Offaxis hybrid surface threemirror optical system

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First Claim
1. An offaxis hybrid surface threemirror optical system comprising:
 a primary mirror located on an outgoing light path of rays;
a secondary mirror located on a first reflected light path, which is emitted from the primary mirror;
a tertiary mirror located on a second reflected light path, which is emitted from the secondary mirror; and
an image sensor located on a third reflected light path, which is emitted from the tertiary mirror;
wherein a first threedimensional rectangular coordinates system (x_{1 }y_{1}, z_{1}) is defined in space;
relative to the first threedimensional rectangular coordinates system (x_{1},y_{1}, z_{1}), a second threedimensional rectangular coordinates system (x_{2 }y_{2 }z_{2}) is defined by a primary mirror location, a third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) is defined by a secondary mirror location, and a fourth threedimensional rectangular coordinates system (x_{4 }y_{4}, z_{4}) is defined by a tertiary mirror location;
in the second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}), a reflective surface of the primary mirror is a sixthorder polynomial freeform surface of x_{2}y_{2};
in the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}), a reflective surface of the secondary mirror is a sixthorder polynomial aspheric surface of x_{3}y_{3}, and the sixthorder polynomial aspheric surface of x_{3 }y_{3 }is;
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Abstract
An offaxis hybrid surface threemirror optical system comprises a primary mirror, a secondary mirror, a tertiary mirror, and an image sensor. A reflective surface of the primary mirror is a sixthorder polynomial freeform surface of xy. A reflective surface of the secondary mirror is a sixthorder polynomial aspheric surface of xy. A reflective surface of the a tertiary mirror is a spherical surface of xy.
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OFFAXIAL THREEMIRROR OPTICAL SYSTEM WITH FREEFORM SURFACES  
Patent #
US 20150253552A1
Filed 12/16/2014

Current Assignee
Tsinghua University, Hon Hai Precision Industry Co. Ltd.

Sponsoring Entity
Tsinghua University, Hon Hai Precision Industry Co. Ltd.

19 Claims
 1. An offaxis hybrid surface threemirror optical system comprising:
a primary mirror located on an outgoing light path of rays; a secondary mirror located on a first reflected light path, which is emitted from the primary mirror; a tertiary mirror located on a second reflected light path, which is emitted from the secondary mirror; and an image sensor located on a third reflected light path, which is emitted from the tertiary mirror; wherein a first threedimensional rectangular coordinates system (x_{1 }y_{1}, z_{1}) is defined in space;
relative to the first threedimensional rectangular coordinates system (x_{1},y_{1}, z_{1}), a second threedimensional rectangular coordinates system (x_{2 }y_{2 }z_{2}) is defined by a primary mirror location, a third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) is defined by a secondary mirror location, and a fourth threedimensional rectangular coordinates system (x_{4 }y_{4}, z_{4}) is defined by a tertiary mirror location;
in the second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}), a reflective surface of the primary mirror is a sixthorder polynomial freeform surface of x_{2}y_{2};
in the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}), a reflective surface of the secondary mirror is a sixthorder polynomial aspheric surface of x_{3}y_{3}, and the sixthorder polynomial aspheric surface of x_{3 }y_{3 }is; View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
 18. An offaxis hybrid surface threemirror optical system comprising:
a primary mirror located on an outgoing light path of rays; a secondary mirror located on a first reflected light path, which is emitted from the primary mirror; a tertiary mirror located on a second reflected light path, which is emitted from the secondary mirror; and an image sensor located on a third reflected light path, which is emitted from the tertiary mirror; wherein a first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}) is defined in space;
relative to the first threedimensional rectangular coordinates system (x_{1},y_{1}, z_{1}), a second threedimensional rectangular coordinates system (x_{2 }y_{2 }z_{2}) is defined by a primary mirror location, a third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) is defined by a secondary mirror location, and a fourth threedimensional rectangular coordinates system (x_{4 }y_{4}, z_{4}) is defined by a tertiary mirror location;
in the second threedimensional rectangular coordinates system (x_{z}, y_{z}, z_{2}), a reflective surface of the primary mirror is a sixthorder polynomial freeform surface of x_{2}y_{2};
in the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}), a reflective surface of the secondary mirror is a sixthorder polynomial aspheric surface of x_{3}y_{3}; and
in the fourth threedimensional rectangular coordinates system (x_{4}, y_{4}, z_{4}), a reflective surface of the tertiary mirror is a spherical surface of x_{4}y_{4}. View Dependent Claims (19)
1 Specification
This application claims all benefits accruing under 35 U.S.C. § 119 from China Patent Application No. 201710059417.9, field on Jan. 24, 2017 in the China Intellectual Property Office, disclosure of which is incorporated herein by reference. The application is also related to copending applications entitled, “METHOD FOR DESIGNING HYBRID SURFACE OPTICAL SYSTEM”, filed Dec. 14, 2017.
The present disclosure relates to an offaxis hybrid surface threemirror optical system.
In a condition of meeting the optical performance requirements of an optical system, using a spherical surface or an aspheric surface to replace a freeform surface of the optical system can reduce a cost and a difficulty of processing and testing. A hybrid surface optical system comprises different surfaces. Each surface of the hybrid surface optical system can be selected from spherical surface, aspheric surface, and freeform surfaces. Thus, compared to freeform surface optical systems, the hybrid surface optical system has low cost and small processing and testing difficulty.
However, conventional offaxis hybrid surface threemirror optical system are mainly applied to linear field of view with small field angles and large Fnumber, but the applications in the field of view with large field angles and small Fnumber are limited.
Implementations of the present technology will now be described, by way of example only, with reference to the attached figures.
It will be appreciated that for simplicity and clarity of illustration, where appropriate, reference numerals have been repeated among the different figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth in order to provide a thorough understanding of the embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein can be practiced without these specific details. In other instances, methods, procedures, and components have not been described in detail so as not to obscure the related relevant feature being described. Also, the description is not to be considered as limiting the scope of the embodiments described herein. The drawings are not necessarily to scale and the proportions of certain parts have been exaggerated to better illustrate details and features of the present disclosure.
Several definitions that apply throughout this disclosure will now be presented.
The term “substantially” is defined to be essentially conforming to the particular dimension, shape, or other feature that the term modifies, such that the component need not be exact. For example, “substantially cylindrical” means that the object resembles a cylinder, but can have one or more deviations from a true cylinder. The term “comprising,” when utilized, means “including, but not necessarily limited to”; it specifically indicates openended inclusion or membership in the sodescribed combination, group, series and the like.
A method for designing a hybrid surface optical system of one embodiment is provided. The method comprises the following steps:
step (S1), establishing a first initial system, wherein the first initial system comprises a plurality of initial surfaces, and each of the plurality of initial surfaces corresponds to a surface of an offaxis hybrid surface optical system to be calculated; and selecting a plurality of feature rays R_{i }(i=1, 2 . . . K) from different fields and different aperture positions;
step (S2), a spherical surface of the offaxis hybrid surface optical system to be calculated is defined as a spherical surface “a”, keeping the plurality of initial surfaces of the first initial system unchanged and calculating a plurality of first feature data points (P_{1}, P_{2}, . . . P_{m}) point by point, wherein m is less than K, and the plurality of first feature data points (P_{1}, P_{2}, . . . P_{m}) are m intersection points of the spherical surface “a” and m of the plurality of feature rays R_{1 }(i=1, 2 . . . K); and surface fitting the plurality of first feature data points (P_{1}, P_{2}, . . . P_{m}) to obtain an initial spherical surface A_{m}; calculating a (m+1)th first feature data point P_{m+1 }based on the initial spherical surface A_{m}, and surface fitting the (m+1) first feature data points (P_{1}, P_{2}, . . . P_{m}, P_{m+1}) to obtain a spherical surface A_{m+1}; repeating such steps until a Kth first feature data point P_{K }is calculated, and surface fitting the first feature data points (P_{1}, P_{2}, . . . P_{K}) to obtain a spherical surface A_{K}, wherein the spherical surface A_{K }is the spherical surface “a”; repeating such steps until all spherical surfaces of the offaxis hybrid surface optical system to be calculated are obtained, to obtain a spherical surface optical system;
step (S3), an aspheric surface of the offaxis hybrid optical system to be calculated is defined as an aspheric surface “b”, the spherical surface optical system is as a second initial system, keeping all spherical surfaces of the aspheric optical system unchanged and calculating a plurality of second feature data points (P′_{1}, P′_{2}, . . . P′_{K}), wherein the plurality of second feature data points (P′_{1}, P′_{2}, . . . P′_{K}) are the intersection points of the spherical surface “a” and the plurality of feature rays R_{i }(i=1, 2 . . . K); and surface fitting the plurality of second feature data points (P′_{1}, P′_{2}, . . . P′_{K}) to obtain the aspheric surface “b”; repeating such steps until all aspheric surfaces of the offaxis hybrid surface optical system to be calculated are obtained, to obtain a first hybrid surface optical system; and
step (S4), a freeform surface of the offaxis hybrid optical system to be calculated is defined as a freeform surface “c”, the first hybrid surface optical system is as a third initial system, keeping all aspheric surfaces of the first hybrid surface optical system unchanged and calculating a plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}), wherein the plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}) are the intersection points of the aspheric surface “b” and the plurality of feature rays R_{i }(i=1, 2 . . . K); and surface fitting the plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}) to obtain the freeform surface “c”; repeating such steps until all freeform surface s of the offaxis hybrid surface optical system to be calculated are obtained.
In step (S1), a premise for establishing the initial system is to eliminate obscuration. The initial surface can be a planar surface or a spherical surface. In one embodiment, the initial system comprises three initial surfaces; the three initial surfaces are a primary mirror initial surface, a secondary mirror initial surface and a tertiary mirror initial surface. Each of the primary mirror initial surface, the secondary mirror initial surface and the tertiary mirror initial surface is a planar surface with eccentricity and inclination.
A method for selecting the plurality of feature rays R_{i }(i=1, 2 . . . K) from different fields and different aperture positions comprises steps of: M fields are selected according to the optical systems actual needs; an aperture of each of the M fields is divided into N equal parts; and, P feature rays at different aperture positions in each of the N equal parts are selected. As such, K=M×N×P different feature rays correspond to different aperture positions and different fields are fixed. The aperture can be circle, rectangle, square, oval or other shapes. In one embodiment, the aperture of each of the M fields is a circle, and a circular aperture of each of the M fields is divided into N angles with equal interval φ, as such, N=2π/φ; then, P different aperture positions are fixed along a radial direction of each of the N angles. Therefore, K=M×N×P different feature rays correspond to different aperture positions and different fields are fixed. In one embodiment, fourteen fields are fixed in the construction process, the fourteen fields are (0°, −16°), (0°, −15°), (0°, −14°), (0°, −13°), (0°, −12°), (0°, −11°), (0°, −10°), (1.5°, −16°), (1.5°, −15°), (1.5°, −14°), (1.5°, −13°), (1.5°, −12°), (1.5°, −11°), and (1.5°, −10°); one hundred and twelve feature rays are fixed from each of the fourteen fields. Therefore, 1568 different feature rays correspond to different aperture positions and different fields are fixed.
Referring to
In step (S2), a value of m is selected to improve an accuracy of the aspheric surface fitting. In one embodiment, the value of m can be ranged from about K/3 to about 2K/3. If the value of m is too small, such as less than K/3, a surface fitting error will be large; on the contrary, if the value of m is too large, such as large than 2K/3, the subsequent feature data points are few, which is not conducive to further reduce the fitting surface error. In one embodiment, the value of m is about K/2=784.
A method for calculating the plurality of first feature data points (P_{1}, P_{2}, . . . P_{m}) includes the following substeps:
Step (a): defining a first intersection point of a first feature ray R_{1 }and the spherical surface “a” as the first feature data point P_{1};
Step (b): when an ith (1≤i≤m−1) first 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) first feature data point P_{i }(1≤i≤m−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≤m−1) first feature data point P_{1 }(1≤i≤m−1); and (m−i) second intersection points can be 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_{1 }(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) first feature data point P_{i }(1≤i≤m−1) is defined as d_{i};
Step (d): making a second tangent plane at (i1) first feature data points that are obtained before the ith first feature data point P_{i }(1≤i≤m−1) respectively; thus, (i−1) second tangent planes can be obtained, and (i1) third intersection points can be obtained by the (i1) second tangent planes intersecting with a feature ray R_{i+1}; in each of the (i1) 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+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 first feature data point P_{1+1 }(1≤i≤m−1); otherwise, Q′_{i+1 }is taken as the next first feature data point P_{i+1 }(1≤i≤m−1); and
Step (f): repeating steps from b to e, until the plurality of first feature data points P_{i }(i=1, 2 . . . m) are all calculated.
In step (b), the unit normal vector {right arrow over (N)}_{i }(1≤i≤m−1) at each of the first feature data point P_{i }(1≤i≤m−1) can be calculated based on the vector form of Snell'"'"'s Law. When the surface Ω is a refractive surface,
wherein
is a unit vector along a direction of an incident ray of the surface Ω;
is a unit vector along a direction of an exit ray of the surface Ω; and n, n′ is refractive index of a media at two opposite sides of the surface Ω respectively.
Similarly, when the surface Ω is a reflective surface,
The unit normal vector {right arrow over (N)}_{i }at the first feature data points P_{i }(i=1, 2 . . . m) is perpendicular to the first tangent plane at the feature data points P_{i }(i=1, 2 . . . m). Thus, the first tangent planes at the first feature data points P_{i }(i=1, 2 . . . m) can be obtained.
Referring to
Referring to
The first feature data point P_{m+1 }is an intersection point between its corresponding feature ray and a tangent plane of the first feature data points (P_{1}, P_{2}, . . . P_{m}) that is closest to the feature data point P_{m+1}.
Referring to
The methods for calculating the first feature data points P_{m+2 }and P_{K }are the same as the method for calculating the first feature data point P_{m+1}. A method for calculating an intermediate point G_{m+1 }in a process of calculating the first feature data point P_{m+2 }and a method for calculating an intermediate point G_{K1 }in a process of calculating the first feature data point P_{K }are the same as the method for calculating the intermediate point G_{m}.
A method for surface fitting the first feature data points (P_{1}, P_{2 }. . . P_{m}) to obtain the initial spherical surface A_{m}, a method for surface fitting the (m+1) first feature data points (P_{1}, P_{2}, . . . P_{m}, P_{m+1}) to obtain the spherical surface A_{m+1}, and a method for surface fitting the first feature data points (P_{1}, P_{2}, . . . P_{K}) to obtain the spherical surface A_{K }are all least squares method.
A coordinate of the first feature data point is (x_{i}, y_{i}, z_{i}), and its corresponding normal vector is (u_{i}, v_{i}, −1). When a sphere center is (A, B, C) and a radius is r, An equation of the spherical surface can be expressed by equation (1):
(x_{i}−A)^{2}+(y_{i}−B)^{2}+(z_{i}−C)^{2}=r^{2} (1).
Calculating a derivation of the equation (1) for x and y, to obtain an expression of a normal vector u_{i }in an xaxis direction and an expression of a normal vector v_{i }in a yaxis direction.
Equations (1) (2) and (3) can be rewrite into the matrix form, and equations (4) (5) and (6) of center coordinates can be obtained through a matrix transformation.
The normal vector (u_{i}, v_{i}, −1) decides a direction of light rays, thus, both a coordinate error and a normal error during the surface fitting should be considered to obtain an accurate spherical surface. The coordinate error and the normal error are linearly weighted to solve the sphere center (A, B, C) and the radius r.
Equation (4)+ω×equation (5)+ω×equation (6) (7),
Equation (1)+ω×equation (2)+ω×equation (3) (8),
wherein, ω is a weight of the normal error. The sphere center (A, B, C) can be obtained by equation (7), and the radius r can be obtained by equation (8).
After the spherical surface “a” is obtained, the radius of the spherical surface “a” can be further changed to obtain a spherical surface “a′”, an optical power of the spherical surface “a” is changed. In one embodiment, r_{a}′=ε_{a}×r_{a}, ε_{a}=0.5˜1.5, wherein, r_{a }is the radius of the spherical surface “a”, and r_{a}′ is the radius of the spherical surface “a′”. The radius of each of the spherical surfaces of the offaxis hybrid surface optical system can be further changed to change the optical power each of the spherical surfaces. Referring to
In step (S3), the normal vector N=(U,V,−1) determines a deflection direction of light rays. If a normal surface fitting error is large, a propagation path of the feature ray will deviate from an expected direction. Therefore, both a coordinate error and a normal error during the surface fitting the plurality of second feature data points (P′_{1}, P′_{2}, P′_{K}) should be considered. A unit normal vector of each of the plurality of second feature data points (P′_{1}, P′_{2}, P′_{K}) is obtained based on the objectimage relationship, and the coordinates and normal of the K second feature data points are surface fitted.
A method for calculating the unit normal vector at each of the second feature data points is the same as the method for calculating the unit normal vector at each of the first feature data points.
A first local coordinate system is defined with a center of the aspheric surface (0, a′, b′) as an origin and an aspherical symmetry axis as a Zaxis. The first local coordinate system xyz can be described by the parameters (a, b, θ), wherein θ is a rotation angle of the first local coordinate system relative to the global coordinate system.
The coordinate error and the normal error are linearly weighted, and an error evaluation function J is proposed:
wherein Z is a surface fitting coordinate, (U, V, −1) is the surface fitting normal vector, z is a real coordinate, (u, v, −1) is a real normal vector, ω is a weight of the normal error, P is an coefficient matrix (A, B, C, D . . . ) of the aspheric surface “b”, A_{1 }is a matrix (r^{2}, r^{4}, r^{6}, r^{8 }. . . ), A_{2 }is a matrix obtained by calculating the partial derivatives of A_{1 }with respect to x, and A_{3 }is a matrix obtained by calculating the partial derivatives of A_{1 }with respect toy.
When the error evaluation function J is smallest, a calculating equation of the coefficient matrix P is:
P=(A_{1}^{T}A_{1}+ωA_{2}^{T}A_{2}+ωA_{3}^{T}A_{3})^{−1}(A_{1}^{T}z+ωA_{2}^{T}u+ωA_{3}^{T}v) (11).
A method for surface fitting the second feature data points (P′_{1}, P′_{2}, . . . P′_{K}) to obtain the aspheric surface “b” comprising the substep:
step (S31), transferring the coordinates (x_{0}, y_{0}, z_{0}) of the second feature data points (P′_{1}, P′_{2}, . . . P′_{K}) and their corresponding normal vectors (α_{0}, β_{0}, γ_{0}) in the global coordinate system to the coordinates (x, y, z) and their corresponding normal vectors (α, β, γ) in the first local coordinate system; and
step (S32), performing the least squares fitting in the first local coordinate system xyz.
In step (S31), a relationship between the coordinates (x_{0}, y_{0}, z_{0}) in the global coordinate system x_{0}y_{0}z_{0 }and the coordinates (x, y, z) in the first local coordinate system xyz can be written as:
A relationship between the normal vectors (α_{0}, β_{0}, γ_{0}) in the global coordinate system and normal vectors (α, β, γ) in the first local coordinate system xyz can be written as:
In one embodiment, a number of the first local coordinate system positions are obtained by using a local search algorithm near the second feature data points, from which a first local coordinate system with the smallest surface fitting error is chosen, and a zaxis of the first local coordinate system with the smallest surface fitting error is as a symmetry axis of the aspheric surface “b”.
Referring to
For each of the plurality of parameters (a′, b′, θ), the coefficient matrix P (A, B, C, D . . . ) can be obtained by equation (11), and its corresponding J is known by equation (10). Selecting a parameter (a′, b′, θ) whose corresponding J is the smallest and defining it as an optimal local coordinate position parameter, and the first local coordinate system is established using the optimal local coordinate position parameter.
The coefficient matrix P (A, B, C, D . . . ) is substituted into the following equation (12) to obtain the aspheric surface “b”,
wherein, L is a more than eighth order term about r. Since an order of L term is too high, a processing of the aspheric surface “b” is more difficult, so the L item can be directly omitted in the actual calculation.
In step (S4), both a coordinate error and a normal error during surface fitting the plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}) should be considered. A unit normal vector of each of the plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}) is obtained based on the objectimage relationship, and the coordinates and normal of the K third feature data points are surface fitted.
A method for calculating the unit normal vector at each of the third feature data points is the same as the method for calculating the unit normal vector at each of the first feature data points.
A method for surface fitting the plurality of third feature data points (P″_{1}, P″_{2}, . . . P″_{K}) to obtain the freeform surface “c” comprising the substep:
step (S41), surface fitting the plurality of third feature data points to a sphere in the global coordinate system, and obtaining a curvature c of the sphere and a curvature center (x_{c}, y_{c}, z_{c}) corresponding to the curvature c of the sphere;
step (S42), defining a feature data point (x_{o}, y_{o}, z_{o}) corresponding to a chief ray of the central field angle among the entire fieldofview (FOV) as the vertex of the sphere, defining a second local coordinate system by the vertex of the sphere as origin and a line passing through the curvature center and the vertex of the sphere as a Zaxis;
step (S43), transforming the coordinates (x_{i}, y_{i}, z_{i}) and the normal vector (α_{i}, β_{i}, γ_{i}), of the plurality of third feature data points in the global coordinate system, into the coordinates (x′_{i}, y′_{i}, z′_{i}) and the normal vector (α′_{i}, β′_{i}, γ′_{i}), of the plurality of third feature data points in the second local coordinate system;
step (S44), surface fitting the plurality of third feature data points into the conic surface in the second local coordinate system, based on the coordinates (x′_{i}, y′_{i}, z′_{i}) and the curvature c of the sphere, and obtaining the conic constant k; and
step (S45), removing the coordinates and the normal vector of the plurality of third feature data points P_{i }(i=1, 2 . . . K), on the conic surface in the second local coordinate system, from the coordinates (x′_{i}, y′_{i}, z′_{i}) and the normal vector (α′_{i}, β′_{i}, γ′_{i}), to obtain a residual coordinate and a residual normal vector; and surface fitting the residual coordinate and the residual normal vector to obtain a freeform surface; the equation of the freeform surface “c” can be obtained by adding an conic surface equation and an freeform surface equation.
Generally, the optical systems are symmetric about the yoz plane. Therefore, a tilt angle θ of the sphere, in the yoz plane of the second local coordinate system relative to in the yoz plane of the global coordinate system, is:
A relationship between the coordinates (x′_{i}, y′_{i}, z′_{i}) and the coordinates (x_{i}, y_{i}, z_{i}) of each of the plurality of third feature data points can be expressed as following:
A relationship between the normal vector (α′_{i}, β′_{i}, γ′_{i}) and the normal vector (α_{i}, β_{i}, γ_{i}) of each of the plurality of third feature data points can be expressed as following:
In the second local coordinate system, the coordinates and the normal vector of the plurality of third feature data points on the conic surface are defined as (x′_{i}, y′_{i}, z′_{is}) and (α′_{is}, β′_{is}, γ′_{is}) respectively. An Z′axis component of the normal vector is normalized to −1. The residual coordinate (x″_{i}, y″_{i}, z″_{i}) and the residual normal vector (α″_{i}, β″_{i}, −1) can be obtained, wherein, (x_{i}″,y_{i}″,z_{i}″)=(x_{i}′,y_{i}′,z_{i}″) and
In step (S45), a method of surface fitting the residual coordinate and the residual normal vector comprises:
step (S451): in the second local coordinate system, expressing a polynomial surface by the polynomial surface equation leaving out the conic surface term, the polynomial surface can be expressed in terms of the following equation:
wherein g_{j}(x, y) is one item of the polynomial, and P=(p_{1}, p_{2}, . . . , p_{J})^{T }is the coefficient sets;
step (S452): acquiring a first sum of squares d_{1}(P), of residual coordinate differences in z′ direction between the residual coordinate value (x″_{i}, y″_{i}, z″_{i}) (i=1, 2, . . . , K) and the freeform surface; and a second sum of squares d_{2}(P), of modulus of vector differences between the residual normal vector N_{i}=(α″_{i}, β″_{i}, −1) (i=1, 2, . . . , K) and a normal vector of the freeform surface, wherein the first sum of squares d_{1}(P) is expressed in terms of a first equation:
and
the second sum of squares d_{2}(P) is expressed in terms of a second equation:
wherein,
step (S453): obtaining an evaluation function,
P=(A_{1}^{T}A_{1}+wA_{2}^{T}A_{2}+wA_{3}^{T}A_{3})^{−1}·(A_{1}^{T}Z+wA_{2}^{T}U+wA_{3}^{T}V),
wherein w is a weighting greater than 0;
step (S454): selecting different weightings w and setting a gradient ∇f(P) of the evaluation function equal to 0, to obtain a plurality of different values of P and a plurality of freeform surface shapes z=f (x, y; P) corresponding to each of the plurality of different values of P; and
step (S455): choosing a final freeform surface shape Ω_{opt }which has a best imaging quality from the plurality of freeform surface shapes z=f (x, y; P).
Furthermore, a step of optimizing the hybrid surface optical system obtained after step (S4) can be performed, and the hybrid surface optical system obtained after step (S4) can be as the initial system.
Referring to
In one embodiment, fourteen offaxial fields are selected during a designing process of the offaxis hybrid surface threemirror optical system 100. The fourteen offaxial fields are (0°, −16°), (0°, −15°), (0°, −14°), (0°, −13°), (0°, −12°), (0°, −11°), (0°, −10°), (1.5°, −16°), (1.5°, −15°), (1.5°, −14°), (1.5°, −13°), (1.5°, −12°), (1.5°, −11°), and (1.5°, −10°). 112 feature rays are selected in each offaxial field, and 1568 feature rays that corresponds different pupil positions and different offaxial fields are selected.
Referring to
In space relative to the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}), a second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}) is defined by a primary mirror location, a third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) is defined by a secondary mirror location, a fourth threedimensional rectangular coordinates system (x_{4}, y_{4}, z_{4}) is defined by a tertiary mirror location, and a fifth threedimensional rectangular coordinates system (x_{5}, y_{5 }z_{5}) is defined by an image sensor location.
A second origin of the second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}) in the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}) is (0, 244.51, 193.62), whose unit is millimeter. A z_{2}axis positive direction rotates about 13.39 degrees along a counterclockwise direction relative to a z_{1}axis positive direction.
A third origin of the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) in the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}) is (0, 0, −100), whose unit is millimeter. A z_{3}axis positive direction rotates about 15 degrees along a counterclockwise direction relative to a z_{1}axis positive direction.
A fourth origin of the fourth threedimensional rectangular coordinates system (x_{4}, y_{4}, z_{4}) in the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}) is (0, −160.83, 209.49), whose unit is millimeter. A z_{4}axis positive direction rotates about 0 degrees along a counterclockwise direction relative to a z_{1}axis positive direction.
A fifth origin of the fifth threedimensional rectangular coordinates system (x_{5}, y_{5}, z_{5}) in the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}) is (0, −145.13, −174.41), whose unit is millimeter. A z_{5}axis positive direction rotates about 10 degrees along a counterclockwise direction relative to a z_{1}axis positive direction.
A length of the offaxis hybrid surface threemirror optical system 100 along the y_{1}axis is about 430 millimeters. A length of the offaxis hybrid surface threemirror optical system 100 along the z_{1}axis is about 400 millimeters.
In the second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}); a reflective surface of the primary mirror 120 is a sixthorder polynomial freeform surface of x_{2}y_{2}, and the sixthorder polynomial freeform surface of x_{2}y_{2 }can be expressed as follows:
wherein, z represents surface sag, c represents surface curvature, k represents conic constant, while b_{i }(i=1, 2, . . . , 11, 12) represents the ith term coefficient. In one embodiment, c=4.57e−04, k=0.048, b_{1}=0.0951, b_{2}=5.26e−06, b_{3}=7.90e−05, b_{4}=3.41e−07, b_{5}=3.97e−07, b_{6}=5.54e−10, b_{7}=1.29e−09, b_{8}=6.84e−10, b_{9}=0, b_{10}=0, b_{12}=0.
In the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}), the reflective surface of the secondary mirror 104 is a sixthorder polynomial aspheric surface of x_{3}y_{3}. The sixthorder polynomial aspheric surface of x_{3}y_{3 }can be expressed as follows:
wherein z represents surface sag, c represents surface curvature, k represents conic constant, a1 and a2 are polynomial coefficients. In one embodiment, c=5.73e−04,k=0, a_{1}=1.21e−12, a_{2}=−8.85e−16.
In the fourth threedimensional rectangular coordinates system (x_{4}, y_{4}, z_{4}), the reflective surface of the tertiary mirror 106 is a spherical surface of x_{4}y_{4}, and the spherical surface of x_{4}y_{4 }can be expressed as (x−A)^{2}+(y−B)^{2}+(z−C)^{2}=r^{2}. In one embodiment, A=0, B=−160.83, C=209.49, r=−988.48.
In other embodiments, the values of c, k, and A, in the sixthorder polynomial freeform surface of x_{2}y_{2}, the values of z, c, k, a_{1 }and a_{2 }of sixthorder polynomial aspheric surface of x_{3}y_{3}, and the values of A, B, C and r of the spherical surface of x_{4}y_{4 }can be selected according to actual needs.
Referring to
The offaxis hybrid surface threemirror optical system 100 can be optimized to improve the imaging quality and reduce the relative distortion. The offaxis hybrid surface threemirror optical system is used as the initial structure for subsequent optimization. In one embodiment, the offaxis hybrid surface threemirror optical system 100 is optimized via a CODEV software. In one embodiment, after the offaxis hybrid surface threemirror optical system 100 is optimized, in the sixthorder polynomial freeform surface of x_{2}y_{2}, c=5.54e−04, k=90.31, b_{1}=0, b_{2}=0.0003, b_{3}=0.0005, b_{4}=9.07e−07, b_{5}=1.03e−06, b_{6}=−2.37e−10, b_{7}=9.88e−10, b_{8}=1.31e−09, b_{9}=−4.64e−14, b_{10}=−1.91e−13, b_{11}=−2.05e−13 b_{12}=−7.56e−14; in the sixthorder polynomial aspheric surface of x_{3}y_{3}, c=9.19e−04, k=0, a_{1}=−4.49e−11, a_{2}=−1.35e−15; in the spherical surface of x_{4}y_{4}, A=0, B=−266.75, C=313.84, r=−996.65.
In one embodiment, after the offaxis hybrid surface threemirror optical system 100 is optimized, the second origin of the second threedimensional rectangular coordinates system (x_{2}, y_{2}, z_{2}) is in (0, 18.57, 274.09) position of the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}), whose unit is millimeter. A z_{2}axis positive direction rotates about 7.63 degrees along a counterclockwise direction relative to a z_{1}axis positive direction. A third origin of the third threedimensional rectangular coordinates system (x_{3}, y_{3}, z_{3}) is in (0, −227.00, −48.81) position of the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}), whose unit is millimeter. A z_{3}axis positive direction rotates about 18.03 degrees along a counterclockwise direction relative to a z_{1}axis positive direction. A fourth origin of the fourth threedimensional rectangular coordinates system (x_{4}, y_{4}, z_{4}) is in (0, −266.75, 313.84) position of the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}), whose unit is millimeter. A z_{4}axis positive direction rotates about 10.77 degrees along a counterclockwise direction relative to a z_{1}axis positive direction. A fifth origin of the fifth threedimensional rectangular coordinates system (x_{5}, y_{5}, z_{5}) is in (0, −365.47, −27.10) position of the first threedimensional rectangular coordinates system (x_{1}, y_{1}, z_{1}), whose unit is millimeter. A z_{5}axis positive direction rotates about 9.74 degrees along a counterclockwise direction relative to a z_{1}axis positive direction.
Referring to
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An effective entrance pupil diameter of the hybrid surface threemirror optical system 100 is about 100 millimeter.
The hybrid surface threemirror optical system 100 adopts an offaxis field of view in a vertical direction. A field angle of the hybrid surface threemirror optical system 100 is about 3°×6°, wherein an angle in an horizontal direction is in a range from about −1.5° to about 1.5°, and an angle in the vertical direction is in a range from about −16° to about −10°.
A wavelength of the hybrid surface threemirror optical system 100 is not limited, in one embodiment, the wavelength is in a range from about 8 microns to about 12 microns.
An effective focal length (EFL) of the hybrid surface threemirror optical system 100 is about 220 millimeters.
Fnumber of the hybrid surface threemirror optical system 100 is a D/f reciprocal. In one embodiment, the relative aperture (D/f) of the hybrid surface threemirror optical system 100 is about 0.45, and the Fnumber is about 2.2.
The method for designing hybrid surface threemirror optical system can have many advantages. First, the method is calculated directly in an offaxis state, an error produced during a process from the coaxial system transformed into the offaxis system can be avoided, thus, a deviation between the offaxis hybrid surface optical system obtained by the above method and an ideal optical system is small. Second, during calculating the spherical surface optical system, the surface fitting process is combined with the data point calculating process, the unknown surface is calculated by repeating the process of data point calculatingspherical surface fitting, which improve the accuracy of the method. Third, the optical power of the spherical surface is changed by changing the radius of the spherical surface, then the remaining spherical surface is calculated to compensate for changed optical power. Therefore, an optical power distribution of the spherical surface optical system is more uniform, and the spherical surface optical system can be a better initial system for the following steps. Fourth, the global coordinate system and the local coordinate system are defined, the coordinates and the normal vector of the plurality of feature data points in the global coordinate system are transformed into the local coordinate system, then the aspheric surfaces are obtained by surface fitting in the local coordinate system, thus, the method is more precisely compared to conventional methods. Fifth, when surface fitting the second plurality of feature data points and the third plurality of feature data points, both the coordinates and the normal vectors of the second plurality of feature data points and the third plurality of feature data points are considered; therefore, the shape of the freeform surface and shape of the aspheric surfaces are accurate. Finally, the pointbypoint design method can be used to design hybrid surface systems comprise different surfaces, increasing the diversity of optical designs.
It is to be understood that the abovedescribed embodiments are intended to illustrate rather than limit the present disclosure. Variations may be made to the embodiments without departing from the spirit of the present disclosure as claimed. Elements associated with any of the above embodiments are envisioned to be associated with any other embodiments. The abovedescribed embodiments illustrate the scope of the present disclosure but do not restrict the scope of the present disclosure.