Vector aberration theory-based off-axis three-mirror system design method and system

Abstract

The invention relates to an off-axis three-reflector system design method and system based on a vector aberration theory. The method comprises the following steps: determining the focal length of an off-axis three-reflector system; determining the distance between the mirrors and the distance between the three reflectors and the image surface; according to the design requirements of the coaxial three-reflector system, calculating the curvature radiuses and quadric surface coefficients of the three reflectors; calculating the pupil radius of the pupil off-axis front three-reflector system according to the relationship between the pupil radius before and after the pupil off-axis and the pupil eccentric vector, and determining a wave aberration expression of the pupil off-axis rear three-reflector system; based on a paraxial ray tracing method and a vector aberration theory, establishing analytic expressions of a visual axis error, an increased coma error and an increased astigmatic aberration on a primary imaging surface about an inclination amount and an eccentricity amount; by taking optical axis error, coma error minimization and astigmatic aberration minimization as constraint conditions, optimally solving inclination amounts and eccentricity amounts of the three reflectors; structural parameters of the three-mirror system are optimized through optical simulation software. The efficient and reliable design method and system are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to off-axis three-mirror optical systems, in particular to an off-axis three-mirror system design method and system based on vector aberration theory. BACKGROUND

[0002] Three-mirror anastigmat (TMA) has important application value in the field of space optics due to its achromatic characteristics, large-aperture long-focus design, excellent system stability, and wide working waveband. By adopting a three-mirror compact configuration, the TMA system can correct primary aberrations such as spherical aberration, coma, and astigmatism, and achieve excellent imaging quality in a large field of view. However, the traditional on-axis three-mirror system has a central obstruction problem, which leads to a decline in imaging quality and energy loss. To overcome this defect, the off-axis three-mirror optical system adjusts the tilt and eccentricity of the mirrors to achieve an unobstructed design while ensuring imaging quality, and further improves the system compactness, making it exhibit significant advantages in the field of large field of view, large aperture, and high resolution imaging (such as space-to-ground observation, astronomical exploration, etc.).

[0003] Although the progress of modern optical processing and detection technology provides technical support for the realization of off-axis optical systems, the design process still faces severe challenges. The introduction of tilt and decentration will destroy the symmetry of the system, leading to a significant increase in asymmetric aberrations (such as coma and astigmatism), and the traditional aberration theory based on coaxial systems is difficult to apply directly. Vector aberration theory (Nodal Aberration Theory) provides a theoretical tool to solve this problem, and its research shows that the center of the aberration field of the off-axis system will deviate from the center of the Gaussian image plane, and the offset amount is determined by the center offset vector σ of the aberration field, while the aberration distribution characteristics can be related to the strict mathematical derivation and optical structure parameters and tilt decentration amount. However, the existing off-axis three-mirror system design method (such as the 2017 "Initial system design method for nonrotationally symmetric systems based on Gaussian brackets and Nodal aberration theory") still highly depends on numerical calculation and ray tracing, and lacks explicit expression of the analytical relationship between aberration and structure parameters, resulting in the risk of blind optimization in the design process. In addition, although the paper "Compensation factors for 3rd order coma in three mirror anastigmatic (TMA) telescopes" [S. Xu, Z. Cui, B. Qi, Published in Optics Express 8 January 2018, Engineering, Physics] derives the analytical relationship between coma and misalignment parameters, it does not systematically solve the problem of view axis guidance and aberration cooperative optimization in the initial structure design.

[0004] Therefore, it is urgent to establish an off-axis three-mirror system design method and system based on analytical basis and view axis regulation to improve the efficiency and reliability of off-axis three-mirror system design. SUMMARY

[0005] Therefore, it is necessary to provide an off-axis three-mirror system design method and system based on vector aberration theory to improve the efficiency and reliability of off-axis three-mirror system design.

[0006] To solve the above problems, the present application adopts the following technical solutions:

[0007] In a first aspect, the present application provides an off-axis three-mirror system design method based on vector aberration theory, comprising the following steps:

[0008] Step one, determine the focal length of the off-axis three-mirror system according to the application requirements;

[0009] Step two, determining the mirror spacing d1 between the primary mirror and the secondary mirror, the mirror spacing d2 between the secondary mirror and the tertiary mirror, and the spacing d3 between the tertiary mirror and the image plane;

[0010] Step three, calculating the curvature radius and the quadratic surface coefficient of the primary mirror, the secondary mirror and the tertiary mirror according to the design requirements of the coaxial three-mirror system, the design requirements of the coaxial three-mirror system including the focal length being a determined value, the field curvature being 0, the height of the paraxial marginal ray on the image plane being 0, the spherical aberration being 0, the coma being 0, and the astigmatism being 0;

[0011] Step four, calculating the pupil radius of the three-mirror system before pupil off-axis according to the relationship between the pupil off-axis front and rear pupil radius and the pupil eccentricity vector; combining the relationship between the normalized pupil vector and the normalized pupil eccentricity vector to determine the wave aberration expression of the three-mirror system after pupil off-axis;

[0012] Step five, based on the paraxial ray tracing method and the vector aberration theory, establishing the analytical expression of the viewing axis error about the tilt and eccentricity, the analytical expression of the increased coma about the tilt and eccentricity, and the analytical expression of the increased astigmatism about the tilt and eccentricity at the primary imaging plane according to the structural parameters of the three-mirror system, the viewing axis error being the relative deviation of the off-axis three-mirror system before and after the misadjustment of the optical axis ray and the intersection point of the primary image plane;

[0013] Step six, optimizing and solving the tilt and eccentricity of the three mirrors with the viewing axis error tending to the preset error determination value, the coma being minimized, and the astigmatism being minimized as the constraint conditions;

[0014] Step seven, optimizing the structural parameters of the three-mirror system through the optical simulation software.

[0015] In a preferred embodiment, the step two is specifically: determining the d1, d2 and d3 according to the envelope size of the off-axis three-mirror system and / or the position requirements of the mirrors in the off-axis three-mirror system.

[0016] In a preferred embodiment, the structural parameters include: d1, d2, d3, the curvature radius of the primary mirror, the quadratic surface coefficient of the primary mirror, the curvature radius of the secondary mirror, the quadratic surface coefficient of the secondary mirror, the curvature radius of the tertiary mirror, and the quadratic surface coefficient of the tertiary mirror.

[0017] In a preferred embodiment, the analytical expression of the increased coma about the tilt and eccentricity is:

[0018]

[0019] The analytical expression of the increased astigmatism about the tilt and eccentricity is:

[0020]

[0021] Where ΔW 131 Indicates the added coma, ΔW 222 Indicates the increased astigmatism aberration, j = PM, SM, TM, j = PM represents the primary mirror, j = SM represents the secondary mirror, j = TM represents the third mirror, represents the normalized field of view vector, represents the normalized aperture vector, represents the aberration field decentering vector of the spherical component of j, represents the aberration field decentering vector of the aspheric component of j.

[0022] In a preferred embodiment, the aberration field decentering vector is determined by paraxial ray tracing.

[0023] In a preferred embodiment, the process of establishing an analytical expression of the increased coma with respect to the tilt and decentering amount and an analytical expression of the increased astigmatism with respect to the tilt and decentering amount includes: substituting the aberration field center offset vector into the wave aberration expression obtained in step four to obtain an analytical expression of the increased coma with respect to the tilt and decentering amount and an analytical expression of the increased astigmatism with respect to the tilt and decentering amount.

[0024] In a preferred embodiment, the and stated Specifically:

[0025]

[0026] Among them, BDE PM Indicates the tilt value of the primary mirror around the x-axis, ADE PM Indicates the tilt value of the primary mirror around the y-axis, XDE PM Indicates the eccentricity of the primary mirror along the x-axis, YDE PM Indicates the eccentricity of the primary mirror along the y-axis, BDE SM Indicates the tilt value of the secondary mirror around the x-axis, ADE SM Indicates the tilt value of the secondary mirror around the y-axis, XDE SM Indicates the eccentricity of the secondary mirror along the x-axis, YDE SM Indicates the eccentricity of the secondary mirror along the y-axis, BDE TM Indicates the tilt value of the three mirrors around the x-axis, ADE TM Indicates the tilt value of the three mirrors around the y-axis, XDE TM Indicates the eccentricity of the three mirrors along the x-axis, YDE TM represents the eccentricity of the three mirrors along the y-axis, c SM represents the curvature of the secondary mirror surface, c TM represents the curvature of the mirror surface of the three mirrors, u PMIndicates the incident angle of the chief ray on the primary mirror.

[0027] In a preferred embodiment, the step four comprises a step of off-axis aperturing the three-mirror system, and the off-axis aperturing is implemented according to the following formula:

[0028]

[0029] Wherein, R1 represents the aperture radius of the three-mirror system before the pupil off-axis, R2 represents the aperture radius of the three-mirror system after the pupil off-axis, α1 is the obscuration ratio of the secondary mirror to the primary mirror, w is the designed half field angle, h off Indicates the pupil off-axis amount.

[0030] In a second aspect, the present application provides an off-axis three-mirror system designed by the method for designing an off-axis three-mirror system based on the vector aberration theory.

[0031] In a third aspect, the present application provides an off-axis three-mirror system design system based on the vector aberration theory, comprising:

[0032] A focal length determination module is configured to determine the focal length of the off-axis three-mirror system according to application requirements;

[0033] A distance determination module is configured to determine the mirror distance d1 between the primary mirror and the secondary mirror, the mirror distance d2 between the secondary mirror and the tertiary mirror, and the distance d3 between the tertiary mirror and the image plane;

[0034] A first calculation module is configured to calculate the curvature radius and the quadratic surface coefficient of the primary mirror, the secondary mirror and the tertiary mirror according to the design requirements of the on-axis three-mirror system, wherein the design requirements of the on-axis three-mirror system include that the focal length is a determined value, the field curvature is 0, the height of the paraxial marginal ray on the image plane is 0, the spherical aberration is 0, the coma aberration is 0, and the astigmatism aberration is 0;

[0035] A second calculation module is configured to calculate the pupil radius of the three-mirror system before the pupil off-axis according to the relationship between the pupil radius before and after the pupil off-axis and the pupil decentration vector, and to determine the wave aberration expression of the three-mirror system after the pupil off-axis in combination with the relationship between the normalized pupil vector and the normalized pupil decentration vector;

[0036] An expression establishment module is configured to establish, based on the paraxial ray tracing method and the vector aberration theory, the analytical expressions of the boresight error about the tilt and decentration, the analytical expressions of the added coma about the tilt and decentration, and the analytical expressions of the added astigmatism aberration about the tilt and decentration at the first image plane according to the structural parameters of the three-mirror system, wherein the boresight error is the relative shift of the optical axis rays before and after the misadjustment of the off-axis three-mirror system.

[0037] The third calculation module is configured to optimize and solve the tilt amount and the eccentric amount of the three mirrors with the constraint conditions of the boresight error tending to a preset error determination value, coma minimization and astigmatism minimization;

[0038] The optimization module is configured to optimize the structural parameters of the three-mirror system by using optical simulation software.

[0039] The design method and system of the off-axis three-mirror system based on the vector aberration theory are based on the design method using the boresight guidance based on the vector aberration theory, and aim to solve the problem of lacking of analytical method in the design of the existing off-axis three-mirror system. The design method and system first determine the focal length of the system according to the application requirement, determine the mirror spacing d1, d2 and d3, and then solve the curvature radius and the quadratic surface coefficient of the mirror based on certain conditions. For the pupil off-axis three-mirror system, the wave aberration expression is established by analyzing the relationship between the pupil radius and the pupil eccentricity vector before and after the pupil off-axis, and the analytical relationship of the boresight error and the coma and astigmatism about the tilt and eccentricity is constructed by combining the paraxial ray tracing and the vector aberration theory. On this basis, the mirror tilt and eccentricity are optimized under the conditions of the boresight error constraint, the coma minimization and the astigmatism minimization. Finally, the initial structural parameters are input into the optical simulation software for further optimization, and the off-axis three-mirror system with good imaging quality is obtained. The initial structure design is guided by the analytical method, and the efficient and reliable design method and system are realized based on the analytical basis and the boresight regulation. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 It is a flowchart of the method in one embodiment of the present application;

[0041] Figure 2 It is a structural schematic diagram of the system in one embodiment of the present application;

[0042] Figure 3 It is a schematic diagram of the three-mirror system after the pupil off-axis obtained in an application example of the present application;

[0043] Figure 4 It is a schematic diagram of the off-axis three-mirror system obtained in an application example of the present application. DETAILED DESCRIPTION

[0044] The technical solutions of the present application will be described in detail below with reference to the preferred embodiments and the accompanying drawings.

[0045] Please refer to Figure 1 The design method of the off-axis three-mirror system based on the vector aberration theory comprises the following steps:

[0046] Step one, determining the focal length of the off-axis three-mirror system according to the application requirement;

[0047] Step two, determining the mirror spacing d1 between the primary mirror and the secondary mirror, the mirror spacing d2 between the secondary mirror and the tertiary mirror, and the spacing d3 between the tertiary mirror and the image plane;

[0048] Step three, calculating the curvature radius of the primary mirror, the secondary mirror and the tertiary mirror, and solving the quadratic surface coefficients of the primary mirror, the secondary mirror and the tertiary mirror according to the design requirements of the coaxial three-mirror system, wherein the design requirements of the coaxial three-mirror system include that the focal length is a determined value, the field curvature is 0, the height of the paraxial marginal ray on the image plane is 0, the spherical aberration is 0, the coma is 0, and the astigmatism is 0;

[0049] Step four, calculating the pupil radius of the three-mirror system before pupil off-axis according to the relationship between the pupil radius and the pupil eccentricity vector, and determining the wavefront aberration expression of the three-mirror system after pupil off-axis in combination with the relationship between the normalized pupil vector and the normalized pupil eccentricity vector;

[0050] Step five, based on the paraxial ray tracing method and the vector aberration theory, establishing the analytical expression of the visual axis error about the tilt and eccentricity, the analytical expression of the increased coma about the tilt and eccentricity, and the analytical expression of the increased astigmatism about the tilt and eccentricity at the primary imaging plane according to the structural parameters of the three-mirror system, wherein the visual axis error is the relative deviation of the off-axis three-mirror system before and after the off-axis three-mirror system is out of adjustment.

[0051] Step six, optimizing and solving the tilt and eccentricity of the three mirrors under the constraint conditions that the visual axis error approaches the preset error determination value, the coma is minimized, and the astigmatism is minimized.

[0052] Step seven, optimizing the structural parameters of the three-mirror system through an optical simulation software.

[0053] In this embodiment, the structural parameters of the three-mirror system include d1, d2, d3, the curvature radius of the primary mirror, the quadratic surface coefficients of the primary mirror, the curvature radius of the secondary mirror, the quadratic surface coefficients of the secondary mirror, the curvature radius of the tertiary mirror, and the quadratic surface coefficients of the tertiary mirror.

[0054] The off-axis three-mirror system design method will be described in detail below. The design method includes:

[0055] Step one, determining the focal length of the off-axis three-mirror system according to the application requirements.

[0056] If the TMA system with an intermediate image plane is designed, the focal length is set to a positive value; if the TMA system without an intermediate image plane is designed, the focal length is set to a negative value.

[0057] Step two, according to the envelope size of the off-axis three-mirror system and / or the position requirements of the mirrors in the off-axis three-mirror system, determine d1, d2 and d3.

[0058] Step three, according to d1, d2 and d3, according to the design requirements of the on-axis three-mirror system, according to d1, d2 and d3 determined in step two, calculate the curvature radius of the three mirrors, and solve the quadratic surface coefficients of the primary mirror, the secondary mirror and the tertiary mirror according to the curvature radius.

[0059] The design requirements of the on-axis three-mirror system include meeting the first-order parameter condition and meeting the aberration-cancelling condition, wherein the first-order optical parameter condition is that the focal length is a certain value, the field curvature is 0, and the height of the near-axis marginal ray on the image plane is 0. The aberration-cancelling condition is that the spherical aberration, coma and astigmatism are all 0.

[0060] Here, the curvature radius and the quadratic surface coefficients of the three mirrors are solved by an analytical method.

[0061] It can be understood that here the on-axis TMA optical system is designed, and in the subsequent steps, the off-axis processing is performed.

[0062] Step four, calculate the pupil radius of the off-axis three-mirror system through the relationship between the front and rear pupil radii of the pupil off-axis and the pupil eccentricity vector, and obtain the wave aberration expression of the off-axis three-mirror system in combination with the relationship between the normalized pupil vector and the normalized pupil eccentricity vector.

[0063] Step five, according to the structure parameters (d1, d2, d3, the curvature radius of the three mirrors, the quadratic surface coefficients of the three mirrors) of the off-axis three-mirror system, according to the wave aberration expression, based on the near-axis ray tracing method and the vector aberration theory, establish the analytical expression of the boresight error about the tilt value and the eccentricity value at the first imaging plane, based on the near-axis ray tracing method and the vector aberration theory, establish the analytical expression of the increased coma about the tilt value and the eccentricity value, and based on the near-axis ray tracing method and the vector aberration theory, establish the analytical expression of the increased astigmatism about the tilt value and the eccentricity value.

[0064] It can be understood that the increased coma is the coma increased compared with the coma of the on-axis TMA optical system obtained in step three, and the increased astigmatism is the astigmatism increased compared with the astigmatism of the on-axis TMA optical system obtained in step three.

[0065] It can be understood that step three designs the on-axis TMA optical system, step four performs the eccentricity, and step five performs the tilt. The off-axis optical system refers to a system in which the optical elements have tilt and eccentricity. The off-axis system can be understood as an optical system in which the optical elements only have eccentricity.

[0066] The increased coma and the increased astigmatism aberration are calculated by a wave aberration expression in vector form (wave aberration expression obtained in step four).

[0067] Specifically, aberration field eccentricity vectors of the primary mirror, the secondary mirror and the tertiary mirror are obtained according to paraxial ray tracing.

[0068]

[0069] wherein PM represents the primary mirror (the first reflecting mirror), SM represents the secondary mirror (the second reflecting mirror), TM represents the tertiary mirror (the third reflecting mirror), sph represents a spherical component, asph represents an aspherical component, BDE represents a tilt value along the x-axis, ADE represents a tilt value along the y-axis, XDE represents an eccentricity value in the x direction, YDE represents an eccentricity value in the y direction, and c represents a curvature of a mirror surface, represents an incident angle of a chief ray on the PM, represents an aberration field eccentricity vector of the spherical component of the primary mirror, represents an aberration field eccentricity vector of the aspherical component of the primary mirror, represents an aberration field eccentricity vector of the spherical component of the secondary mirror, represents an aberration field eccentricity vector of the aspherical component of the secondary mirror, represents an aberration field eccentricity vector of the spherical component of the tertiary mirror, represents an aberration field eccentricity vector of the aspherical component of the tertiary mirror, BDE PM represents a tilt value of the primary mirror around the x-axis, ADE PM represents a tilt value of the primary mirror around the y-axis, XDE PM represents an eccentricity value of the primary mirror along the x-axis, YDE PM represents an eccentricity value of the primary mirror along the y-axis, BDE SM represents a tilt value of the secondary mirror around the x-axis, ADE SM represents a tilt value of the secondary mirror around the y-axis, XDE SM represents an eccentricity value of the secondary mirror along the x-axis, YDE SM represents an eccentricity value of the secondary mirror along the y-axis, BDE TM represents a tilt value of the tertiary mirror around the x-axis, ADE TM represents a tilt value of the tertiary mirror around the y-axis, XDE TM represents an eccentricity value of the tertiary mirror along the x-axis, YDE TM represents an eccentricity value of the tertiary mirror along the y-axis, c SM represents a curvature of a mirror surface of the secondary mirror, c TM represents a curvature of a mirror surface of the tertiary mirror.

[0070] Based on the paraxial ray tracing theory, an accurate expression of the visual axis error at the first imaging plane can be derived.

[0071] The effective field of view is brought into the wavefront aberration expression in vector form, and a wavefront aberration vector expression of the tilted and decentered optical system is obtained. If only the third-order aberration is considered, the astigmatism in the primary wavefront aberration is derived from three parts: the third-order astigmatism, the third-order coma, and the third-order spherical aberration; the coma in the primary wavefront aberration is derived from two parts: the third-order coma and the third-order spherical aberration. After reintegration, the increased coma ΔW 131 and the increased astigmatism ΔW 222 are obtained as follows:

[0072]

[0073] wherein j represents a mirror (PM, SM, TM), j=PM represents a primary mirror, j=SM represents a secondary mirror, and j=TM represents a tertiary mirror, and the summation is summed for j=PM, j=SM, and j=TM. W 131 represents a wavefront aberration coefficient of the coma, represents a wavefront aberration coefficient of the coma of the spherical component of the surface j, represents a wavefront aberration coefficient of the coma of the aspherical component of the surface j, W 222 represents a wavefront aberration coefficient of the astigmatism, represents a wavefront aberration coefficient of the astigmatism of the spherical component of the surface j, represents a wavefront aberration coefficient of the astigmatism of the aspherical component of the surface j, represents a normalized field of view vector, represents a normalized aperture vector, represents a decentering vector of the aberration field of the spherical component of j, represents a decentering vector of the aberration field of the aspherical component of j.

[0074] It should be noted that an off-axis system is one in which optical elements exhibit tilt and decentering. Coma and astigmatism introduced by tilt and decentering are the primary aberrations, and the analysis primarily focuses on these two aberrations. Based on vector aberration theory, it is found that the wavefront aberration of an asymmetric optical system image plane is still the sum of the contributions of the aberrations from each surface and does not introduce new aberration types. The center of symmetry of the aberrations caused by off-axis surfaces in the system will deviate from the Gaussian image plane center of the system. The specific position of the aberration field center of symmetry in the field of view depends on the aberration field center offset vector σ. The aberration field center offset vector is determined by paraxial ray tracing. This method can calculate an analytical expression for the visual axis error at the imaging plane with respect to optical structural parameters and tilt and decentering. Substituting the aberration field center offset vector into the vectorial wavefront aberration expression yields analytical expressions for the increased coma and astigmatism in the off-axis system. The wavefront aberration coefficient can be calculated based on the corresponding relationship between the wavefront aberration coefficient and the Seidel coefficient. The Seidel coefficient can be expressed as an expression related to optical structural parameters. The boresight indicates the general orientation of an optical system, while the boresight error represents the offset of the image plane after system misalignment relative to the image plane without misalignment. It is defined as the relative offset between the intersection of the optical axis ray (OAR) and the primary image plane before and after system misalignment. By controlling the boresight error at the primary image plane, the system can be made more compact while avoiding occlusion. Paraxial ray tracing methods provide an analytical basis for controlling the boresight error through tilt and decentration.

[0075] Step 6: With the boresight error approaching the preset error value, and the coma and astigmatism aberrations minimized as constraints, optimize the tilt and decentering of each mirror to achieve a compact system design while avoiding optical obstructions and controlling the aberrations and coma to the optimal levels.

[0076] The visual axis error is defined as the relative offset of the intersection of the optical axis light and the primary image plane before and after the off-axis three-mirror system is misaligned. Specifically, the visual axis error is precisely controlled by adjusting the tilt and eccentricity.

[0077] The optimization solution is achieved through an iterative algorithm, ensuring that the system meets the dual goals of minimizing astigmatism and achieving a compact structure while avoiding obstruction.

[0078] Step 7: Input the structural parameters of the off-axis three-mirror system into the optical simulation software for further optimization to achieve better imaging quality.

[0079] After the above steps 1 to 7, the designed off-axis three-mirror system is obtained.

[0080] In one embodiment, an off-axis three-mirror system is provided, wherein the system is designed using the above-mentioned off-axis three-mirror system design method based on vector aberration theory.

[0081] Referring to Figure 2 , provide a kind of off-axis three-mirror system design system based on vector aberration theory, comprising:

[0082] focal length determination module, for determining the focal length of off-axis three-mirror system according to application requirement;

[0083] interval determination module, for determining the mirror interval d1 of primary mirror and secondary mirror, the mirror interval d2 between secondary mirror and three-mirror, the interval d3 between three-mirror and image plane;

[0084] first calculation module, for calculating the curvature radius and quadratic surface coefficient of primary mirror, secondary mirror and three-mirror according to the design requirement of coaxial three-mirror system, the design requirement of coaxial three-mirror system includes focal length is determined value, field curvature is 0, the height of near-axis marginal ray on image plane is 0, spherical aberration is 0, coma is 0 and astigmatic aberration is 0;

[0085] second calculation module, for calculating the pupil radius of three-mirror system before pupil off-axis according to the relationship between pupil off-axis front and rear pupil radius and pupil eccentric vector, for determining the wave aberration expression of three-mirror system after pupil off-axis in combination with the relationship between normalized pupil vector and normalized pupil eccentric vector;

[0086] expression establishment module, for establishing the analytical expression of visual axis error about tilt and eccentricity, the analytical expression of added coma about tilt and eccentricity, the analytical expression of added astigmatic aberration about tilt and eccentricity at primary imaging plane based on near-axis ray tracing method and vector aberration theory according to the structural parameters of three-mirror system, the visual axis error is the relative deviation of primary mirror before and after off-axis three-mirror system;

[0087] third calculation module, for optimizing and solving the tilt and eccentricity of three mirrors with the constraint condition that visual axis error approaches preset error determination value, coma minimization and astigmatic aberration minimization;

[0088] optimization module, for optimizing the structural parameters of three-mirror system by optical simulation software.

[0089] The off-axis three-mirror system design system based on vector aberration theory can be implemented by referring to any one of the above embodiments when implemented, and the specific implementation steps will not be repeated.

[0090] A design example is given as follows:

[0091] An off-axis three-mirror system with an aperture of 1300mm, F number of 15.9 and field angle of 1.084°x0.469° is designed, and the stop is located on the primary mirror. According to the given focal length of 20670mm and the mirror spacing, the optical structure parameters of the initial structure are shown in Table 1.

[0092] Table 1

[0093]

[0094] Then the aperture off-axis of the three-mirror system is performed, and the specific formula is as follows:

[0095]

[0096] Wherein, R1 represents the aperture radius of the three-mirror system before pupil off-axis, R2 represents the aperture radius of the three-mirror system after pupil off-axis, α1 is the obscuration ratio of the secondary mirror to the primary mirror, w is the designed half field angle, h off represents the pupil off-axis amount, R2=1300mm, R1=2368.5mm is calculated, and the off-axis amount h off =1160mm. The schematic diagram of the three-mirror system after pupil off-axis is shown in Figure 3 . The h off , R1 and R2 are brought into the expressions of coma and astigmatism, the off-axis three-mirror system structure schematic diagram is shown in Figure 4 .

[0097] Table 2

[0098]

[0099] The application provides a method and system for designing an off-axis three-mirror system based on vector aberration theory, and a method for designing an off-axis three-mirror system based on vector aberration theory and guided by a visual axis, aiming to solve the problem of lack of analytical method for designing an off-axis three-mirror system. The method and system first determine the focal length of the system according to application requirements, determine the mirror spacing d1, d2 and d3, and then solve the curvature radius and quadratic surface coefficient of the mirror based on certain conditions. For a pupil off-axis three-mirror system, the wave aberration expression is established by analyzing the relationship between the pupil radius and the pupil eccentricity vector before and after the pupil off-axis, and the analytical relationship between the visual axis error and the coma and astigmatism aberrations about the tilt eccentricity is constructed by combining the paraxial ray tracing and the vector aberration theory. On this basis, the mirror tilt and eccentricity are optimized under the conditions of visual axis error constraint and minimization of coma and astigmatism aberrations, and finally the initial structure parameters are input into an optical simulation software for further optimization to obtain an off-axis three-mirror system with good imaging quality. The application guides the initial structure design through the analytical method, and controls the visual axis based on the analytical foundation, thereby avoiding the blindness of traditional numerical optimization and providing an efficient and reliable design method for the design of compact and high-performance off-axis three-mirror systems.

[0100] The application establishes an off-axis three-mirror system design method with a rigorous analytical foundation, and clearly reveals the mathematical correlation between the aberration field center shift vector, the visual axis error and the structure parameters by combining the paraxial ray tracing and the vector aberration theory, thereby providing theoretical guidance for initial structure generation. This method fills the gap between analytical design and visual axis control in the prior art, and significantly improves the efficiency and reliability of off-axis system design.

[0101] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described, but as long as the combinations of the technical features do not contradict, they should be considered as within the scope of the present disclosure.

[0102] The above-described embodiments only express several implementation manners of the application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for those skilled in the art, without departing from the concept of the application, some modifications and improvements can be made, which are within the scope of the application. Therefore, the protection scope of the patent of the application should be subject to the appended claims.

Claims

1. A design method for an off-axis three-mirror system based on vector aberration theory, characterized in that: The steps include: Step 1: Determine the focal length of the off-axis three-mirror system based on application requirements; Step 2: Determine the mirror spacing d1 between the primary reflector and the secondary reflector, the mirror spacing d2 between the secondary reflector and the third reflector, and the spacing d3 between the third reflector and the image plane; Step 3: Calculate the curvature radius and quadric surface coefficient of the primary reflector, secondary reflector, and tertiary reflector according to the design requirements of the coaxial three-mirror system, wherein the design requirements of the coaxial three-mirror system include a fixed focal length, zero field curvature, zero height of the paraxial marginal ray on the image plane, zero spherical aberration, zero coma, and zero astigmatism; Step 4: Calculate the pupil radius of the three-mirror system before and after the pupil is off-axis based on the relationship between the pupil radius and the pupil eccentricity vector; determine the wavefront aberration expression of the three-mirror system after the pupil is off-axis based on the relationship between the normalized pupil vector and the normalized pupil eccentricity vector; Step 5: Based on the structural parameters of the three-mirror system, paraxial ray tracing and vector aberration theory, establish an analytical expression for the boresight error at the primary imaging plane with respect to the tilt and decentering amount, an analytical expression for the added coma with respect to the tilt and decentering amount, and an analytical expression for the added astigmatism with respect to the tilt and decentering amount. The boresight error is the relative offset of the intersection point of the optical axis light and the primary image plane before and after the off-axis three-mirror system is misaligned. Step 6: Optimize the tilt and decentering of the three mirrors with the constraints of the line of sight error approaching the preset error value, minimizing coma aberration, and minimizing astigmatism aberration. Step 7: Optimize the structural parameters of the three-mirror system through optical simulation software.

2. The off-axis three-mirror system design method based on vector aberration theory according to claim 1, characterized in that: The step 2 specifically includes: determining d1, d2 and d3 according to the envelope size of the off-axis three-mirror system and / or the position requirements of the reflective mirrors in the off-axis three-mirror system.

3. The off-axis three-mirror system design method based on vector aberration theory according to claim 1, characterized in that: The structural parameters include: d1, d2, d3, the curvature radius of the primary reflector, the quadratic surface coefficient of the primary reflector, the curvature radius of the secondary reflector, the quadratic surface coefficient of the secondary reflector, the curvature radius of the third reflector, and the quadratic surface coefficient of the third reflector.

4. The off-axis three-mirror system design method based on vector aberration theory according to claim 1, characterized in that: The analytical expression of the increased coma with respect to the tilt and decentering is: The analytical expression of the increased astigmatism with respect to the tilt and decentering is: Where ΔW 131 Indicates the added coma, ΔW 222 Indicates the increased astigmatism aberration, j = PM, SM, TM, j = PM represents the primary mirror, j = SM represents the secondary mirror, j = TM represents the third mirror, represents the normalized field of view vector, represents the normalized aperture vector, represents the aberration field decentering vector of the spherical component of j, represents the aberration field decentering vector of the aspheric component of j.

5. The off-axis three-mirror system design method based on vector aberration theory according to claim 4, characterized in that: The aberration field eccentricity vector is determined by paraxial ray tracing method.

6. The off-axis three-mirror system design method based on vector aberration theory according to claim 5, characterized in that: The process of establishing an analytical expression of the increased coma with respect to the tilt and decentering amount and an analytical expression of the increased astigmatism with respect to the tilt and decentering amount includes: substituting the aberration field center offset vector into the wave aberration expression obtained in step four to obtain an analytical expression of the increased coma with respect to the tilt and decentering amount and an analytical expression of the increased astigmatism with respect to the tilt and decentering amount.

7. The off-axis three-mirror system design method based on vector aberration theory according to claim 5, characterized in that: described and stated Specifically: Among them, BDE PM Indicates the tilt value of the primary mirror around the x-axis, ADE PM Indicates the tilt value of the primary mirror around the y-axis, XDE PM Indicates the eccentricity of the primary mirror along the x-axis, YDE PM Indicates the eccentricity of the primary mirror along the y-axis, BDE SM Indicates the tilt value of the secondary mirror around the x-axis, ADE SM Indicates the tilt value of the secondary mirror around the y-axis, XDE SM Indicates the eccentricity of the secondary mirror along the x-axis, YDE SM Indicates the eccentricity of the secondary mirror along the y-axis, BDE TM Indicates the tilt value of the three mirrors around the x-axis, ADE TM Indicates the tilt value of the three mirrors around the y-axis, XDE TM Indicates the eccentricity of the three mirrors along the x-axis, YDE TM represents the eccentricity of the three mirrors along the y-axis, c SM represents the curvature of the secondary mirror surface, c TM represents the curvature of the mirror surface of the three mirrors, u PM It represents the incident angle of the chief ray on the primary mirror.

8. The off-axis three-mirror system design method based on vector aberration theory according to claim 1, characterized in that: The fourth step includes the step of performing an aperture off-axis on the three-mirror system, and the aperture off-axis is achieved according to the following formula: Where R1 is the aperture radius of the three-mirror system before the pupil is off-axis, R2 is the aperture radius of the three-mirror system after the pupil is off-axis, α1 is the blocking ratio of the secondary mirror to the primary mirror, w is the designed half field angle, h is off Indicates the amount of pupil off-axis.

9. An off-axis three-mirror system, characterized in that: The off-axis three-mirror system is designed using the off-axis three-mirror system design method based on vector aberration theory described in any one of claims 1 to 8.

10. A design system for an off-axis three-mirror system based on vector aberration theory, characterized in that: include: A focal length determination module is used to determine the focal length of the off-axis three-mirror system according to application requirements; A spacing determination module is used to determine the mirror spacing d1 between the primary reflector and the secondary reflector, the mirror spacing d2 between the secondary reflector and the third reflector, and the spacing d3 between the third reflector and the image plane; a first calculation module, configured to calculate the curvature radii and quadric surface coefficients of the primary reflector, the secondary reflector, and the tertiary reflector according to design requirements of the coaxial three-mirror system, wherein the design requirements of the coaxial three-mirror system include a focal length of a certain value, zero field curvature, zero height of the paraxial marginal ray on the image plane, zero spherical aberration, zero coma, and zero astigmatism; The second calculation module is used to calculate the pupil radius of the three-mirror system before the pupil is off-axis based on the relationship between the pupil radius before and after the pupil is off-axis and the pupil eccentricity vector, and to determine the wavefront aberration expression of the three-mirror system after the pupil is off-axis by combining the relationship between the normalized pupil vector and the normalized pupil eccentricity vector; An expression establishment module is used to establish, based on the structural parameters of the three-mirror system, a paraxial ray tracing method and vector aberration theory, an analytical expression for the boresight error at the primary imaging surface with respect to the tilt and decentering amount, an analytical expression for the added coma with respect to the tilt and decentering amount, and an analytical expression for the added astigmatism with respect to the tilt and decentering amount, wherein the boresight error is the relative offset of the intersection point of the optical axis ray and the primary image surface before and after the off-axis three-mirror system is misaligned; The third calculation module is used to optimize the tilt and decentering of the three mirrors under the constraints of the visual axis error approaching a preset error determination value, minimizing coma aberration and minimizing astigmatism aberration; The optimization module is used to optimize the structural parameters of the three-mirror system through optical simulation software.

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