Method for designing off-axis three-mirror imaging system with freeform surfaces

• US 10,495,875 B2
• Filed: 07/30/2015
• Issued: 12/03/2019
• Est. Priority Date: 12/11/2014
• Status: Active Grant

• Current Assignee: Hon Hai Precision Industry Co., Ltd., Tsinghua University
• Original Assignee: Tsinghua University
• Inventors: Hou, Wei, Zhu, Jun, Jin, Guo-Fan, Fan, Shou-Shan
• Primary Examiner(s): Shafer, Ricky D
• Application Number:
  US14/814,497
• Publication Number:
  US 20160170191A1
• Time in Patent Office: 1,587 Days
• Field of Search: 359365, 359727, 359730, 359858, 359861, 359900
• CPC Class Codes: G02B 17/0626 using three curved mirrors G02B17/0668, G02B17/0694 take precedence
• CPC Class Codes: G02B 17/0642 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 Class Codes: G02B 27/0012 Optical design, e.g. procedures, algorithms, optimisation routines

Abstract

A method for designing an off-axis three-mirror imaging system with freeform surfaces is provided. A primary mirror initial structure, a secondary mirror initial structure, and a tertiary mirror initial structure are established. A number of first feature rays are selected, while the primary mirror initial structure and the secondary mirror initial structure unchanged. The first feature rays are forward ray tracked from an object space to an image detector. A number of first feature data points are calculated to obtain a tertiary mirror. A number of fields and a number of second feature rays are selected, while the secondary mirror initial structure and the tertiary mirror unchanged. The second feature rays are reverse ray tracked from the image detector to the object space. A number of second feature data points are calculated to obtain the primary mirror.

Claims

1. A method for designing an off-axis three-mirror imaging system with freeform surfaces, the method comprising:

establishing an initial system, the initial system includes a primary mirror initial structure, a secondary mirror initial structure, and a tertiary mirror initial structure;

keeping the primary mirror initial structure and the secondary mirror initial structure unchanged;

selecting a plurality of first feature rays, the plurality of first feature rays are forward rays tracked from an object space to an image detector; and

calculating a plurality of first feature data points point by point based on an object-image relationship of the plurality of first feature rays, to obtain a tertiary mirror by surface fitting the plurality of first feature data points; and

keeping the secondary mirror initial structure and the tertiary mirror unchanged;

selecting a plurality of fields and a plurality of second feature rays, the plurality of second feature rays are reverse rays tracked from the image detector to the object space; and

calculating a plurality of second feature data points point by point based on an object-image relationship of the plurality of second feature rays, to obtain a primary mirror by surface fitting the plurality of second feature data points.

2. The method of claim 1, further comprising optimizing the off-axis three-mirror imaging system with freeform surfaces.

3. The method of claim 2, wherein the off-axis three-mirror imaging system with freeform surfaces is as the initial system for further optimization.

4. The method of claim 1, wherein the primary mirror initial structure, the secondary mirror initial structure, or the tertiary mirror initial structure is planar or spherical.

5. The method of claim 1, wherein the selecting the plurality of first feature rays comprises:

selecting M fields;

dividing an aperture of each of the M fields into N equal parts; and

P feature rays at different positions in each of the N equal parts are selected, thus, K=M×

N×

P different first feature rays are selected.

6. The method of claim 5, wherein the aperture of each of the M fields is circle, the aperture of each of the M fields is divided into N angles with equal intervals, and P different positions are selected along a radial direction of each of the N angles.

7. The method of claim 1, wherein a number of_the plurality of first feature data points is defined as i, a number of the plurality of first feature rays is defined as K, the calculating the plurality of first feature data points comprises:

defining a first intersection of a first feature ray R₁ and the tertiary mirror initial structure as a first feature data point P₁;

after j first feature data points are calculated, wherein j is a number of first feature data points that have been calculated, a value of j is less than a value of i, a jth first feature data point is defined as a first feature data point P_j, calculating an unit normal vector {right arrow over (N_j)}^⋅

at the first feature data point P_j based on a vector form of Snell'"'"'s Law; and

making a tangent plane at the first feature data point P_j, thus, K-j intersections are obtained by the tangent plane intersecting with remaining K-j first feature rays; and

the intersection, which is nearest to the first feature data point P_j, is fixed from the K-j intersections as a next first feature data point, until all the plurality of first feature data points are calculated.

8. The method of claim 7, wherein the first feature ray R₁ is most close to an optical axis of the off-axis three-mirror imaging system with freeform surfaces.

9. The method of claim 7, wherein the unit normal vector {right arrow over (N_j)} is calculated as follows:

10. The method of claim 1, wherein a number of the plurality of second feature data points is defined as i, a number of the plurality of first feature rays is defined as K, the calculating the plurality of second feature data points comprises:

defining a first intersection of a second feature ray R′

₁ and the primary mirror initial structure as a second feature data point P′

₁;

after j second feature data points are calculated, wherein j is a number of second feature data points that have been calculated, a value of j is less than a value of i, a jth second feature data point is defined as a second feature data point P_j, calculating an unit normal vector {right arrow over (N_j)}^⋅

at the second feature data point P_j based on a vector form of Snell'"'"'s Law; and

making a tangent plane at the second feature data point P_j, thus, K-j intersections are obtained by the tangent plane intersecting with remaining K-j second feature rays; and

the intersection, which is nearest to the j second feature data points, is fixed from the K-j intersections as a next second feature data point, until all the plurality of second feature data points are calculated.

11. The method of claim 10, wherein the second feature ray R′

₁ is most close to an optical axis of the off-axis three-mirror imaging system with freeform surfaces.

12. The method of claim 10, wherein the unit normal vector {right arrow over (N_j)}^⋅

is calculated as follows;

13. The method of claim 1, wherein the selecting the plurality of fields comprises:

(I);

selecting a field “

a”

;

(II);

selecting a field “

b”

, and a chief ray of the field “

b” and

the primary mirror initial structure are substantially intersect at an intersection of a margin ray of the field “

a” and

the primary mirror initial structure; and

(III) repeating steps (I) and (II), until the plurality of fields are all selected, and adjacent fields on the primary mirror initial structure are partially overlapping.

14. The method of claim 13, wherein the adjacent fields on the primary mirror initial structure are 30%-70% overlapping.

15. The method of claim 14, wherein the adjacent fields on the primary mirror initial structure are about 50% overlapping.

16. The method of claim 1, wherein the plurality of second feature rays transport as follows;

firstly, the plurality of second feature rays from the image detector reaches the tertiary mirror obtained by surface fitting the plurality of first feature data points, and is reflected by the tertiary mirror obtained by surface fitting the plurality of first feature data points to form a first reflected light;

secondly, the first reflected light reaches the secondary mirror initial structure, and is reflected by the secondary mirror initial structure to form a second reflected light;

thirdly, the second reflected light reaches the primary mirror initial structure, and is reflected by the primary mirror initial structure to form a third reflected light;

finally, the third reflected light is received by the object space.