METHOD FOR DESIGNING OFF-AXIS ASPHERIC OPTICAL SYSTEM

• US 20180157017A1
• Filed: 08/09/2017
• Published: 06/07/2018
• Est. Priority Date: 12/05/2016
• Status: Active Grant

• Current Assignee: Hon Hai Precision Industry Co., Ltd., Tsinghua University
• Original Assignee: Hon Hai Precision Industry Co., Ltd., Tsinghua University
• Inventors: GONG, TONG-TONG, ZHU, JUN, JIN, GUO-FAN, FAN, SHOU-SHAN
• Granted Patent: US 10,642,009 B2
• Time in Patent Office: Days
• 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
• CPC Class Codes: G02B 5/10 with curved faces

Abstract

A method for designing an off-axis aspheric optical system comprises establishing an initial system and selecting a plurality of feature rays R_i (i=1, 2 . . . K); solving a plurality of feature data points (P₁, P₂, . . . P_m) to obtain an initial off-axis aspheric surface A_m by surface fitting the plurality of feature data points (P₁, P₂, . . . P_m), wherein m is less than K; introducing an intermediate point G_m to solve a (m+1)th feature data point P_m+1, and fitting a plurality of feature data points (P₁, P₂, . . . P_m, P_m+1) to obtain an off-axis aspheric surface A_m+1; repeating such steps until a Kth feature data point P_K is solved, and fitting a plurality of feature data points (P₁, P₂, . . . P_K) to obtain an off-axis aspheric surface A_K; and repeating above steps until all the aspheric surfaces of the off-axis aspheric optical system are obtained.

Claims

1. A method for designing an off-axis aspheric optical system comprising:

step (S1), establishing an initial system, the initial system comprising a plurality of initial surfaces, and each of the plurality of initial surfaces corresponding to an aspheric surface of the off-axis aspheric optical system; and

selecting a plurality of feature rays R_i (i=1, 2 . . . K) from different fields and different aperture positions;

step (S2), keeping the plurality of initial surfaces unchanged, and solving a plurality of feature data points (P₁, P₂, . . . P_m) point by point based on given object-image relationship and Snell'"'"'s law to obtain an initial off-axis aspheric surface A_m by surface fitting the plurality of feature data points (P₁, P₂, . . . P_m), wherein m is less than K;

step (S3), introducing an intermediate point G_m based on the initial off-axis aspheric A_m to solve a (m+1)th feature data point P_m+1, and fitting a plurality of feature data points (P₁, P₂, . . . P_m, P_m+1) to obtain an off-axis aspheric surface A_m+1;

introducing an intermediate point G_m+1 based on the off-axis aspheric surface A_m+1 to solve a (m+2)th feature data point P_m+2, and fitting a plurality of feature data points (P₁, P₂, . . . P_m, P_m+1, P_m+2) to obtain an off-axis aspheric surface A_m+2;

repeating such steps until a Kth feature data point P_K is solved, and fitting a plurality of feature data points (P₁, P₂, . . . P_K) to obtain an off-axis aspheric surface A_K, wherein the off-axis aspheric surface A_K is a first aspheric surface of the off-axis aspheric optical system;

step (S4), keeping the first aspheric surface and other initial surfaces except the initial surface corresponds to a second aspheric surface of the off-axis aspheric optical system unchanged, and solving a plurality of feature data points (P′

_I, P′

₂, . . . P′

_m) based on given object-image relationship and Snell'"'"'s law to obtain an initial off-axis aspheric surface A′

_m by surface fitting the plurality of feature data points (P′

_I, P′

₂, . . . P′

_m), wherein m is less than K;

step (S5), introducing an intermediate point G′

_m based on the initial off-axis aspheric surface A_m to solve a (m+1)th feature data point P′

_m+1, and fitting a plurality of feature data points (P′

_I, P′

₂, . . . P′

_m+1) to obtain an off-axis aspheric surface A′

_m+1;

introducing an intermediate point G_m+1 based on the off-axis aspheric surface A′

_m+1 to solve a (m+2)th feature data point P′

_m+2, and fitting a plurality of feature data points (P′

₁, P′

₂, . . . P′

_m+1, P′

_m+2) to obtain an off-axis aspheric surface A′

_m+2;

repeating such steps until a Kth feature data point P′

_K is solved, and fitting a plurality of feature data points (P′

₁, P′

₂, . . . P′

_K) to obtain an off-axis aspheric surface A′

_K, wherein the off-axis aspheric A′

_K is the second aspheric surface of the off-axis aspheric optical system; and

step (S6), repeating the steps (S2)˜

(S5) until all the aspheric surfaces of the off-axis aspheric optical system are obtained.

2. The method as claimed in claim 1, wherein a step of obtaining the plurality of feature data points (P₁, P₂, . . . P_m) comprises:

step (a);

defining a first intersection point of a first feature ray R₁ and the initial surface corresponding to the first aspheric surface as the feature data point P₁;

step (b);

when i (1≤

i≤

m−

1) feature data points P_i(1≤

i≤

m−

1) have been obtained, a unit normal vector {right arrow over (N)}_i (1≤

i≤

m−

1) at each of the i (1≤

i≤

m−

1) first feature data points P_i(1≤

i≤

m−

1) are calculated based on a vector form of Snell'"'"'s Law;

step (c);

making a first tangent plane at each of the i (1≤

i≤

m−

1) feature data points P_i(1≤

i≤

m−

1);

thus i first tangent planes are obtained, and i×

(m−

i) second intersection points are obtained by the i first tangent planes intersecting with remaining (m−

i) feature rays; and

a second intersection point, which is nearest to the i (1≤

i≤

m−

1) first feature data points P₁, is fixed from the i×

(m−

i) second intersection points as a next feature data point P_i+(1≤

i≤

m−

1); and

step (d);

repeating steps b and c, until all the plurality of feature data points P_i (i=1, 2 . . . m) are calculated.

3. The method as claimed in claim 1, wherein a step of obtaining the plurality of feature data points (P₁, P₂, . . . P_m) comprises:

step (a′

);

defining a first intersection point of a first feature ray R₁ and the first aspheric surface as the feature data point P₁;

step (b′

);

when an ith (1≤

i≤

m−

1) feature data point P_i(1≤

i≤

m−

1) has been obtained, a unit normal vector {right arrow over (N)}_i at the ith (1≤

i≤

m−

1) feature data point P_i (1≤

i≤

m−

1) are calculated based on a vector form of Snell'"'"'s Law;

step (c′

);

making a first tangent plane through the ith (1≤

i≤

m−

1) feature data point P_i(1≤

i≤

m−

1); and

(m−

i) second intersection points are obtained by the first tangent plane intersects with remaining (m−

i) feature rays;

a second intersection point Q_i+1, which is nearest to the ith (1≤

i≤

m−

1) feature data point P_i(1≤

i≤

m−

1), is fixed; and

a feature ray corresponding to the second intersection point Q_i+1 is defined as R_i+1, a shortest distance between the second intersection point Q_i+1 and the ith (1≤

i≤

m−

1) feature data point P_i(1≤

i≤

m−

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≤

m−

1) respectively;

thus, (i−

1) second tangent planes are obtained, and (i−

1) third intersection points are 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 third intersection points and its corresponding feature data point form an intersection pair;

the intersection pair, which has the shortest distance between a third intersection point and its corresponding feature data point, is fixed; and

the third intersection point and the shortest distance is defined as Q′

_i+i 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 (1≤

i≤

m−

1);

otherwise, Q′

_i+1 is taken as the next feature data point P_i+1 (1≤

i≤

m−

1); and

step (f);

repeating steps from b′

to e′

, until the plurality of feature data points P_i (i=1, 2 . . . m) are all calculated.

4. The method as claimed in claim 1, wherein a value of m is ranged from K/3 to 2K/3.

5. The method as claimed in claim 1, wherein a global coordinate system x₀y₀z₀ is defined by a location of the initial system, a beam propagation direction is defined as a Z₀-axis, and a plane perpendicular to the Z₀-axis is defined as an x₀o₀y₀ plane.

6. The method as claimed in claim 5, wherein a method for introducing the intermediate point G_m comprises:

a tangent plane T_m at the feature data point P_m is solved, the tangent plane T_m intersects with the initial off-axis aspheric surface A_m at an intersection line L_m; and

in the global coordinate system x₀y₀z₀, a feature data point located on the intersection line L_m whose x coordinate is the same as an x coordinate of the feature data point P_m is defined as the intermediate point G_m.

7. The method as claimed in claim 1, wherein a method for solving the (m+1)th feature data point P_m+1 comprises the sub steps:

finding a feature ray R_m+1 corresponding to the (m+1)th feature data point P_m+1, wherein the feature ray R_m+1 is nearest to the intermediate point G_m in the remaining K-m characteristic rays;

finding a feature data point closest to the feature data point P_m+1 from the plurality of feature data points (P₁, P₂, . . . P_m); and

solving an intersection point between the feature ray R_m+1 and a tangent plane of the feature data point closest to the feature data point P_m+1, wherein the intersection point is the (m+1)th feature data point P_m+1.

8. The method as claimed in claim 7, wherein a method for finding the feature ray R_m+1 corresponding to the (m+1)th feature data point P_m+1 comprises:

a normal vector nm and a tangent plane of the intermediate point G_m at the initial off-axis aspheric A_m are obtained according to an aspheric expression;

(K-m) intersection points are obtained by the tangent plane of the intermediate point G_m intersecting with remaining (K-m) feature rays;

an intersection point P_m, which is nearest to the intermediate point G_m is fixed from the (K-m) intersection points; and

the feature ray where the intersection point P_m is located on is the feature ray R_m+i that corresponds to the feature data point P_m+1.

9. The method as claimed in claim 7, wherein a method for solving the intersection point between the feature ray R_m+1 and the tangent plane of the feature data point closest to the feature data point P_m+1 comprises:

m intersection points P′

_i (1≤

i≤

m) are obtained by the feature ray R_m+1 intersects with each of the tangent planes of the feature data points (P₁, P₂ . . . P_m), and an intersection point G′

_m is obtained by the feature ray R_m+1 intersects with the intermediate point G_m;

the plurality of feature data points (P₁, P₂ . . . P_m) and the intermediate point G_m are defined as “

F”

, and the m intersection points P′

_i(1≤

i≤

m) and the intersection point G′

_m are defined as “

F′

”

; and

a pair of (F-F′

) which has shortest distance is fixed from (P₁, P₂ . . . P_m)-P′

_i and G′

_m-G_m, F is closest to the feature data point P_m+1, and F′

is the (m+1)th feature data point P_m+1.

10. The method as claimed in claim 5, wherein a local coordinate system xyz is defined with an aspheric symmetric center (0, a, b) as an origin and an aspherical symmetry axis as a Z-axis.

11. The method as claimed in claim 10, wherein a method for fitting the plurality of feature data points (P₁, P₂ . . . P_k) to obtain the off-axis aspheric surface A_K comprising the sub-step:

step (S31), transferring the coordinates (x₀, y₀, z₀) of the feature data points P_i(i=1, 2 . . . K) and their corresponding normal vectors (α

₀, β

₀, γ

₀) in the global coordinate system x0y0z0 to the coordinates (x, y, z) and their corresponding normal vectors (α

, β

, γ

) in the local coordinate system xyz; and

step (S32), performing a least squares fitting in the local coordinate system xyz.

12. The method as claimed in claim 11, wherein a relationship between the coordinates (x0, y0, z0) in the global coordinate system x0y0z0 and the coordinates (x, y, z) in the local coordinate system xyz is:

13. The method as claimed in claim 11, wherein a relationship between the normal vectors (α

₀, β

₀, γ

₀) in the global coordinate system and the normal vectors (α

, β

, γ

) in the local coordinate system xyz is

14. The method as claimed in claim 10, wherein a value of the aspheric symmetric center (0, a, b) is obtained by using a local search algorithm in a rectangle with a diagonal of the connection between the feature data points P₁ and P_k.

15. The method as claimed in claim 10, wherein the local coordinate system xyz is described by parameters (a, b, θ

), wherein θ

is a rotation angle of the local coordinate system xyz relative to the global coordinate system x₀o₀y₀.