Method for designing freeform surface imaging systems

Patent metadata

Field	Value
Publication number	US-11294148-B2
Application number	US-202016998185-A
Country	US
Kind code	B2
Filing date	Aug 20, 2020
Priority date	May 29, 2020
Publication date	Apr 5, 2022
Grant date	Apr 5, 2022

Abstract

A method for designing freeform surface imaging system comprises: constructing a series of coaxial spherical systems with different optical power (OP) distributions; tilting all optical elements of each coaxial spherical system by a series of angles to obtain a series of off-axis spherical systems; finding all unobscured off-axis spherical systems; and then specifying a system size or structural constraints, and finding a series of compact unobstructed off-axis spherical systems; constructing a series of freeform surface imaging systems based on the series of compact unobstructed off-axis spherical system, and correcting the OP of entire system; improving an image quality of each freeform surface imaging systems and finding an optimal tilt angle of an image surface; and automatically evaluating an image quality of each freeform surface imaging system based on an evaluation metric, and outputting the freeform surface imaging systems that meet a given requirements.

First claim

What is claimed is:

1. A method for designing freeform surface imaging system, the method comprises:
S 1 : constructing a series of coaxial spherical systems with different optical power (OP) distributions, wherein the series of coaxial spherical systems with different OP distributions are defined as P 1 , P 2 , . . . , P m , . . . , P M , and a set of P 1 , P 2 , . . . , P m , . . . , P M is defined as a set {P}; and the OP distribution refers to a combination of radii of curvature of surfaces of the coaxial spherical system and distances between surfaces of the coaxial spherical system;
S 2 : tilting all optical elements of each coaxial spherical system in the set {P} by a series of angles to obtain a series of off-axis spherical systems, wherein the series of off-axis spherical systems are defined as C m,1 , C m,2 , . . . , C m,s , . . . , C m,S m , and a set of the C m,1 , C m,2 , . . . , C m,s is defined as a set {C} m ; finding all unobscured off-axis spherical systems from the set {C} m , wherein the unobscured off-axis spherical systems are defined as C m,1 , C m,2 , . . . , C m,r , . . . , C m,R m , and a set of C m,1 , C m,2 , . . . , C m,r , . . . , C m,R m is defined as a set { C } m ; and then specifying a system size or structural constraints, and finding a series of compact unobstructed off-axis spherical systems from the set { C }m, wherein the series of compact unobstructed off-axis spherical systems are defined as {tilde over (C)} m,1 , {tilde over (C)} m,2 , . . . {tilde over (C)} m,t , . . . , {tilde over (C)} m,T m , and a set of {tilde over (C)} m,1 , {tilde over (C)} m,2 , . . . , {tilde over (C)} m,t , . . . , {tilde over (C)} m,T m is defined as a set {{tilde over (C)}} m ;
S 3 : constructing a series of freeform surface imaging systems based on the series of compact unobstructed off-axis spherical system in the set {{tilde over (C)}} m , and correcting an OP of each of the series of freeform surface imaging systems in a process of constructing the series of freeform surface imaging systems, wherein the series of freeform imaging systems are defined as {tilde over (F)} m,1 , {tilde over (F)} m,2 , . . . , {tilde over (F)} m,t , . . . , {tilde over (F)} m,T m , and a set of {tilde over (F)} m,1 , {tilde over (F)} m,2 , . . . , {tilde over (F)} m,t , . . . , {tilde over (F)} m,T m is defined as a set {{tilde over (F)}}m;
S 4 : improving an image quality of each of the series of freeform surface imaging systems in the set {{tilde over (F)}} m by calculating a surface shape of each optical element of each freeform surface imaging system in the set {{tilde over (F)}} m and finding an optimal tilt angle of an image surface, to obtained a series of freeform surface imaging systems with different structural forms and different OP distributions; and
S 5 : automatically evaluating an image quality of each of the series of freeform surface imaging system with different structural forms and different OP distributions based on an evaluation metric, and outputting at least one freeform surface imaging system that meets a given requirements.

2. The method of claim 1 , wherein in step S 1 , the series of coaxial spherical systems with different OP distributions are constructed according to first-order optics and a known focal length.

3. The method of claim 2 , wherein an image focal length f of a coaxial spherical system in the set {P} is expressed as:

f
′

=

n
N

A
⁡

(

r
i

,

d
i

,

n
i

)

,

wherein “A” is a function of r i , d i and n i , “A” is defined as A(r i , d i , n i ), and n N represents a refractive index of a medium between a spherical surface S N and a spherical surface S N+1 .

4. The method of claim 3 , wherein there is a total of 2N−1 parameters for the radii of curvature and the distances, the radii of curvature are defined as r 1 , r 2 , . . . , r N , and the distances are defined as d 1 , d 2 , . . . , d N−1 ; when the image focal length of the coaxial spherical system is given, after the 2N−1 parameters are obtained, a distance between a last spherical surface and the image surface d N is solved by the first order optics, therefore, there are a total of 2N parameters describing the coaxial spherical system.

5. The method of claim 4 , wherein the 2N parameters are placed together in a vector P=[r 1 , r 2 , . . . , r N−1 , r N , d 1 , d 2 , . . . , d N−1 , d N ], and the vector P is configured to describe the OP distribution of the coaxial spherical system.

6. The method of claim 5 , wherein the radii of curvature are defined as r i , and i=1, 2, . . . , N, a range of each r i is [r min , r max ] with an interval Δr, and r i =r min +Δr, r min +2Δr, . . . , r max .

7. The method of claim 6 , wherein the range of each r i is [−1000 mm, 1000 mm], and Δr=100 mm.

8. The method of claim 5 , wherein the distances between surfaces of the coaxial spherical system are defined as d i , and i=1, 2, . . . , N−2, a range of each d i is [d min , d max ] with an interval Δd, and d i =d min +Δd, d min +2Δd, . . . , d max .

9. The method of claim 8 , wherein EPD≤|d 1 |≤4×EPD, wherein EPD is an entrance pupil diameter of the coaxial spherical system.

10. The method of claim 1 , wherein a global coordinate system O-XYZ is defined, an incident direction of light ray in a central field (0°) is defined as a Z axis, and a plane perpendicular to the Z axis is defined as an XOY plane; a local coordinate system is established at each surface of each off-axis spherical system in the set {C} m ; an incident point of the chief light ray of the central field on a mirror surface S i is defined as V i , and a local coordinate system V i -XYZ is established with V i as origin, a unit axis vector V i Z and a surface normal direction of a surface at V i are parallel, a unit axis vector V i Y is in a plane O-YZ of the global coordinate system O-XYZ and is perpendicular to the unit axis vector V i Z, and a unit axis vector V i X and a unit axis vector OX have the same direction; a projection of a light beam between the mirror surface S i and a mirror surface S i+1 in the O-YZ plane is defined as B i , wherein i=0, 1, . . . , N, an area illuminated by a light beam on the mirror surface is defined as a working area of the mirror surface, a curve segment of a working area of a mirror surface S j intercepted by the O-YZ plane is defined as E 1 (j) E 2 (j) , wherein j=0, 1, . . . , N, I, and S I means the image surface; and a condition of no obstruction in the off-axis spherical system is: for any B i (i=0, 1, . . . , N), any curve segment E 1 (j) E 2 (j) (=1, 2, . . . , N, I) has no overlap with B i , and the unobscured off-axis spherical systems C m,1 , C m,2 , . . . , C m,r , . . . , C m,R m are obtained

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

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

Classifications

• G02B27/4266

  Diffraction theory; Mathematical models · CPC title

• G02B5/08

  Mirrors {(vehicle mirrors involving special optical features B60R1/08)} · CPC title

• G02B27/0012 Primary

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

• G02B27/0025

  for optical correction, e.g. distorsion, aberration · CPC title

• G02B17/0621

  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