Method for analyzing tolerance distributions in a freeform surface mirror of an optical system

Patent metadata

Field	Value
Publication number	US-11435261-B2
Application number	US-201816003015-A
Country	US
Kind code	B2
Filing date	Jun 7, 2018
Priority date	Aug 14, 2017
Publication date	Sep 6, 2022
Grant date	Sep 6, 2022

Abstract

A method for analyzing distribution of tolerances on a freeform surface in an optical system. Establishes a freeform surface imaging optical system. A plurality of fields is selected, and maximum and minimum margins of wavefront errors in each field are defined. One freeform surface in one field is selected, an isolated point jumping model is established, and an isolated point is placed in different areas of the freeform surface of the one field. A local figure error with extreme values corresponding to each field is resolved, based on the maximum and minimum margins of wavefront errors, and the local surface tolerance distributions of the freeform surface in the plurality of fields are integrated together.

First claim

What is claimed is:

1. A method for analyzing tolerance distribution in freeform surface mirror of optical system comprising:
step (S 10 ), establishing a freeform surface imaging optical system;
step (S 11 ), selecting a plurality of fields in a range of fields of the freeform surface imaging optical system, defining a maximum margin and a minimum margin of a wavefront error in each of the plurality of fields; and selecting a freeform surface mirror in the freeform surface imaging optical system;
step (S 12 ), establishing an isolated point jumping model, and sequentially applying an isolated point to different areas of the freeform surface mirror in each of the plurality of fields;
step (S 13 ), reverse solving a local figure error extremum corresponding to each of the plurality of fields based on the maximum margin and the minimum margin to obtain local surface tolerance distributions; and
step (S 14 ), integrating the local surface tolerance distributions of the freeform surface mirror in the plurality of fields, to obtain a surface tolerance distribution of the freeform surface mirror.

2. The method of claim 1 , wherein an expression of the maximum margin is

W
+

=

W
_

+

1
8

⁢
λ

,

wherein W + is positive, λ represents wavelength, and W represents an average value of the wavefront error.

3. The method of claim 1 , wherein an expression of the minimum margin is

W
-

=

W
_

-

1
8

⁢
λ

,

wherein W − is negative, λ represents wavelength, and represents an average value of the wavefront error.

4. The method of claim 1 , wherein when the wavefront errors of all rays are between the maximum margin and the minimum margin, a wavefront error value of each ray is set to be less than or equal to ¼ wavelength.

5. The method of claim 1 , wherein the isolated point jumping model is established to simulate and apply a local figure error, a position of an isolated point represents a point of action of the local figure error, and a jumping distance of the isolated point represents a value of the local figure error.

6. The method of claim 1 , wherein the local figure error extremum corresponding to each field is solved based on the isolated point jumping model, and a method for solving the extremum of the local figure error corresponding to each field based on the isolated point jumping model comprises:
step(S 20 ), selecting an isolated point P on the freeform surface mirror in one of the plurality of fields;
step(S 21 ), making the isolated point P jump to an isolated point O along a surface normal at the isolated point P; and
step(S 22 ), calculating a distance between the isolated point P and the isolated point O, wherein the distance between the isolated point P and the isolated point O is defined as d, and d is a local figure error extremum at the isolated point P.

7. The method of claim 6 , wherein the isolated point P is located within an effective distribution of an imaging beam on the freeform surface.

8. The method of claim 6 , wherein the freeform surface mirror is divided into a plurality of meshes, and an edge point of the mesh is select as the isolated point P.

9. The method of claim 6 , wherein in step (S 21 ), applying a disturbance to the freeform surface mirror to produce a local figure error.

10. The method of claim 9 , wherein during the disturbance, except for the isolated point P, other local areas of the freeform surface mirror are not affected by the disturbance.

11. The method of claim 9 , wherein a jumping of the isolated point P only affects a ray passing through the isolated point P in the one of the plurality of fields, the ray is defined as “error ray”.

12. The method of claim 11 , wherein when the wavefront error of the error ray is the maximum margin of the wavefront error, a positive extremum of the isolated point P is obtained by reverse solving, and the positive extremum of the isolated point P is defined as d + .

13. The method of claim 11 , wherein when the wavefront error of the error ray is the minimum margin of the wavefront error, a negative extremum of the isolated point P is obtained by reverse solving, and the negative extremum of the isolated point P is defined as d − .

14. The method of claim 13 , wherein two boundary values d 1 , d 2 are given, based on a monotonous relationship between the jumping distance of the isolated point P and the wavefront error of the error ray, the wavefront error W E1 corresponding to d 1 and the wavefront errors W E2 corresponding to d 2 are obtained.

15. The method of claim 13 , wherein when the W E1 , W E2 are not equal to W + or W − , repeated iterations are carried on based on a mathematical dichotomy, and d + and d − of the jumping distance of the isolated point P are obtained by reverse solving.

16. The method of claim 6 , wherein after the local figure error extremum at the isolated point P is obtained, constantly changing a position of a disturbance applied on the freeform surface mirror in the one of the plurality of fields to select a plurality of isolated points, solving the local figure error extremums at the plurality of isolated points to obtain the local surface tolerance distribution of the freeform surface in the one of the plurality of fields.

17. The method of claim 16 , wherein the local surface tolerance distribution is a two-dimensional distribution of the local figure error extremums on the freeform surface mirror.

18. The method of claim 1 , wherein a method for integrating the freeform surface tolerance distributions of the plurality of fields comprises: according to a strict principle, a smallest positive extremum is selected as a comprehensive positive extremum, a negative extremum with a smallest absolute value is selected as a comprehensive negative extremum, and finally, the surface tolerance distribution of the freeform surface after integrating is obtained.

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

• Zhu Jun
• Wu xiao-fei
• Deng yu-ting
• Jin Guo-Fan
• Fan Shou-Shan

Classifications

• G02B27/0012 Primary

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

• G01M11/005 Primary

  Testing of reflective surfaces, e.g. mirrors · CPC title