CN113777779A - Method for structure calculation and free-form surface type conversion of dual-focal-length deformation optical system - Google Patents

Method for structure calculation and free-form surface type conversion of dual-focal-length deformation optical system Download PDF

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CN113777779A
CN113777779A CN202111014855.6A CN202111014855A CN113777779A CN 113777779 A CN113777779 A CN 113777779A CN 202111014855 A CN202111014855 A CN 202111014855A CN 113777779 A CN113777779 A CN 113777779A
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mirror
optical system
primary
secondary mirror
curvature
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CN113777779B (en
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是逸
郑玉权
蔺超
纪振华
张佳伦
韩艳雪
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Abstract

The invention provides a method for structure calculation and free-form surface type conversion of a dual-focal-length deformation optical system. The primary aberration formula of the coaxial rotationally symmetric optical system with the real entrance pupil is deduced, the curvature radius relational expression of each reflector in the bifocal anamorphic optical system in the meridian and sagittal directions is established, the conversion relation between the Biconic surface type and the XY polynomial free-form surface type is established, and the rapid calculation of the initial structure of the bifocal anamorphic free-form surface optical system is realized. The optical system designed by the method provided by the invention has good imaging characteristics, greatly saves the time for design and optimization compared with the method for realizing the deformation design from a single focal length to a double focal length by relying on optical design software, and has high efficiency and good stability.

Description

Method for structure calculation and free-form surface type conversion of dual-focal-length deformation optical system
Technical Field
The invention belongs to the technical field of optical design, and particularly relates to a free-form surface type conversion method and a method for calculating an initial structure of a bifocal deformable free-form surface telescopic objective lens by using the free-form surface type conversion method.
Background
Space optical telescopes can be divided into refractive, reflective and catadioptric systems. The reflective system has the advantages of long focal length, no chromatic aberration, wide spectral range and the like, and has important use value in a space system. The design freedom of the rotationally symmetric spherical or traditional aspheric surface type telescope is low, the large field edge aperture aberration is difficult to correct, and the off-axis bifocal deformation design cannot be realized.
In 10 months in 2017, the ESA successfully launches a dedicated global atmospheric pollution detection satellite Sentinel-5P (Sentinel-5P), and the satellite carries a remote sensing sensor troposphere observation instrument (TROPOMI), so that the trace gas components in the atmosphere of all parts of the world can be effectively monitored, and the observation of aerosol and cloud is enhanced. The imaging width of TROPOMI reaches 2600km, the TROPOMI covers all over the world every day, and the measured spectral regions comprise an ultraviolet-visible light spectral region (UV-VIS), a near infrared spectral region (NIR) and a short wave infrared spectral region (SWIR). The front telescope system consists of two concave free-form surface reflectors, the field angle is 108 degrees, and the spatial resolution reaches 7 multiplied by 7km2The aperture is F/9 XF/10, and the focal length is 34mm X68 mm. Reading the relevant documents and patents, the method for acquiring the initial structure of the deformable lens group with different magnifications in the meridian direction and the sagittal direction, such as the TROPOMI front telescope, is not discussed in detail.
Disclosure of Invention
The invention provides a method for resolving a bifocal anamorphic optical system structure and converting a free-form surface type, aiming at solving the problem of how to obtain an initial structure of an off-axis bifocal reflective anamorphic free-form surface telescope, wherein a Biconic surface type is selected as an initial surface type for system fitting, the Biconic surface type is converted into an XY polynomial free-form surface type for off-axis optimization, surface type deviation caused by converting the Biconic surface type into the XY polynomial free-form surface type is compensated by adding an XY polynomial item, and the original Biconic surface type is refitted to obtain a free-form surface for realizing off-axis bifocal anamorphic design in the bifocal anamorphic free-form surface optical system; at the beginning of design, parameters of the initial structure of the bifocal deformable free-form surface optical system can be solved by determining the design indexes and constraint conditions of the bifocal deformable free-form surface optical system. In order to achieve the purpose, the invention adopts the following specific technical scheme:
a free-form surface type conversion method comprises the following steps:
a1, constructing a bifocal aspheric optical system based on a Biconic surface type by using optical design software, wherein the expression of the Biconic surface type is as follows:
Figure BDA0003239490280000021
wherein, CxAnd CyCurvatures of the Biconic surface type in the X direction and the Y direction respectively;
kxand kyRespectively representing the conconic coefficients of the Biconic surface type in the X direction and the Y direction;
a2, converting the Biconic surface type into an XY polynomial free-form surface type, wherein the expression of the XY polynomial free-form surface type is as follows:
Figure BDA0003239490280000022
wherein, c is 1/R,
r is the curvature radius of the XY polynomial free-form surface;
k is the conc coefficient of the XY polynomial free-form surface;
Aiis a polynomial xmynM is more than or equal to 0, n is more than or equal to 0;
a3, determining the conversion relation of polynomial terms of the XY polynomial free-form surface type expression to obtain the XY polynomial free-form surface type expression for surface type conversion:
Figure BDA0003239490280000023
wherein the polynomial term x2Is used to achieve a variation of the radius of curvature in the X direction,
polynomial term x4The coefficient of (2) is used for compensating the consecutive coefficient in the X direction in the face type conversion;
polynomial term y2Is used to achieve a modification of the radius of curvature in the Y direction;
polynomial term y4Is used to compensate the consecutive coefficients in the Y direction in the face-type conversion.
A double-focal length anamorphic optical system structure calculating method comprises the following steps:
b1, solving a primary aberration formula of the coaxial rotational symmetry optical system, constructing a curvature radius relational expression of the primary mirror and the secondary mirror in the dual-focal length deformation optical system in the meridian and sagittal directions, and acquiring all parameters for free-form surface type conversion by using the primary aberration formula of the coaxial rotational symmetry optical system and the curvature radius relational expression of the primary mirror and the secondary mirror in the dual-focal length deformation optical system in the meridian direction and the sagittal direction, wherein the curvature radius relational expression is as follows:
Figure BDA0003239490280000031
wherein R is1x、R1yRespectively the curvature radius of the primary mirror in the sagittal direction and the meridional direction,
R2x、R2ythe curvature radiuses of the secondary mirror in the sagittal direction and the meridional direction respectively,
n is the ratio of the focal length in the preset meridional direction and sagittal direction;
all parameters include: principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure BDA0003239490280000032
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000033
Meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMeridional aspheric coefficient of primary mirror
Figure BDA0003239490280000034
Meridional aspheric coefficient of secondary mirror
Figure BDA0003239490280000035
B2, converting the curvature radius and aspheric coefficients of the primary mirror and the secondary mirror in the meridian and sagittal directions into polynomial terms of an XY polynomial free-form surface using the free-form surface conversion method of claim 1 using all the parameters obtained in step B1 to obtain initial structural parameters of the bifocal anamorphic optical system;
the initial structural parameters include: radius of curvature R of primary mirror1Radius of curvature R of secondary mirror2Aspheric coefficient of primary mirror
Figure BDA0003239490280000036
Aspheric coefficient of secondary mirror
Figure BDA0003239490280000037
Polynomial term x of primary mirror2Coefficient A of3Polynomial term x of primary mirror4Coefficient A of10Polynomial term y of primary mirror2Coefficient A of4Polynomial term y of primary mirror4Coefficient A of11Polynomial term x of secondary mirror2Coefficient A'3Polynomial term x of secondary mirror4Coefficient A'10Polynomial term of the secondary mirror y2Coefficient A'4Polynomial term of the secondary mirror y4Coefficient A'11。
Preferably, step B1 includes the steps of:
b11, deriving a primary aberration formula of the coaxial rotationally symmetric optical system;
and B12, acquiring all parameters of the primary mirror and the secondary mirror for free-form surface conversion in the meridional direction and the sagittal direction by using a primary aberration formula of the coaxial rotational symmetry optical system.
Preferably, step B11 includes the steps of:
b111, tracking the thin light beams at the off-axis points, determining the position l of an entrance pupil in the coaxial rotationally symmetric optical system, wherein the position of the entrance pupil and the curvature radii of the primary mirror and the secondary mirror satisfy the following relational expression:
Figure BDA0003239490280000041
wherein R is1、R2The curvature radius of the primary mirror and the curvature radius of the secondary mirror are respectively;
b112, tracking the marginal field-of-view light beam to obtain the projection height y of the light beam passing through the entrance pupil on the primary mirror in the coaxial rotationally symmetric optical system1And the projection height y of the light beam on the secondary mirror through the entrance pupil2Expression (c):
Figure BDA0003239490280000042
wherein theta is the field angle of the edge view,
alpha is the ratio of the obscuration to the total weight of the film,
beta is the magnification of the secondary mirror,
f2' is the focal length of the secondary mirror,
u2is the object space aperture angle of the secondary mirror;
b113, passing the light beam through the entrance pupil and projecting the light beam on the primary mirror to a height y1And the projection height y of the light beam on the secondary mirror through the entrance pupil2Substituting the primary aberration expression to obtain a primary aberration formula of the coaxial rotationally symmetric optical system with the real entrance pupil structure:
Figure BDA0003239490280000043
preferably, step B12 includes the steps of:
b121, acquiring a first parameter of the primary mirror and the secondary mirror in a sagittal direction or acquiring a second parameter of the primary mirror and the secondary mirror in a meridional direction according to a design index and a Gaussian formula by using a primary aberration formula (6) of a coaxial rotationally symmetric optical system with a real entrance pupil structure;
the first parameter includes: principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure BDA0003239490280000051
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000052
The second parameters include: meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMeridional aspheric coefficient of primary mirror
Figure BDA0003239490280000053
Meridional aspheric coefficient of secondary mirror
Figure BDA0003239490280000054
B122, solving the meridional curvature radius R of the primary mirror by using the relational expression (4)1yRadius of curvature R in meridian direction of secondary mirror2yOr solving the curvature radius R of the principal mirror in the sagittal direction by using the relation (4)1xRadius of curvature R in sagittal direction of secondary mirror2x；
B123, solving the aspheric coefficient in the meridian direction of the primary mirror by using the primary aberration formula (6) of the coaxial rotationally symmetric optical system with the real entrance pupil again
Figure BDA0003239490280000055
Meridional aspheric coefficient of secondary mirror
Figure BDA0003239490280000056
Or sagittal of primary mirrorDirection aspheric coefficient
Figure BDA0003239490280000057
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000058
And obtaining all parameters of the primary mirror and the secondary mirror for free-form surface conversion.
The invention can obtain the following technical effects:
1. the invention constructs the conversion relation between the Biconic surface type and the XY polynomial free-form surface type, and the conversion relation is suitable for a dual-focus reflective system.
2. The invention provides a method for calculating an initial structure of a dual-focal-length deformed free-form surface optical system.
3. Each reflector in the dual-focal-length off-axis two-reflector telescopic optical system designed by the invention adopts 6-order XY polynomial except necessary x2、x4In addition, only x is additionally increased2y、x2y2、x4y2The polynomial term aberration elimination realizes the design of a 110-degree ultra-wide field of view, the free-form surface with low complexity reduces the processing and detection difficulty, and the realizability of the system is improved.
4. The invention takes the specific design steps of the dual-focal-length two-inverse deformation free-form surface optical system as an example, and provides reference for the design of an N-inverse deformation optical system, wherein N is more than or equal to 2.
Drawings
FIG. 1 is a flow chart of a method of free-form surface type conversion in accordance with one embodiment of the present invention;
FIG. 2 is a flow chart of a method of designing a dual focal length anamorphic optical system in accordance with one embodiment of the present invention;
FIG. 3 is a schematic diagram of an off-axis spot beamlet ray trace for a coaxial rotationally symmetric optical system, in accordance with one embodiment of the present invention;
FIG. 4 is a schematic diagram of an edge field ray trace of a coaxial rotationally symmetric optical system according to one embodiment of the present invention;
FIG. 5 is a schematic diagram of a dual focal length anamorphic optical system in the sagittal direction according to one embodiment of the present invention;
FIG. 6 is a schematic view of a structure of a bi-focal anamorphic optical system in the meridional direction in accordance with an embodiment of the present invention;
FIG. 7 is a graph of MTF optical modulation transfer functions for one embodiment of the present invention;
fig. 8 is a flowchart of a method for designing a bifocal anamorphic free-form surface optical system according to another embodiment of the present invention.
Reference numerals:
primary mirror 1, secondary mirror 2, diaphragm 3, slit 4.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention.
The invention aims to provide a method for structure calculation and free-form surface type conversion of a dual-focal-length deformation optical system. The following describes a method for structure calculation and free-form surface shape conversion of a dual focal length anamorphic optical system according to the present invention in detail by using specific embodiments.
Fig. 1 shows a flow of conversion between Biconic surface type and XY polynomial free-form surface type in the method for free-form surface type conversion, including the following steps:
a1, constructing a bifocal aspheric reflection optical system based on a Biconic surface type by using optical design software;
a2, converting the Biconic surface type into an XY polynomial free-form surface type;
and A3, determining the conversion relation of polynomial terms of the XY polynomial free-form surface type expression to obtain the XY polynomial free-form surface type expression for surface type conversion.
The surface type fitted by the quadric surface item of the XY polynomial is considered to belong to a rotationally symmetric optical surface during design, and the Biconic surface type belongs to a non-rotationally symmetric optical surface, so the invention compensates the surface type deviation brought by converting the Biconic surface type into the XY polynomial free-form surface type by adding the XY polynomial item during the conversion of the Biconic surface type into the XY polynomial free-form surface type.
The following detailed description is provided for specific steps:
a1, constructing a bifocal aspheric reflection optical system based on a Biconic surface type by using optical design software Zemax;
in a preferred embodiment of the present invention, the Biconic surface type can obtain an ideal image quality in the coaxial optical system, and therefore the Biconic surface type is selected as a surface type of a reflecting mirror in the bifocal anamorphic optical system in the optical setup software Zemax, and the expression of the Biconic surface type is as follows:
Figure BDA0003239490280000071
wherein, CxAnd CyCurvatures of the Biconic surface type vertex in the X direction and the Y direction respectively;
kxand kyThe second coefficients of the Biconic surface type in the X direction and the Y direction are respectively.
A2, converting the Biconic surface type into an XY polynomial free-form surface type;
although the Biconic surface type can obtain ideal image quality in an on-axis system, for an off-axis system, since the Biconic surface type is symmetrical about xoz and the yoz plane, and the ability to correct aberrations is limited, it is converted into an XY polynomial free-form surface type and further optimized, resulting in an XY polynomial free-form surface type expression for surface type conversion as follows:
Figure BDA0003239490280000072
wherein, c is 1/R,
r is the curvature radius of the XY polynomial free-form surface;
k is the conc coefficient of the XY polynomial free-form surface;
Aiis a polynomial xmynM is not less than 0, n is not less than 0.
And A3, determining the conversion relation of polynomial terms of the XY polynomial free-form surface type expression to obtain the XY polynomial free-form surface type expression for surface type conversion.
Specifically, in the optical design software Zemax, the optical curved surface represented by the XY polynomial is obtained by rotating a curve in the yoz plane around the Z axis. For a free form surface characterized by an XY polynomial, R entered in the software is the radius of curvature in the Y direction of the quadratic equation, and the radius of the apex of the surface of the actual XY polynomial is determined by R and the coefficients preceding the polynomial term, so in a preferred embodiment of the invention, x is added to the quadratic term of the XY polynomial2The term is used to achieve deformation of the radius of curvature in the X direction;
similarly, k input in the XY polynomial free-form surface in the optical design software Zemax is the conic coefficient in the Y direction of the quadric surface equation, and x is added4The term compensates the concc coefficient in the X direction, so that the surface type conversion is realized;
the expression of the obtained XY polynomial free-form surface shape for surface shape conversion is as follows:
Figure BDA0003239490280000081
ray tracing original Biconic surface type point coordinate, fitting to XY polynomial free-form surface type expression for surface type conversion, determining x in polynomial2Term and x4Coefficient of term A3And A10。
The polynomial choice of the XY polynomial free-form surface may be different according to different rules of different design software, and therefore, further, in a preferred embodiment of the present invention, y is added to the quadratic term of the XY polynomial2Item for practical useThe curvature radius in the Y direction is deformed;
similarly, increase y4And (3) compensating the conconic coefficient in the Y direction by the term so as to realize surface type conversion, wherein the obtained expression of the XY polynomial free-form surface type for the surface type conversion is as follows:
Figure BDA0003239490280000082
ray tracing original Biconic surface type point coordinate, fitting to XY polynomial free-form surface type expression for surface type conversion again, determining y in polynomial2Item and y4Coefficient A of4And A11。
Thus, the final XY polynomial free-form surface form expression for surface form conversion is obtained as follows:
Figure BDA0003239490280000091
FIG. 2 is a flowchart of a method for calculating an initial structure of a dual focal length anamorphic optical system according to the present invention, comprising the following steps:
b1, obtaining all parameters for free-form surface type conversion by solving a primary aberration formula of the coaxial rotationally symmetric optical system with a single focal length and a curvature radius relational expression of a primary mirror and a secondary mirror in the constructed dual-focal length deformation optical system in the meridian direction and the sagittal direction;
b2, using all the parameters obtained in step B1 for free-form surface type conversion, the curvature radius and aspheric coefficients of the primary mirror and the secondary mirror in the meridian and sagittal directions are converted into polynomial terms of the free-form surface by using the conversion method of Biconic surface type and XY polynomial free-form surface type of the present invention, and the initial structure parameters of the bifocal anamorphic optical system are obtained.
Specifically, the curvature radii and aspheric coefficients of the primary mirror and the secondary mirror in the meridian and sagittal directions include: meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMain mirrorAspheric coefficient in meridian direction
Figure BDA0003239490280000092
Aspheric coefficient of secondary mirror in meridian direction
Figure BDA0003239490280000093
Principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure BDA0003239490280000094
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000095
The polynomial term coefficients are: a. the3、A4、A10、A11；
The initial structure parameters of the bifocal deformed free-form surface optical system comprise: radius of curvature R of primary mirror1Radius of curvature R of secondary mirror2Aspheric coefficient of primary mirror
Figure BDA0003239490280000096
Aspheric coefficient of secondary mirror
Figure BDA0003239490280000097
Polynomial term x of primary mirror2Coefficient A of3Polynomial term x of primary mirror4Coefficient A of10Polynomial term y of primary mirror2Coefficient A of4Polynomial term y of primary mirror4Coefficient A of11Polynomial term x of secondary mirror2Coefficient A'3Polynomial term x of secondary mirror4Coefficient A'10Polynomial term of the secondary mirror y2Coefficient A'4Polynomial term of the secondary mirror y4Coefficient A'11。
According to the method for calculating the initial structure of the bifocal anamorphic optical system, the primary aberration formula of the coaxial rotationally symmetric optical system with the single focal length is calculated, the curvature radius relational expression of each reflector in the bifocal anamorphic optical system in the meridian and sagittal directions is constructed, the conversion relation between the Biconic surface type and the XY polynomial free-form surface type is established, and the rapid calculation of the initial structure of the bifocal anamorphic free-form surface optical system is realized.
The problems of long time consumption and uncertainty in calculation caused by an optimization mode that the double-focal-length deformation is realized by controlling optical variables by optical design software based on a single-focal-length rotational symmetry system to obtain the double-focal-length deformation free-form-surface optical system in the prior art are solved, and the time used for designing the double-focal-length deformation free-form-surface optical system is saved. The initial structural parameters of the bifocal deformed free-form surface optical system can be solved only by determining the indexes (such as the focal length in the meridian direction, the focal length in the sagittal direction, the F number and the like) and the constraint conditions (such as the number of optical lenses, the ratio of the focal length in the meridian direction to the focal length in the sagittal direction and the like) of the bifocal deformed free-form surface optical system at the beginning of the design.
With reference to the flowchart shown in fig. 8, a detailed description is given to a structure calculation process of the dual-focal-length off-axis two-telescope optical system according to a preferred embodiment of the present invention, which specifically includes the following steps:
b1, solving a primary aberration formula of the coaxial rotational symmetry optical system with the real entrance pupil structure, constructing a curvature radius relational expression of the primary mirror and the secondary mirror in the dual-focal length deformation optical system in the meridional direction and the sagittal direction, and acquiring all parameters for free-form surface type conversion by using the primary aberration formula of the coaxial rotational symmetry optical system and the curvature radius relational expression of the primary mirror and the secondary mirror in the constructed dual-focal length deformation optical system in the meridional direction and the sagittal direction.
B11, deriving a primary aberration formula of the coaxial rotationally symmetric optical system;
in a preferred embodiment of the present invention, referring to fig. 3-4, tracking the off-axis point beamlets to determine the position of the entrance pupil, l, in the on-axis rotationally symmetric optical system has the following relationship:
Figure BDA0003239490280000101
wherein R is1、R2The radii of curvature of the primary mirror 1 and the secondary mirror 2, respectively.
The light beam of the edge field of view is traced, the angle of the edge field of view is theta, and the incident angle of the chief ray of the edge field of view on the primary mirror 1 is I1The half aperture of the primary mirror 1 is h1The secondary mirror 2 has a half aperture of h2、
Figure BDA0003239490280000102
Is the obscuration ratio of the coaxial rotationally symmetric optical system, and beta is the magnification of the secondary mirror 2.
Normalizing the focal length of the system to obtain f' ═ 1, and normalizing the half aperture of the primary mirror to obtain h 11, the curvature radius R of the vertex of the primary mirror can be obtained according to the relation of the object and the image1The vertex curvature radius R of the secondary mirror2And the relationship of the entrance pupil position l with α, β is as follows:
Figure BDA0003239490280000111
Figure BDA0003239490280000112
let the edge half field angle θ be-1, obtain the projection height of the diaphragm 3 on the main mirror 1:
Figure BDA0003239490280000113
according to the sine theorem, in Δ ABE,
Figure BDA0003239490280000114
then the process of the first step is carried out,
Figure BDA0003239490280000115
Figure BDA0003239490280000116
Figure BDA0003239490280000117
will y1And y2Substituting the primary aberration expression (prior art), the primary aberration formula for a coaxial rotationally symmetric optical system with a real entrance pupil structure is found as follows:
Figure BDA0003239490280000118
b12, acquiring all parameters of the primary mirror and the secondary mirror for free-form surface conversion in the meridian and sagittal directions;
according to the object-image relationship and the dual focal length (nf)x＝fyN is the focal length f in the meridian directionyFocal length f from sagittal directionxThe ratio of the two components to the primary mirror of the bifocal anamorphic optical system) and the structural parameter requirements of the anamorphic optical system, and the relationship of the curvature radius in the meridian and sagittal directions between the primary mirror and the secondary mirror of the bifocal anamorphic optical system is established:
Figure BDA0003239490280000121
wherein R is1x、R1yRespectively the curvature radius in the sagittal direction and the meridional direction of the primary mirror,
R2x、R2ythe curvature radiuses in the sagittal direction and the meridional direction of the secondary mirror are respectively.
Obtained in step B11
Figure BDA0003239490280000122
The projection height in any direction of the meridian or the sagittal direction can be set, and in a preferred embodiment of the invention, the projection height in the sagittal direction is set. According to design requirements and combined with a Gaussian formula, the obscuration ratio alpha and the number of the coaxial rotationally symmetric optical system can be determinedMirror magnification β and principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2x；
Substituting the obscuration ratio alpha and the secondary lens magnification beta into a primary aberration formula (6) of a coaxial rotationally symmetric optical system with a real entrance pupil structure to obtain aspheric coefficients in the sagittal direction of the primary lens
Figure BDA0003239490280000123
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000124
Namely, the first parameters include: principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure BDA0003239490280000125
Aspheric coefficient of secondary mirror in sagittal direction
Figure BDA0003239490280000126
The radius of curvature R in the sagittal direction of the primary mirror is obtained1xRadius of curvature R in sagittal direction of secondary mirror2xThe meridian curvature radius R of the primary mirror can be obtained by solving the relation (4)1yRadius of curvature R in meridian direction of secondary mirror2y；
Solving the aspheric coefficient in the meridian direction of the primary mirror by using the primary aberration formula (6) of the coaxial rotationally symmetric optical system with the real entrance pupil structure again
Figure BDA0003239490280000127
Meridional aspheric coefficient of secondary mirror
Figure BDA0003239490280000128
And obtaining all parameters of the primary mirror and the secondary mirror for free-form surface conversion.
In another embodiment of the present invention, let y1And y2Height of projection in the meridian directionAccording to design requirements, the obscuration ratio alpha and the secondary lens magnification beta of the coaxial rotationally symmetric optical system and the meridian curvature radius R of the primary lens can be determined1yRadius of curvature R of meridian of secondary mirror2y；
Substituting the obscuration ratio alpha and the magnification beta of the secondary mirror into a primary aberration formula (6) of a primary aberration formula optical system of a coaxial rotationally symmetric optical system with a real entrance pupil structure to obtain the meridional aspheric coefficient of the primary mirror
Figure BDA0003239490280000131
Aspheric coefficient of secondary mirror in meridian direction
Figure BDA0003239490280000132
Namely, the second parameters include: meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMeridional aspheric coefficient of primary mirror
Figure BDA0003239490280000133
Meridional aspheric coefficient of secondary mirror
Figure BDA0003239490280000134
In the same way, all parameters of the primary mirror and the secondary mirror for free-form surface conversion can be obtained finally, and are not described again.
And B2, converting the curvature radius and aspheric coefficients of the primary mirror and the secondary mirror in the meridian and sagittal directions into polynomial terms of a free-form surface by using all the parameters acquired in the step B1 and by using the Biconic surface type and XY polynomial free-form surface type conversion method of the invention, and acquiring initial structure parameters of the bifocal anamorphic optical system.
Specifically, the curvature radius R in the sagittal direction of the primary mirror1xRadius of curvature R in meridian direction of primary mirror1yIn the formula (1), obtaining a Biconic surface type expression of a primary mirror in a bifocal off-axis two-mirror telescopic optical system;
further, by adding a compound related to x2、x4、y2、y4The Biconic surface type is converted into an XY polynomial free-form surface type, and a final XY polynomial free-form surface type expression used for primary mirror type conversion is obtained:
Figure BDA0003239490280000135
similarly, the curvature radius R of the secondary mirror in the sagittal direction2xRadius of curvature R in meridian direction of primary mirror2yIn the formula (1), obtaining a Biconic surface type expression of a secondary lens in a bifocal off-axis two-mirror telescopic optical system;
further, a final XY polynomial free-form surface type expression for the secondary mirror type conversion is obtained:
Figure BDA0003239490280000136
from this, all the initial structural parameters of the bifocal off-axis two-mirror telescopic optical system are calculated, including:
radius of curvature R of primary mirror1Radius of curvature R of secondary mirror2Aspheric coefficient of primary mirror
Figure BDA0003239490280000141
Aspheric coefficient of secondary mirror
Figure BDA0003239490280000142
Polynomial term x of primary mirror2Coefficient A of3Polynomial term x of primary mirror4Coefficient A of10Polynomial term y of primary mirror2Coefficient A of4Polynomial term y of primary mirror4Coefficient A of11Polynomial term x of secondary mirror2Coefficient A'3Polynomial term x of secondary mirror4Coefficient A'10Polynomial term of the secondary mirror y2Coefficient A'4Polynomial term of the secondary mirror y4Coefficient A'11。
In a preferred embodiment of the invention, the large-field off-axis two-lens dual-focal-length anamorphic free-form surface optical system with the working wavelength band within the range of 270mm-2400mm, the field angle of 110 degrees, the relative aperture of F/9 XF/10 degrees and the focal length of 34 mm-68 mm is designed.
5-6 show the optical structure of the dual-focus off-axis two-telescope system designed by the invention in the meridional and sagittal directions, the large field of view direction is the spatial dimension direction of the system, and the direction perpendicular to the large field of view is the spectral dimension direction. The primary mirror 1 and the secondary mirror 2 are both concave mirrors, light emitted from infinity enters the primary mirror 1 through an entrance pupil, a distant scene forms a primary real image between the primary mirror 1 and the secondary mirror 2, the secondary mirror 2 re-images the real image at an entrance slit 4 of a subsequent optical system, and the diaphragm 3 is positioned on a front focal plane of the secondary mirror, so that main rays of different fields of view are close to parallel when leaving the telescope, image space telecentricity is realized, and the primary and secondary mirrors are matched with the pupil of a spectrometer.
The primary mirror and the secondary mirror both adopt a 6-order XY polynomial free-form surface type, and the expression is as follows:
Figure BDA0003239490280000143
wherein, c is 1/R, and R is the curvature radius of the free-form surface;
k is the conic coefficient in the meridian direction of the primary mirror, and k is-e2；
In the expression (9), except for the necessary x2，x4In addition, only x is additionally increased2y、x2y2、x4y2The polynomial term aberration elimination realizes the design of a 110-degree ultra-wide field of view, the free-form surface with low complexity reduces the processing and detection difficulty, and the realizability of the system is improved.
The first table shows the optimized structural parameters of the large-field-of-view off-axis two-mirror dual-focal-length deformed free-form surface optical system under the focal length normalization condition:
table I, structural parameters optimized under focal length normalization condition of dual focal length anamorphic optical system
Noodle Radius (mm) Spacing (mm) Material Coefficient of cone Y eccentricity X tilt
1 (Main mirror) -5.406 -5.551 MIRROR 1.682 7.073 -4.217
2 (diaphragm) - -2.389 - - - -
3 (Secondary mirror) 4.433 3.824 MIRROR 0.089 -0.013 1.192
4 (image plane) - - - - - -
The second table shows the parameters of the free-form surface after the off-axis two-mirror two-focus telescopic optical system is optimized:
table two, free-form surface parameters
xmynItem(s) Main mirror Secondary mirror
x2 -1.728E-03 -2.150E-04
x2y -3.133E-06 1.004E-06
x4 -2.542E-08 -3.603E-09
x2y2 -9.657E-08 -2.020E-08
x4x2 -3.114E-11 -
Fig. 7 is a graph of MTF optical transfer function of the designed system, and it can be known from fig. 7 that the optical transfer function is greater than 0.6 within the cut-off frequency, which indicates that the initial structure obtained by the designed method of the present invention has good imaging characteristics, and the parameters of the optical system design with high imaging quality and reasonable structure are obtained through simple subsequent optimization.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
The above embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (5)

1. A free-form surface type conversion method is characterized by comprising the following steps:
a1, constructing a bifocal aspheric optical system based on a Biconic surface type by using optical design software, wherein the expression of the Biconic surface type is as follows:
Figure FDA0003239490270000011
wherein, CxAnd CyThe curvatures of the Biconic surface type in the X direction and the Y direction respectively;
kxand kyRespectively representing the conconic coefficients of the Biconic surface type in the X direction and the Y direction;
a2, converting the Biconic surface type into an XY polynomial free-form surface type, wherein the expression of the XY polynomial free-form surface type is as follows:
Figure FDA0003239490270000012
wherein, c is 1/R,
r is the curvature radius of the XY polynomial free-form surface;
k is the conc coefficient of the XY polynomial free-form surface;
Aiis a polynomial xmynM is more than or equal to 0, n is more than or equal to 0;
a3, determining the conversion relation of polynomial terms in the expression of the XY polynomial free-form surface type, and obtaining the expression of converting the Biconic surface type into the XY polynomial free-form surface type:
Figure FDA0003239490270000013
wherein the polynomial term x2Is used to achieve a variation of the radius of curvature in the X direction,
polynomial term x4The coefficient of (2) is used for compensating the consecutive coefficient in the X direction in the face type conversion;
polynomial term y2Is used to achieve a modification of the radius of curvature in the Y direction;
polynomial term y4Is used to compensate the consecutive coefficients in the Y direction in the face-type conversion.
2. A double-focal length anamorphic optical system structure calculating method is characterized by comprising the following steps:
b1, obtaining a primary aberration formula of the coaxial rotationally symmetric optical system, constructing a curvature radius relational expression of the primary mirror and the secondary mirror in the dual-focal-length anamorphic optical system in the meridional and sagittal directions, and obtaining all parameters for free-form surface type conversion by using the primary aberration formula of the coaxial rotationally symmetric optical system and the curvature radius relational expression of the primary mirror and the secondary mirror in the dual-focal-length anamorphic optical system in the meridional and sagittal directions, wherein the curvature radius relational expression is as follows:
Figure FDA0003239490270000021
wherein R is1x、R1yRespectively the curvature radius of the primary mirror in the sagittal direction and the meridional direction,
R2x、R2ythe curvature radiuses of the secondary mirror in the sagittal direction and the meridional direction respectively,
n is the ratio of the focal length in the preset meridional direction and sagittal direction;
all the parameters include: principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure FDA0003239490270000022
Aspheric coefficient of secondary mirror in sagittal direction
Figure FDA0003239490270000023
Meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMeridional aspheric coefficient of primary mirror
Figure FDA0003239490270000024
Meridional aspheric coefficient of secondary mirror
Figure FDA0003239490270000025
B2, using the all parameters obtained in step B1, converting the curvature radius and aspheric coefficients of the primary mirror and the secondary mirror in the meridional and sagittal directions into polynomial terms of an XY polynomial free surface using the free-form surface conversion method according to claim 1, respectively, to obtain initial structural parameters of the bifocal anamorphic optical system;
the initial structural parameters include: radius of curvature R of primary mirror1Radius of curvature R of secondary mirror2Aspheric coefficient of primary mirror
Figure FDA0003239490270000026
Aspheric coefficient of secondary mirror
Figure FDA0003239490270000027
Polynomial term x of primary mirror2Coefficient A of3Polynomial term x of primary mirror4Coefficient A of10Polynomial term y of primary mirror2Coefficient A of4Polynomial term y of primary mirror4Coefficient A of11Polynomial term x of secondary mirror2Coefficient A'3Polynomial term x of secondary mirror4Coefficient A'10Polynomial term of the secondary mirror y2Coefficient A'4Polynomial term of the secondary mirror y4Coefficient A'11。
3. The dual focal length anamorphic optical system structure solution method of claim 2, wherein the step B1 includes the steps of:
b11, deriving a primary aberration formula of the coaxial rotationally symmetric optical system;
and B12, acquiring all parameters of the primary mirror and the secondary mirror for free-form surface conversion in the meridian and sagittal directions by using the primary aberration formula of the coaxial rotationally symmetric optical system.
4. The dual focal length anamorphic optical system structure solution method of claim 3, wherein step B11 includes the steps of:
b111, tracking the thin light beams at the off-axis points, and determining the position l of an entrance pupil in the coaxial rotationally symmetric optical system, wherein the position of the entrance pupil and the curvature radii of the primary mirror and the secondary mirror satisfy the following relational expression:
Figure FDA0003239490270000031
wherein R is1、R2The curvature radii of the primary mirror and the secondary mirror are respectively;
b112, tracking the marginal field-of-view light beam to obtain the projection height y of the light beam on the primary mirror through the entrance pupil in the coaxial rotationally symmetric optical system1And the projection height y of the light beam on the secondary mirror through the entrance pupil2Expression (c):
Figure FDA0003239490270000032
wherein theta is the field angle of the edge view,
alpha is the ratio of the obscuration to the total weight of the film,
beta is the magnification of the secondary mirror,
f′2is the focal length of the secondary mirror and,
u2is the object space aperture angle of the secondary mirror;
b113, passing the light beam through the entrance pupil to form a projection height y on the primary mirror1And the projection height y of the light beam on the secondary mirror through the entrance pupil2Substituting the primary aberration expression to obtain a primary aberration formula of the coaxial rotationally symmetric optical system with the real entrance pupil structure:
Figure FDA0003239490270000033
5. the dual focal length anamorphic optical system structure solution method of claim 2, wherein step B12 includes the steps of:
b121, acquiring a first parameter of the primary mirror and the secondary mirror in a sagittal direction or acquiring a second parameter of the primary mirror and the secondary mirror in a meridional direction according to a design index and a Gaussian formula by using a primary aberration formula (6) of the coaxial rotationally symmetric optical system with a real entrance pupil structure;
the first parameter includes: principal mirror sagittal curvature radius R1xRadius of curvature R in sagittal direction of secondary mirror2xAspheric coefficient of primary mirror in sagittal direction
Figure FDA0003239490270000041
Aspheric coefficient of secondary mirror in sagittal direction
Figure FDA0003239490270000042
The second parameter includes: meridian radius of curvature R of primary mirror1yRadius of curvature R of meridian direction of secondary mirror2yMeridional aspheric coefficient of primary mirror
Figure FDA0003239490270000043
Meridional aspheric coefficient of secondary mirror
Figure FDA0003239490270000044
B122, solving the meridional curvature radius R of the primary mirror by using the relational expression (4)1yRadius of curvature R in meridian direction of secondary mirror2yOr solving the curvature radius R of the principal mirror in the sagittal direction by using the relation (4)1xRadius of curvature R in sagittal direction of secondary mirror2x；
B123, solving the aspheric coefficient in the meridian direction of the primary mirror by using the primary aberration formula (6) of the coaxial rotational symmetric optical system again
Figure FDA0003239490270000045
Meridional aspheric coefficient of secondary mirror
Figure FDA0003239490270000046
Or aspheric coefficient of principal mirror in sagittal direction
Figure FDA0003239490270000047
Aspheric coefficient of secondary mirror in sagittal direction
Figure FDA0003239490270000048
And obtaining all parameters of the primary mirror and the secondary mirror for free-form surface conversion.
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