Method for designing freeform surface off-axial three-mirror imaging system

Patent metadata

Field	Value
Publication number	US-11409101-B2
Application number	US-201916502148-A
Country	US
Kind code	B2
Filing date	Jul 3, 2019
Priority date	Jan 25, 2019
Publication date	Aug 9, 2022
Grant date	Aug 9, 2022

Abstract

A method of designing an freeform surface off-axial three-mirror imaging system is provided. The method includes: establishing an initial system and T (T≥2) object-image relationships according to a design goal, and selecting M feature fields for each object-image relationship; using feature rays of the T object-image relationships to construct a freeform surface system by using the initial system; step (S3), the freeform surface system obtained in step (S2) is used as another initial system, using iterative process to reduce a deviation between actual intersection points and ideal target points of the feature rays and feature surfaces, iteratively reconstructing free-form surfaces in the free-form surface system.

First claim

What is claimed is:

1. A method of designing a freeform surface off-axial three-mirror imaging system comprising:
step (S1), establishing an initial system and T object-image relationships according to a design goal, and selecting M feature fields for each of the object-image relationships, wherein the initial system comprises L initial surfaces L j , j is equal to 1, 2, . . . L, M is greater than L, and T is equal to or greater than 2;
step (S2), using feature rays of the T object-image relationships to construct a freeform surface system by using the initial system;
step (S3), repeating the step (S1) by using the freeform surface system obtained in the step (S2) as a new initial system, reducing a deviation between actual intersection points and ideal target points of the feature rays and feature surfaces by iteratively reconstructing free-form surfaces in the free-form surface system, until an average RMS (root mean square) dispersion spot is no longer shrinking, the freeform surface off-axial three-mirror imaging system to be designed is obtained.

2. The method of claim 1 , wherein in step S1, the initial system comprises an initial primary mirror, an initial secondary mirror, an initial tertiary mirror and an aperture.

3. The method of claim 2 , wherein the aperture is located on a surface of the initial secondary mirror, and is adapted for moving from a first location and a second location on a surface of the initial secondary.

4. The method of claim 3 , wherein in step S1, two object-image relationships are selected from the object-image relationships, a T1 object-image relationship is corresponding to an infinity object from the freeform surface off-axial three-mirror imaging system, and the aperture is located at the first location; a T2 object-image relationship is corresponding to an object with a distance of 125 mm from the freeform surface off-axial three-mirror imaging system, and the aperture is located at a second location.

5. The method of claim 4 , wherein in the T1 object-image relationship, a field of the initial planar three-mirror imaging system in meridian direction is from approximately −2° to approximately 2°, and a field of the initial planar three-mirror imaging system in sagittal direction is from approximately −2° to approximately 2°.

6. The method of claim 1 , wherein in step S1, K feature rays are selected in each of the M feature fields, a method of selecting the K feature rays comprises steps of: an aperture of each of the M feature fields is divided into N equal parts; and, P feature rays at different aperture positions in each of the N equal parts are selected.

7. The method of claim 4 , wherein step S2 comprises steps of:
step (S21), selecting a T1 object-image relationship from the T object-image relationships, and constructing an initial surface L 1 into a freeform surface N 1 using the T1 object-image relationship;
step (S22), moving the aperture to a location corresponding to a T2 object-image relationship from the T object-image relationships, searching for a best focal plane of the T2 object-image relationship, wherein the astigmatism RMS radius of the field of view is minimum in the best focal plane position, intersections of the chief feature rays of the field of view and the best focal plane are an ideal image points of the T2 object-image relationship, reconstructing the free surface N1 to a free surface N1′ using the feature rays of the two object-image relationships;
step (S23), repeating steps (S21) and (S22), finding the best focal planes and the ideal image points of T object-image relationships, reconstructing freeform surfaces using feature rays of the T object-image relationships;
step (S24), using the feature rays of the T object-image relationships to construct L j (j=3, . . . L) initial surfaces to N i (i=3, . . . L) freeform surfaces.

8. The method of claim 7 , wherein in step (S21), a method of constructing the initial surface L 1 into the freeform surface N 1 in the T1 object-image relationship comprises: calculating a plurality of feature data points P i (i=1, 2 . . . K) on the freeform surface N 1 ; and surface fitting the plurality of feature data points to obtain an equation of the freeform surface N 1 .

9. The method of claim 8 , wherein a method of calculating the plurality of feature data points P i (i=1, 2 . . . K) comprises:
step (a): defining a first intersection of a first feature light ray R 1 and the initial surface as a feature data point P 1 ;
step (b): when an ith (1≤i≤K−1) feature data point P i (1≤i≤K−1) has been obtained, a unit normal vector {right arrow over (N)} i | at the ith (1≤i≤K−1) feature data point P i (1≤i≤K−1) can be calculated based on the vector form of Snell's law;
step (c): making a first tangent plane through the ith (1≤i≤K−1) feature data point P i (l≤i≤K−1), and (K−i) second intersections can be obtained by the first tangent plane intersecting with remaining (K−i) feature rays; a second intersection Q i+1 , which is nearest to the ith (1≤i≤K−1) feature data point P i (1≤i≤K−1), is fixed; and a feature ray corresponding to the second intersection Q i+1 is defined as R i+1 , a shortest distance between the second intersection Q i+1 and the ith feature data point P i (1≤i≤K−1) is defined as d i ;
step (d): making a second tangent plane at (i−1) feature data points that are obtained before the ith feature data point P i (1≤i≤K−1) respectively; thus, (i−1) second tangent planes can be obtained, and (i−1) third intersections can be obtained by the (i−1) second tangent planes intersecting with a feature ray R i+1 ; in each of the (i−1) second tangent planes, each of the (i−1) third intersections and its corresponding feature data point form an intersection pair; the intersection pair, which has the shortest distance between a third intersection and its corresponding feature data point, is fixed; and the third intersection and the shortest distance is defined as Q′ i+1 and d′ i respectively;
step (e): comparing d i and d′ i , if d i ≤d′ i , Q i+1 is taken as the next feature data point P i+1 (l≤i≤K−1); otherwise, Q′ i+1 is taken as the next feature data point P i+1 (1≤i≤K−1); and
step (f): repeating steps from (b) to (e), until the plurality of feature data points P i (i=1, 2 . . . K) on N1 freeform surface are all calculated.

10. The method of claim 9 , wherein in step (b), the unit normal vector (1≤i≤K−1) at each of the feature data point P i (1≤i≤K−1) is calculated based on the vector form of Snell's Law, wherein if the freeform surface N 1 is a refractive surface,

N
→

i

=

n
′

⁢

r
i
′

→

-

n
⁢

r
i

Assignees

• Univ Tsinghua
• Hon Hai Prec Ind Co Ltd

Inventors

• Tang rui-rui
• Zhu Jun
• Jin Guo-Fan
• Fan Shou-Shan

Classifications

• G02B17/0642 Primary

  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

• G02B27/0012 Primary

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

• G02B17/0657

  off-axis or unobscured systems in which all of the mirrors share a common axis of rotational symmetry · CPC title