Method for designing imaging optical system

Patent metadata

Field	Value
Publication number	US-11675187-B2
Application number	US-202117233825-A
Country	US
Kind code	B2
Filing date	Apr 19, 2021
Priority date	Jan 15, 2021
Publication date	Jun 13, 2023
Grant date	Jun 13, 2023

Abstract

A method for designing an imaging optical system is a point-by-point calculation method based on characteristic light rays (FLR) and characteristic data points (FDP). The basic function of the point-by-point calculation method includes the following steps: according to the given object-image relationship, based on Fermat's principle and the law of retraction and reflection, calculating the propagation path of the FLR passing through a system and the FDP on each optical surface, to obtain a surface shape equation of each optical surface by fitting; and repeating the above process, to solve the surface shape equation of each optical surface one by one, and finally complete the design and solution of the entire imaging optical system.

First claim

What is claimed is:

1. A method for designing an imaging optical system, comprising:
S 1 , defining a focal length of a field of view as FFL and an effective aperture of a field of view entrance pupil as FEPD, and providing functions FFL X (ω), FEPD X (ω) and FEPD Y (ω) of the FFL and the FEPD according to the FFL and the FEPD of a target system, wherein the FFL and the FEPD change with the field of view, ω=ω x , and ω y =0;
S 2 , considering no obstruction, constructing a three-reflecting mirror coaxial spherical system with a first-order focal length equal to FFL X (0) and comprising a primary mirror, a secondary mirror and a tertiary mirror; and then adjusting positions and inclination angles of the primary minor, the secondary mirror, and the tertiary mirror, to eliminate the obstruction and obtain an unobstructed system; wherein an aperture stop, defined as AS, is located on the secondary mirror, a diameter of the aperture stop is defined as D AS , and the D AS is calculated according to FEPD X (0) and FEPD Y (0); the unobstructed system comprises a first spherical mirror surface defined as M1, a second spherical mirror surface defined as M2, and a third spherical mirror surface defined as M3; and the diameter of the aperture stop in the unobstructed system is equal to D AS and coincides with the M2;
S 3 , taking a series of field angles ω k (k=1, . . . , K) as characteristic fields of view;
S 4 , defining a radial grid G MN (d x , d y ) on a xy plane, wherein M and N are integers, the radial grid G MN (d x , d y ) comprises a plurality of grid points: coordinates of the plurality of grid points are G mn (d x , d y )=(d x /2)ρ m COSθ n x+(d y /2)ρ m sinθ n y; ρ m =m/M, and m=0, 1, . . . , M; and θ n =n×360°N, and n=0, 1, . . . , N−1;
S 5 , letting k=1;
S 6 , taking k fields of view of ω 1 , ω 2 , . . . , ω k as research object to be denoted as {ω k }; according to a position of a center of the aperture stop, and a position and a surface shape of the M1, solving a starting point o({ω k }) of a chief ray of the {ω k } on the xy plane; defining a grid G MN, {ωk} =G MN (FEPD X ({ω k })×cosω k , FEPD Y ({ω k })) on the xy plane according to FEPD X ({ω k }) and FEPD Y ({ω k }); moving a center of the grid to the o({ω k }); to get a series of moved grid points G mn ({ω k })+o({ω k }); and taking moved grid point as the starting point, and defining a series of characteristic light rays of the field of view as FLR({ω k }); wherein light beams of a field of view {ω k } in the x and y directions are defined as the FEPD X ({ω k }) and the FEPD Y ({ω k }), and directions of the characteristic light rays are the same as propagation directions of light rays in the field of view {ωk};
S 7 , defining a grid GA MN, AS =G MN (D AS , D AS ) in the aperture stop, solving coordinates and normal directions of characteristic data points on the M1 in the unobstructed system according to a mapping relationship between a grid point G MN ({ω k )}+o({ω k }) and the G MN, AS , and based on FLR({ω k }); and getting a surface shape equation of M1 by fitting; wherein the characteristic light ray FLR({ω k }) from the grid point G MN ({ω k }+o({ωw k }) intersects with the aperture stop at the grid points corresponding to G MN, AS ;
S 8 , defining a grid G M′N′,{ωk} =G M′N′ (FEPD X ({ω k })×cos{ω k }), FEPD Y ({ω k })) on the xy plane, and using the grid point G m′n′,{ωk} +o({ω k }) as the starting point to define a new characteristic light FLR′({ω k }), wherein M′>M, N′>N;
S 9 , obtaining an image height H k of the field of view {ω k } on an image surface according to a formula H k =∫ 0 ω k FFL x (ω)dω and an integral of the FFL to the field angle that is in a range from 0 degrees to {ω k } degrees, thereby obtaining image point coordinates IMG({ω k }) of the field of view;
S 10 , according to an object-image relationship of the unobstructed system, intersecting FLR′({ω k }) with the image surface at IMG({ k }) after being deflected by the M1, the M2 and the M3; according to a mapping relationship between FLR′({ω k }) and IMG({ω k }), and based on FLR′({ω k }), solving coordinates and normal directions of FDP on the M3 in the unobstructed system, to obtain a surface shape equation of the M3 by fitting;
S 11 , according to the mapping relationship between FLR′({ω k }) and IMG({ω k }) in the step S 10 , and based on FLR′({ω k }), solving coordinates and normal directions of FDP on the M2 in the unobstructed system, to obtain a surface shape equation of the M2 by fitting;
S 12 , according to the surface shape equation of the M2 in the step S 11 , obtaining a position and a direction of a new aperture stop; and
S 13 , letting k=k+1, and repeating the steps S 6 to S 12 until k=K.

2. The method of claim 1 , wherein the FFL X of the target system is in a range from 20 mm to 40 mm, and the function of the FFL X is FFL X (ω X )=40−20×(ω/0.349) 2 , wherein a unit of an angle ω x is radian.

3. The method of claim 1 , wherein the EEPD X, Y of the target system is in a range from 10 mm to 20 mm, and the FFN X of each field of view is 2, the function of the FEPD X is FEPD X (ω x )=40−10×(ω x /0.349) 2 .

4. The method of claim 1 , wherein an initial system of the target system is obtained by performing the step S 1 to the step S 13 , and the diameter of the aperture stop in the initial system is 14.67 mm.

5. The method of claim 4 , wherein the initial system comprises three reflecting mirrors, each reflecting mirror has a freeform surface, and the freeform surface is described by an XY polynomial with the highest order of 4th.

6. The method of claim 4 , further comprising a step of optimizing the initial system to improve an imaging quality of the initial system after the step S 13 .

7. The method of claim 6 , further comprising a step of processing after the step S 14 , so that a physical element of an imaging optical system is obtained.

8. The method of claim 7 , wherein the imaging optical system comprises a primary reflecting minor, a secondary reflecting mirror, a tertiary reflecting mirror, and an aperture stop; and the aperture stop is located on the secondary reflecting mirror.

9. The method of claim 8 , wherein the FFL and the FEPD at a central field of view are greater than that of the edge field of views, and the FFL and the FEPD change continuously.

10. The method of claim 8 , wherein the primary reflecting mirror, the secondary reflecting mirror, and the tertiary reflecting mirror are freeform surface reflecting mirrors, and the imaging optical system is a freeform surface off-axis three-reflecting mirror optical system.

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

• Zhang Ben-Qi
• Zhu Jun
• Jin Guo-Fan
• Fan Shou-Shan

Classifications

• G02B27/0012 Primary

  Optical design, e.g. procedures, algorithms, optimisation routines · CPC title

• G02B5/10

  with curved faces · CPC title

• G02B17/0832

  off-axis or unobscured systems in which not all of the mirrors share a common axis of rotational symmetry, e.g. at least one of the mirrors is warped, tilted or decentered with respect to the other elements · CPC title