromatic aberration defocusing term coefficient, transverse chromatic aberration tilt term coefficient, sagittal field curvature coefficient, intermediate field curvature coefficient, and meridional field curvature coefficient. These wave aberration coefficients can be directly converted to the seven types of Seidel aberration coefficients (including spherical aberration, coma, field curvature, astigmatism, distortion, positional chromatic aberration, and magnification chromatic aberration) derived in this invention for metasurfaces, thereby achieving a unified description and coordinated compensation of aberrations between metasurfaces and traditional catadioptric optical elements.

[0135] Meanwhile, in this invention, the relationship between lateral aberrations and axial aberrations and the Seidel coefficient is consistent with that of traditional catadioptric systems.

[0136] In some embodiments, the optical system design method based on metalens Seidel aberration further includes: when the target optical system includes a metasurface and other optical surfaces besides the metasurface, determining a first type of Seidel aberration function of the metasurface and a second type of Seidel aberration function of the other optical surfaces respectively; determining a hybrid objective function based on the first type of Seidel aberration function and the second type of Seidel aberration function; optimizing the hybrid objective function to obtain a hybrid optimization result; and determining the structural parameters of the target optical system based on the hybrid optimization result.

[0137] In some embodiments, the step of determining the first type of Seidel aberration function of the metasurface and the second type of Seidel aberration function of the other optical surfaces may specifically include:

[0138] The corresponding Seidel aberration function is determined according to the type of each surface in the target optical system; if the i-th surface in the target optical system is determined to be a metasurface, the first type of Seidel aberration function of the i-th surface is determined according to the first method; if the i-th surface in the target optical system is determined to be another optical surface, the second type of Seidel aberration function of the i-th surface is determined according to the second method.

[0139] Among them, the first type of Seidel aberration function is the Seidel coefficient of the metasurface newly proposed in the embodiments of the present invention, and the second type of Seidel aberration function refers to the traditional Seidel coefficient of the aspherical surface of refraction and reflection.

[0140] Please see Figure 3 , Figure 3 This is the second schematic flowchart of the optical system design method based on the Seidel aberration of a metalens provided in this embodiment of the invention. In this embodiment, the optical system design method based on the Seidel aberration of a metalens may include steps S310 to S340, each step of which is as follows:

[0141] S310: Determine the corresponding Seidel aberration function according to the type of each surface in the target optical system.

[0142] S311: If the i-th surface in the target optical system is determined to be a metasurface, then the first type of Seidel aberration function of the i-th surface is determined in the first manner.

[0143] S312: If the i-th surface in the target optical system is determined to be another optical surface, then the second type of Seidel aberration function of the i-th surface is determined in the second manner.

[0144] S313: Determine the first type of Seidel aberration function of the metasurface and the second type of Seidel aberration function of other optical surfaces in the target optical system.

[0145] S320: Determine the mixed objective function based on the first type Seidel aberration function and the second type Seidel aberration function.

[0146] S330: Optimize the mixed objective function to obtain the mixed optimization result.

[0147] S340: Determine the structural parameters of the target optical system based on the results of hybrid optimization processing.

[0148] This invention provides a design method for hybrid optical systems based on Seidel aberration superposition. The core of this method lies in directly superimposing the Seidel aberration coefficients of the metalens with those of the traditional catadioptric optical system to obtain the overall system aberration characteristics. Specifically, for any hybrid optical system, its total Seidel aberration coefficient can be expressed as the superposition of the Seidel aberration coefficients of the metalens and the traditional catadioptric system. This superposition calculation method provides a novel approach and possibility for the design of hybrid optical systems.

[0149] Specifically, under the first notation system, the spherical aberration coefficients of other optical surfaces It can be represented as:

[0150] .

[0151] Coma coefficients of other optical surfaces under the first notation system It can be represented as:

[0152] .

[0153] In the first notation system, the astigmatism coefficients of other optical surfaces It can be represented as:

[0154] .

[0155] Field curvature coefficients of other optical surfaces under the first notation system It can be represented as:

[0156] .

[0157] Distortion coefficients of other optical surfaces under the first notation system It can be represented as:

[0158] .

[0159] In the first notation system, the positional chromatic aberration coefficients of other optical surfaces It can be represented as:

[0160] .

[0161] Magnification chromatic aberration coefficients of other optical surfaces under the first notation system It can be represented as:

[0162] .

[0163] Specifically, under the second notation system, the spherical aberration coefficients of other optical surfaces It can be represented as:

[0164] .

[0165] Coma coefficients of other optical surfaces under the second notation system It can be represented as:

[0166] .

[0167] In the second notation system, the astigmatism coefficients of other optical surfaces It can be represented as:

[0168] .

[0169] Field curvature coefficients of other optical surfaces under the second notation system It can be represented as:

[0170] .

[0171] In the second notation system, the distortion coefficients of other optical surfaces It can be represented as:

[0172] .

[0173] In the second notation system, the positional chromatic aberration coefficients of other optical surfaces It can be represented as:

[0174] .

[0175] Magnification chromatic aberration coefficients of other optical surfaces under the second notation system It can be represented as:

[0176] .

[0177] in, Represents the curvature of the sphere or plane with index i; This represents the conic coefficient of the sphere with index i.

[0178] For the i-th surface of the target optical system, if it is a metasurface, then the Seidel aberration function of the metasurface is referenced, i.e.:

[0179] .

[0180] If the i-th element is a traditional catadioptric spherical mirror, conic surface, or aspherical surface, then the Seidel aberration method is used, referring to that of traditional catadioptric optical systems, i.e.:

[0181] .

[0182] The total Seidel aberration of the system is used as an intermediate variable:

[0183] ; ; ;

[0184] ; ; ;

[0185] ;

[0186] Where m represents the total number of metasurfaces and other optical surfaces in the target optical system; the P(S) function is any increasing function with respect to S.

[0187] Specifically, It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i.

[0188] In some embodiments, the hybrid objective function It can be represented as:

[0189] ;

[0190] Here, the function A(T) is any increasing function with respect to T or 0.

[0191] Specifically, The function is about An increasing function or 0; The correlation spherical aberration coefficients are obtained based on the spherical aberration coefficients in the first-type Seidel aberration function and the spherical aberration coefficients in the second-type Seidel aberration function. The function is about An increasing function or 0; The coma coefficients are obtained based on the coma coefficients in the first type of Seidel aberration function and the coma coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The correlation astigmatism coefficient is obtained based on the astigmatism coefficient in the first type Seidel aberration function and the astigmatism coefficient in the second type Seidel aberration function; The function is about An increasing function or 0; The relevant field curvature coefficients are obtained based on the field curvature coefficients in the first type of Seidel aberration function and the field curvature coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The relevant distortion coefficients are obtained based on the distortion coefficients in the first type Seidel aberration function and the distortion coefficients in the second type Seidel aberration function; The function is about An increasing function or 0; The relevant positional chromatic aberration coefficients are obtained based on the positional chromatic aberration coefficients in the first type of Seidel aberration function and the positional chromatic aberration coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The correlation chromatic aberration coefficient is obtained based on the chromatic aberration coefficients in the first type of Seidel aberration function and the chromatic aberration coefficients in the second type of Seidel aberration function.

[0192] In the process of using optimization algorithms, one or more F... 目标函数 As the objective function, find its minimum value or -F 目标函数 The maximum value.

[0193] During the optimization process, selectable variables include the distance d between two adjacent surface vertices, the structural parameters f of the metalens and the additional phase term ΔΦ (fourth order or higher), the curvature c of traditional optical elements, and the conic coefficient k, among other parameters. This multivariate optimization method can fully utilize the design freedom of the hybrid optical system and achieve overall optimization of system performance.

[0194] Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of the hybrid optical system provided in an embodiment of the present invention.

[0195] This embodiment employs an optical system containing a cemented doublet lens and a metalens. Wherein:

[0196] The first lens is a biconvex lens, made of conventional optical glass (taking BK7 as an example);

[0197] The second lens is a concave lens, made of conventional optical glass (taking F2 as an example);

[0198] The independent variables are: the curvature c1 and conic coefficient k1 of the first surface (refracting surface); the curvature c2 and conic coefficient k2 of the second surface (refracting surface); the curvature c3 and conic coefficient k3 of the third surface (refracting surface); the focal length f and the additional fourth-order phase coefficient dΦ of the fifth surface (metasurface); the distance d1 between the first and second surfaces (refracting surfaces); the distance d2 between the second and third surfaces (refracting surfaces); the distance d3 between the third surface (refracting surface) and the fourth surface (base surface); the distance d4 between the fourth surface (base surface) and the fifth surface (metasurface); the distance d5 between the fifth surface (metasurface) and the sixth surface (image distance); the entrance pupil radius h1; and the principal ray incident angle U3 of the third surface (aperture surface), for a total of 17 independent variables.

[0199] The types, values, and descriptions of each parameter are shown in the table below:

[0200]

[0201]

[0202] The target function is set as follows:

[0203] ;

[0204] In this process, the weight coefficient 'a' can be any positive number, but it is always set to 1.

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211]

[0212] .

[0213] Based on this, two constraint functions are defined, where constraint function g1 represents the focal length constraint and constraint function g2 represents the property constraint of the edge rays, as detailed below:

[0214] .

[0215] The present invention provides an optical system design method based on metalens Seidel aberration, establishes a complete theoretical system of metalens Seidel aberration, and realizes quantitative analysis of aberrations; by separating the contributions of paraxial parameter terms and phase modulation terms, the formation mechanism of metalens aberrations is revealed; and the aberration co-design of metalens and traditional optical systems is realized, providing a theoretical basis for the design of composite optical systems.

[0216] On the other hand, embodiments of the present invention also provide an electronic device, please refer to... Figure 5 , Figure 5 This is a schematic diagram of the physical structure of the electronic device provided in the embodiments of the present invention, such as... Figure 5 As shown, the electronic device may include a memory 520, a processor 510, and a computer program stored in the memory 520 and executable on the processor 510. When the processor 510 executes the program, it implements the optical system design method based on meta-lens Seidel aberration provided by the methods described above.

[0217] Optionally, the electronic device may further include a communication bus 530 and a communication interface 540, wherein the processor 510, the communication interface 540, and the memory 520 communicate with each other via the communication bus 530. The processor 510 can call a computer program in the memory 520 to execute an optical system design method based on the Seidel aberration of a metalens, which may include:

[0218] Determine the Seidel aberration function of the metasurface; wherein the Seidel aberration function includes spherical aberration coefficient, coma coefficient, and astigmatism coefficient; determine the target function based on the Seidel aberration function; perform optimization processing based on the target function to obtain the optimization processing result; determine the structural parameters of the target optical system based on the optimization processing result.

[0219] Furthermore, the logical instructions in the aforementioned memory 520 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0220] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the optical system design method based on meta-lens Seidel aberration provided by the above methods. The steps and principles of the method have been described in detail in the above methods and will not be repeated here.

[0221] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the optical system design method based on meta-lens Seidel aberration provided by the above methods. The steps and principles of the method have been described in detail in the above methods and will not be repeated here.

[0222] Non-transitory computer-readable storage media can be any available medium or data storage device that can be accessed by a processor, including but not limited to magnetic storage (e.g., floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (e.g., CDs, DVDs, BDs, HVDs, etc.), and semiconductor storage (e.g., ROMs, EPROMs, EEPROMs, non-volatile memory (NAND flash), solid-state drives (SSDs)).

[0223] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0224] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0225] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing an optical system based on the Seidel aberration of a metalens, characterized in that, include: Determine the Seidel aberration function of the metasurface; The Seidel aberration function mentioned above includes spherical aberration coefficient, coma coefficient, and astigmatism coefficient; The objective function is determined based on the Seidel aberration function. The optimization process is performed based on the objective function to obtain the optimization result; The structural parameters of the target optical system are determined based on the optimization results. The aberration coefficient Represented as: ， or, ; The coma coefficient Represented as: ， or, ; The astigmatism coefficient Represented as: ， or, ; in, This represents the refractive index of the medium to the left of the metasurface with index i. This represents the refractive index of the medium to the left of the metasurface with index i+1; This represents the angle of incidence between the first paraxial ray and the metasurface with index i; This represents the incident height of the first paraxial ray with the metasurface of index i; This represents the angle between the first paraxial ray and the exit angle of the metasurface with index i; This represents the angle of incidence between the second paraxial ray and the metasurface with index i; This represents the incident height of the second paraxial ray with the metasurface of index i; This represents the angle between the second paraxial ray and the exit angle of the metasurface with index i; the first paraxial ray is the edge ray, and the second paraxial ray is the principal ray; This represents the image-side focal length of the metasurface with index i. Indicates the dominant wavelength of the incident light; This represents the additional phase term of order four or higher for the metasurface with index i.

2. The optical system design method based on Seidel aberration of metalenses according to claim 1, characterized in that, The Seidel aberration function also includes field curvature coefficients and distortion coefficients; The field curvature coefficient Represented as: ; The distortion coefficient Represented as: ， or, .

3. The optical system design method based on Seidel aberration of metalenses according to claim 1, characterized in that, The Seidel aberration function also includes positional chromatic aberration coefficient and magnification chromatic aberration coefficient; The position color difference coefficient Represented as: ， or, ; The magnification color difference coefficient Represented as: ， or, ; in, This represents the difference in refractive index of the medium on the left side of the metasurface after a change in wavelength; This represents the difference in refractive index of the medium to the right of the metasurface with serial number i after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference in refractive index of the medium on the left side of the metasurface with serial number i+1 after the wavelength changes from the dominant wavelength to the dispersive wavelength. This represents the difference between the image-side focal length and the dominant wavelength image-side focal length of the metasurface with serial number i at the wavelength under study.

4. The optical system design method based on Seidel aberration of metalenses according to any one of claims 1 to 3, characterized in that, Also includes: When the target optical system includes a metasurface and other optical surfaces besides the metasurface, the first type of Seidel aberration function of the metasurface and the second type of Seidel aberration function of the other optical surfaces are determined respectively. The mixing objective function is determined based on the first type of Seidel aberration function and the second type of Seidel aberration function; The hybrid objective function is optimized to obtain the hybrid optimization result; The structural parameters of the target optical system are determined based on the results of the hybrid optimization process.

5. The optical system design method based on Seidel aberration of metalenses according to claim 4, characterized in that, The determination of the first type of Seidel aberration function of the metasurface and the second type of Seidel aberration function of the other optical surfaces includes: Determine the corresponding Seidel aberration function for each surface in the target optical system; If the i-th surface in the target optical system is determined to be a metasurface, then the first type of Seidel aberration function of the i-th surface is determined in the first manner; If the i-th surface in the target optical system is determined to be another optical surface, then the second type of Seidel aberration function of the i-th surface is determined in the second manner.

6. The optical system design method based on Seidel aberration of metalenses according to claim 5, characterized in that, The hybrid objective function Represented as: ； in, The function is about An increasing function or 0; The correlation spherical aberration coefficients are obtained based on the spherical aberration coefficients in the first type of Seidel aberration function and the spherical aberration coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The coma coefficients are obtained based on the coma coefficients in the first type of Seidel aberration function and the coma coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The correlation astigmatism coefficient is obtained based on the astigmatism coefficient in the first type of Seidel aberration function and the astigmatism coefficient in the second type of Seidel aberration function; The function is about An increasing function or 0; The relevant field curvature coefficients are obtained based on the field curvature coefficients in the first type of Seidel aberration function and the field curvature coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The relevant distortion coefficients are obtained based on the distortion coefficients in the first type of Seidel aberration function and the distortion coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The relevant positional chromatic aberration coefficients are obtained based on the positional chromatic aberration coefficients in the first type of Seidel aberration function and the positional chromatic aberration coefficients in the second type of Seidel aberration function; The function is about An increasing function or 0; The relevant chromatic aberration coefficients are obtained based on the chromatic aberration coefficients in the first type of Seidel aberration function and the chromatic aberration coefficients in the second type of Seidel aberration function.

7. The optical system design method based on Seidel aberration of metalenses according to claim 6, characterized in that, ； ； ； ； ； ； ； Where m represents the total number of metasurfaces and other optical surfaces in the target optical system; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i; It is about An increasing function; It refers to the spherical aberration coefficient of the metasurface or other optical surface with serial number i.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the optical system design method based on metalens Seidel aberration as described in any one of claims 1 to 7.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the optical system design method based on metalens Seidel aberration as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the optical system design method based on metalens Seidel aberration as described in any one of claims 1 to 7.

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