CN116149050A - Design method for initial structure of ultra-large visual field off-axis reflection type free-form surface optical system - Google Patents

Design method for initial structure of ultra-large visual field off-axis reflection type free-form surface optical system Download PDF

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CN116149050A
CN116149050A CN202310177631.XA CN202310177631A CN116149050A CN 116149050 A CN116149050 A CN 116149050A CN 202310177631 A CN202310177631 A CN 202310177631A CN 116149050 A CN116149050 A CN 116149050A
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free
form surface
point
omega
characteristic
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是逸
郑玉权
蔺超
纪振华
张佳伦
韩艳雪
高曲悠扬
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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Abstract

The invention provides an initial structural design method of an ultra-large visual field off-axis reflective free-form surface optical system, which comprises the following steps: s1, according to the starting point S i,j And target point T i,k Calculating a first free-form surface Ω 1 All characteristic data points P of (1) i,j,1 Fitting the free-form surface omega by a least square method to obtain a first free-form surface omega 1 The method comprises the steps of carrying out a first treatment on the surface of the S2, according to the first free-form surface omega 1 Calculating second free-form surface Ω 2 All characteristic data points P of (1) i,j,2 Fitting the free-form surface omega by a least square method to obtain a second free-form surface omega 2 Constructing an initial structure of the free-form surface optical system of the two reflectors; s3, further performing iterative optimization on the initial structure through an optical path iterative method until the free-form surface light system meets imaging requirements. S4, obtaining the initial structure of the optimized free-form surface optical system when the number of the reflecting mirrors N is more than 2 through repeating the step S1, the step S2 and the step S3. The optical system designed by the invention has the advantages of high design speed, high stability and good imaging qualityAnd (5) a dot.

Description

Design method for initial structure of ultra-large visual field off-axis reflection type free-form surface optical system
Technical Field
The invention relates to the technical field of optical design, in particular to an initial structural design method of an ultra-large visual field off-axis reflection type free-form surface optical system.
Background
The ultra-large visual field off-axis reflection type optical system has the advantages of wide observation range, no chromatic aberration, no obscuration, light weight, high thermal stability and the like, and has important application value in the field of optical remote sensing. However, the oversized field of view and off-axis design of the system can cause complex aberrations, which are difficult to correct using conventional spherical and aspherical optical elements with rotational symmetry, resulting in limited imaging quality of the system.
The free curved surface is a curved surface with non-rotational symmetry, and can be applied to the design of an oversized view field off-axis reflection type optical system, so that the degree of freedom of the system design can be greatly improved, and the imaging quality of the system can be optimized. Generally, in optical design, a good initial structure and subsequent optimization of optical design software are very important steps. Wherein, reasonable initial structure is the key of designing the off-axis free-form surface system with ultra-large field of view. If the initial architecture is not reasonable, it takes a significant amount of time for the optical designer to perform system optimization.
The traditional method for obtaining the initial structure of the ultra-large visual field off-axis free-form surface system comprises the following steps: 1. searching similar optical structures from a lens library or a patent as an initial system, and then using optical design software to change index parameters such as focal length or F number and the like to re-optimize the initial structure. 2. And obtaining a coaxial spherical surface/quadric surface system solution through paraxial aberration theory, and then using optical design software to gradually expand the system view field and increase the off-axis quantity through a progressive optimization method until the system meets the requirement of an oversized view field and does not have a blocking quantity. The two methods are usually far from an ideal system, so that a designer often needs to spend a great deal of time optimizing the system, and the design efficiency is low. In addition, the optimization of the system has higher experience requirements for designers, otherwise, the system is easy to fall into a local optimal solution, and a reasonable system structure cannot be obtained.
Disclosure of Invention
In view of the above problems, the present invention aims to provide an initial structure design method for an off-axis reflective free-form surface optical system with an oversized view field, which solves the problem that the existing off-axis reflective free-form surface optical system with an oversized view field lacks a direct solution method for an initial structure in the design optimization process, thereby improving the design efficiency of the optical system.
In order to achieve the above purpose, the present invention adopts the following specific technical scheme:
the invention provides an initial structural design method of an ultra-large visual field off-axis reflective free-form surface optical system, which comprises the following steps:
the preprocessing step S0 is to define system parameters:
the number of free-form surfaces of the free-form surface optical system is K, and the kth free-form surface is defined as omega k ，k＝1,2,…K；
Dividing a free-form surface optical system into M fields of view, uniformly sampling the full aperture light rays of each field of view by a grid method to obtain J characteristic light rays, and defining the J characteristic light rays of the i field of view as R i,j ，i＝1,2,…M；j＝1,2,…J；
Definition of characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j Defining a characteristic ray R i,j And the kth free-form surface omega k Is the characteristic data point P i,j,k ；
Definition of characteristic ray R i,j After being reflected by k free curved surfaces, the target point T is reached i,k When k=k, point T i,k I.e. ideal image point I i ；
In the free-form surface optical system, the free-form surface optical system is formed from a starting point S i,j Emitted characteristic ray R i,j At characteristic data point P i,j,k Free-form surface Ω of the surface k After reflection, reaches the target point T i,k Rear characteristic ray R i,j Continuing the propagation, at characteristic data point P i,j,K Free-form surface Ω of the surface K Reflection to ideal image point I i ；
S1, according to the starting point S i,j And target point T i,k Calculating a first free-form surface Ω 1 All characteristic data points P of (1) i,j,1 Fitting the free-form surface omega by a least square method to obtain a first free-form surface omega 1 ；
S2, according to the first free-form surface omega 1 Calculating second free-form surface Ω 2 All characteristic data points P of (1) i,j,2 Fitting the free-form surface omega by a least square method to obtain a second free-form surface omega 2 Constructing an initial structure of the free-form surface optical system of the two reflectors;
s3, further performing iterative optimization on the initial structure through an optical path iterative method until the free-form surface light system meets imaging requirements.
S4, obtaining the initial structure of the optimized free-form surface optical system when the number of the reflecting mirrors N is more than 2 through repeating the step S1, the step S2 and the step S3.
Preferably, the characteristic data point P in step S1 i,j,1 The solving step of (1) comprises:
s11, calculating a first characteristic ray R in the first view field 1,1 Through a first free-form surface omega 1 After reflection, reaches the first target point T 1,1 Solving the optical path length of the first free-form surface omega of the first view field 1 Characteristic data point P of (1) 1,j,1 ；
S12, calculating the free curved surface omega of the rest view field characteristic rays except the first view field 1 The ideal optical path of the target point is reached after reflection, and then the coordinate positions of the characteristic data points of the rest fields of view are positioned.
S13, the first free-form surface omega 1 All characteristic data points P of (1) i,j,1 Obtaining a first free-form surface omega through least square fitting 1 。
Preferably, step S11 includes:
first characteristic light ray R under first view 1,1 Through a first free-form surface omega 1 After reflection, reaches the first target point T 11 Is not equal to the optical path length of (2)
Figure BDA0004101451920000031
The method comprises the following steps:
Figure BDA0004101451920000032
wherein ,n1 and n2 Is a first free-form surface omega 1 Refractive index of medium where incident light and emergent light are located;
all characteristic rays R in the first field of view 1,j Through a first free-form surface omega 1 After reflection, converging to a first target point T 1,1 Is not equal to the optical path length of (2)
Figure BDA0004101451920000033
The method comprises the following steps:
Figure BDA0004101451920000034
according to Malus's law, under ideal conditions:
Figure BDA0004101451920000035
solving a first free-form surface Ω of the first field of view according to equation (3) 1 Characteristic data point P of (1) 1,j,1 。
Preferably, step S12 includes:
for the first free-form surface Ω 1 Knowing the characteristic ray R of the ith field of view i,j Is made parallel to the characteristic ray R i,j Is intersected with the first free-form surface omega by the auxiliary line 1 At the curved surface vertex O 1 Through the entrance pupil S i,j Making a vertical line to make S i,j Sσ i,j Perpendicular to S sigma i,j O 1 ；
According to Malus' S law, ray segment S i,j P i,j,1 T i,1 and S′i,j O 1 T i,1 Is equal in optical path length, i.e：
Figure BDA0004101451920000041
Figure BDA0004101451920000042
Figure BDA0004101451920000043
wherein ,
Figure BDA0004101451920000044
is a light ray segment S i,j P i,j,1 T i,1 Is a light path length of (2);
Figure BDA0004101451920000045
is a light line segment S' i,j O 1 T i,1 Is a light path length of (2);
in point S i,j For the origin O ', a local coordinate system X' Y 'Z' is constructed. The field angle of the i-th field of view is known as (ω X ,ω Y ) S is then ji,ji1, P(O′P i,j,1 ) The projection in the X ' OZ ' plane and the Y ' OZ ' plane has an included angle omega with the Z ' axis respectively X and ωY . Let the incident vector S i,j P i,j,1 The projection length on the Z' axis is 1, and the incident vector S is based on the geometric relation i,j P i,j,1 Projection lengths on the X 'axis and the Y' axis are tan omega respectively X and tanωY Unit incident vector S i,j P i,j,1 o The presence is:
Figure BDA0004101451920000046
constructing an optical line segment S' according to equation (7) i,j O 1 Straight at which to locateLine equation:
Figure BDA0004101451920000047
point S i,j Sum point S i,j Plane equation of the tangential plane:
Figure BDA0004101451920000048
combined type (7-9), solving point
Figure BDA0004101451920000049
To determine the first free-form surface Ω according to equation (4-6) 1 All characteristic data points P of (1) i,j,1 ；
The step S13 includes:
the characteristic data point P of the first free-form surface obtained by calculation i,j,1 Fitting to the expression of the XY polynomial to construct a first free-form surface Ω 1 ；
The expression of the XY polynomial is:
Figure BDA00041014519200000410
wherein c is the curvature of the curved surface; l is a quadric coefficient;
Figure BDA00041014519200000411
is a free-form surface polynomial; a is that q Is a polynomial coefficient.
Preferably, step S2 comprises the following sub-steps:
s21, according to the optical line segment S i,j P i,j,1 T i,1 Is not equal to the optical path length of (2)
Figure BDA0004101451920000051
Calculating characteristic ray R i,j From the entrance pupil S i,j To ideal image point I i Optical path of->
Figure BDA0004101451920000052
S22, according to the optical path
Figure BDA0004101451920000053
And a first free-form surface omega 1 Solving the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 ；
S23, the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 Fitting a free-form surface characterized by an XY polynomial using a least squares method to obtain a second free-form surface Ω 2 。
Preferably, step S21 includes:
first characteristic ray R 1,1 Passes through the first target point T 1,1 And then continue to propagate through the second free-form surface omega 2 After reflection, converging to ideal image point I 1 Optical path length
Figure BDA0004101451920000054
The method comprises the following steps:
Figure BDA0004101451920000055
wherein ,n3 Is a first free-form surface omega 2 The refractive index of the medium in which the outgoing light rays are located;
characteristic ray R emitted by ith view field i,j From a first free-form surface Ω 1 After reflection, converging to target point T i,1 Characteristic ray R i,j Through the target point T i,1 Incident on the second free-form surface Ω 2 At point P i,j,2 After reflection, converging to ideal image point I i Is not equal to the optical path length of (2)
Figure BDA0004101451920000056
The method comprises the following steps:
Figure BDA0004101451920000057
Figure BDA0004101451920000058
from point T according to Malus's law i,1 Starting to converge to an ideal image point I i All the characteristic light rays in the space have the same optical path;
thus from point T i,1 Starting to make a second free-form surface omega 2 Surface vertex O 2 Is finally intersected with the image point I i There are:
Figure BDA0004101451920000059
then characteristic ray R i,j From the entrance pupil S i,j To ideal image point I i Is not equal to the optical path length of (2)
Figure BDA00041014519200000510
The method comprises the following steps:
Figure BDA00041014519200000511
wherein ,
Figure BDA00041014519200000512
is the light ray section T i,1 O 2 I i Is provided).
Preferably, step S22 includes:
calculate the exit pupil S i,j Emitted characteristic ray R i,j And the fitted first free-form surface omega 1 Is the actual intersection point P of (2) i,j,1 a Light ray segment S i,j P i,j,1 a Is not equal to the optical path length of (a)
Figure BDA0004101451920000061
The method comprises the following steps:
Figure BDA0004101451920000062
obtaining a second free-form surface omega 2 Is not equal to the optical path length of (a)
Figure BDA0004101451920000063
The method comprises the following steps: />
Figure BDA0004101451920000064
Wherein the characteristic data point P i,j,1 a For passing through the entrance pupil S i,j Emitted characteristic ray R i,j And a first free-form surface omega 1 Is the actual intersection of (1);
for the first free-form surface omega after the least square fitting 1 The surface equation is arranged into an equation expressed in terms of F (x, y, z):
Figure BDA0004101451920000065
the first free-form surface equation F (x, y, z) is biased and then substituted into the characteristic data point P i,j,1 a To obtain the first free-form surface omega 1 Normal vector N of each point on 1 The method comprises the following steps:
Figure BDA0004101451920000066
according to the law of refraction/reflection:
n 1 (A 1 o ×N 1 o )＝n 2 (A 1 o′ ×N 1 o ) (20)
wherein ,
Figure BDA0004101451920000067
Figure BDA0004101451920000068
A 1 o ，A 1 o′ respectively characteristic ray R i,j Relative to the first free-form surface Ω 1 A unit vector of incident light and reflected light;
N 1 o for point P i,j,1 a Unit normal vector at the position;
constructing ray P according to equation (22) i,j,1 a P i,j,2 The equation of the straight line is combined with the formula (17) to calculate the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 。
Preferably, in the optical path iteration method of step S3, the current free-form surface system is used as a new initial structure, and then the optical paths of the feature data points for solving each free-form surface in the free-form surface system are continuously corrected in sequence, which specifically comprises the following steps:
by setting an initial optical path correction amount ΔOPD 1 For the calculated optical path
Figure BDA0004101451920000071
Correction is performed to obtain the optical path length for recalculating the free-form surface feature data points>
Figure BDA0004101451920000072
Figure BDA0004101451920000073
wherein ,εi,1 For correction of
Figure BDA0004101451920000074
Is expressed as:
Figure BDA0004101451920000075
wherein ,
Figure BDA0004101451920000076
based on iteration coefficients, ++>
Figure BDA0004101451920000077
Δε i,1 Is epsilon i,1 Is a iteration quantity of Deltaε i,1 ≥0；
When delta epsilon i,1 When the value of the sum is =0,
Figure BDA0004101451920000078
for the optical path
Figure BDA0004101451920000079
Its modified optical path per iteration +.>
Figure BDA00041014519200000710
The method comprises the following steps:
Figure BDA00041014519200000711
wherein ,
Figure BDA00041014519200000712
wherein ,
ε i,2 for correction of
Figure BDA00041014519200000713
Iteration coefficients of (a);
Figure BDA00041014519200000714
based on iteration coefficients, ++>
Figure BDA00041014519200000715
Δε i,2 Is epsilon i,2 Is a iteration quantity of Deltaε i,2 ≥0；
When delta epsilon i,2 When the value of the sum is =0,
Figure BDA00041014519200000716
ΔOPD 2 is that
Figure BDA00041014519200000717
An optical path correction amount of (a).
Preferably, when the number of the free-form surfaces is N, N is more than 2, the design method is the same as that of the free-form surface system of the off-axis reflector;
setting N-1 target points T in the preprocessing step S0 i,k And N data points P 1,1,k ；
Repeating the step S1 and the step S2 to obtain all characteristic data points of N unknown free-form surfaces;
fitting all characteristic data points into a free-form surface, constructing a free-form surface system, observing the quality of the system, and if the imaging of a part of view field of the free-form surface system does not meet the imaging quality requirement; and (3) performing optimization iteration on the free-form surface system by using the optical path iteration method in the step (S3) until the free-form surface system meets the imaging requirement, and outputting the free-form surface system.
Compared with the prior art, the ultra-large visual field off-axis reflection type free-form surface optical system obtained by the initial structure design method has good imaging characteristics, and the optical system design result with high imaging quality and reasonable optical-mechanical structure can be obtained through simple subsequent optimization. The optical system designed by the method provided by the invention has the advantages of high design speed, high stability and good imaging quality.
Drawings
Fig. 1 is a flow chart of an initial structural design method of an oversized view field off-axis reflective freeform optical system according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of an ideal imaging of an off-axis two-mirror optical system provided in accordance with an embodiment of the present invention.
FIG. 3 is a schematic illustration of a build assist tangential plane provided in accordance with an embodiment of the invention.
FIG. 4 is a schematic diagram of the construction of auxiliary data points provided in accordance with an embodiment of the present invention.
Fig. 5 is a schematic diagram of the construction of a local coordinate system provided according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of a comparison of actual and ideal optical path lengths for imaging of various fields of view provided in accordance with an embodiment of the present invention.
FIG. 7 is a schematic diagram of an optical structure of an off-axis two-mirror system on an XOZ plane using an aplanatic surface extension method according to an embodiment of the present invention.
FIG. 8 is a schematic diagram of an optical structure of an off-axis two-mirror system on the YOZ plane using an aplanatic surface expansion method according to an embodiment of the invention.
Detailed Description
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, like modules are denoted by like reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, a detailed description thereof will not be repeated.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limiting the invention.
Fig. 1 is a schematic flow chart of an initial structural design method of an oversized view field off-axis reflective free-form surface optical system according to an embodiment of the invention.
As shown in fig. 1, the method for designing the initial structure of the ultra-large field off-axis reflective free-form surface optical system provided by the embodiment of the invention comprises the following steps:
the preprocessing step S0 is to define system parameters according to the design requirement of the ultra-large visual field off-axis reflection type free-form surface optical system:
assume thatThe free-form surface optical system has K free-form surfaces, and the kth free-form surface is defined as omega k (k＝1,2,…K)。
Dividing a free-form surface optical system into M fields of view, uniformly sampling the full aperture light rays of each field of view by a grid method to obtain J characteristic light rays, and defining the J characteristic light rays of the i field of view as R i,j (i＝1,2,…M；j＝1,2,…J)。
Definition of characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j Defining a characteristic ray R i,j And the kth free-form surface omega k Is the characteristic data point P i,j,k ；
Definition of characteristic ray R i,j After being reflected by k free curved surfaces, the target point T is reached i,k When k=k, point T i,k I.e. ideal image point I i 。
In the free-form surface optical system, the lens is composed of an entrance pupil S i,j Emitted characteristic ray R i,j At characteristic data point P i,j,k Free-form surface Ω of the surface k After reflection, reaches the target point T i,k 。
The light continues to propagate, ideally at characteristic data point P i,j,K Free-form surface Ω of the surface K Reflection to ideal image point I i 。
FIG. 2 illustrates an ideal imaging schematic of an off-axis two-mirror optical system provided in accordance with an embodiment of the present invention.
As shown in FIG. 2, the origin S at the entrance pupil is defined by the first field of view of the optical system 1,1 Emitted first characteristic ray R 1,1 Incident on a first free-form surface omega 1 Through a first free-form surface omega 1 After reflection at the spatial target surface reaches the first target point T 1,1 Then pass through the second free-form surface omega again 2 After reflection to the ideal image point I i 。
First characteristic ray R 1,1 With a first free-form surface omega 1 Intersecting with the first characteristic data point P 1,1,1 ；
First characteristic ray R 1,1 And a second free-form surface omega 2 Intersecting with the second characteristic data point P 1,1,2 ；
S1, according to the starting point S i,j And target point T i,k Calculating a first free-form surface Ω 1 All characteristic data points P of (1) i,j,1 Fitting the free-form surface omega by a least square method to obtain a first free-form surface omega 1 ；
Step S1 comprises the following sub-steps:
s11, according to the starting point S 1,j First characteristic data point P 1,1,1 And a first target point T 1,1 Solving for characteristic data point P 1,j,1 。
The starting point S of the first field of view of the optical system is known 1,1 First characteristic data point P 1,1,1 And a first target point T 1,1 Position coordinates of (c);
first characteristic light ray R under first view 1,1 Through a first free-form surface omega 1 After reflection, reaches the first target point T 11 Is not equal to the optical path length of (2)
Figure BDA0004101451920000101
The method comprises the following steps: />
Figure BDA0004101451920000102
wherein ,n1 and n2 Is a first free-form surface omega 1 The refractive index of the medium at the spatial position of the incident light ray and the emergent light ray;
according to Malus's law, the condition for perfect imaging of an optical system is that the optical path length between corresponding points of an incident wave surface and an emergent wave surface is constant.
FIG. 3 shows a schematic diagram of a build assist tangential plane provided in accordance with an embodiment of the invention.
As shown in fig. 3, the passing point S 1,1 Characteristic ray R 1,1 Is a plane omega of the auxiliary tangent plane S1 Characteristic ray R 1,j Is parallel to the tangential plane omega S1 Intersecting at point S sigma 1,j . At this time, the tangential plane Ω S1 Can be regarded as point S 1,1 Incident plane wave at point S sigma 1,j And point S 1,1 Located within the same plane wave of incidence.
All characteristic rays R in the first field of view 1,j From point S' 1,j The departure warp first free-form surface omega 1 After reflection, converging to a first target point T 11 Is not equal to the optical path length of (2)
Figure BDA0004101451920000103
The method comprises the following steps:
Figure BDA0004101451920000104
according to Malus's law, under ideal conditions:
Figure BDA0004101451920000105
solving a first free-form surface Ω of the first field of view according to equation (3) 1 Characteristic data point P of (1) 1,j,1 。
S12, calculating ideal optical paths of characteristic light rays of other fields except the first field of view, and further positioning characteristic data point coordinates of the other fields of view.
The method comprises the following specific steps:
FIG. 4 illustrates a schematic construction of auxiliary data points provided in accordance with an embodiment of the present invention.
As shown in fig. 4, for the first free-form surface Ω 1 R is known to be i,j Is made parallel to R i,j Is intersected with the first free-form surface omega by the auxiliary light rays 1 At the curved surface vertex O 1 Through the entrance pupil S i,j Making a vertical line to make S i,j S″ i,j Perpendicular to S' i,j O 1 。
At this time S can be i,j P i,j,1 T i,1 and S″i,j O 1 T i,1 The light emitted by a beam of plane waves passes through the first free-form surface omega 1 After reflection, is converged to T i,1 Two ray segments of the spot. According to Malus' S law, ray segment S i,j P i,j,1 T i,1 and S″i,j O 1 T i,1 Is equal, namely:
Figure BDA0004101451920000111
Figure BDA0004101451920000112
Figure BDA0004101451920000113
wherein ,
Figure BDA0004101451920000114
is a light ray segment S i,j P i,j,1 T i,1 Optical path of->
Figure BDA0004101451920000115
Is a light ray segment S i,j O 1 T i,1 Is provided).
Fig. 5 shows a schematic construction diagram of a local coordinate system provided according to an embodiment of the present invention.
As shown in fig. 5, in point S i,j For the origin O ', a local coordinate system X' Y 'Z' is constructed.
The field angle of the i-th field of view is known as (ω X ,ω Y ) S is then i,j P i,j,1 (O′P i,j,1 ) The projection in the X ' OZ ' plane and the Y ' OZ ' plane has an included angle omega with the Z ' axis respectively X and ωY 。
Let the incident vector S i,j P i,j,1 The projection length on the Z' axis is 1, and the incident vector S is based on the geometric relation i, j P i,j,1 Projection lengths on the X 'axis and the Y' axis are tan omega respectively X and tanωY Unit incident vector S i,j P i,j,1 o The presence is:
Figure BDA0004101451920000116
constructing an optical line segment S' according to equation (7) i,j O 1 The linear equation is:
Figure BDA0004101451920000117
point S ij Sum point S ij The plane equation of the tangential plane is:
Figure BDA0004101451920000118
combined type (7-9), solving point
Figure BDA0004101451920000119
To determine the first free-form surface Ω according to equation (4-6) 1 All characteristic data points P of (1) i,j,1 。
S13, the first free-form surface omega 1 All characteristic data points P of (1) i,j,1 Fitting by a least square method to obtain a first free-form surface omega 1 。
The free-form surface expression used for free-form surface fitting is an XY polynomial, and the equation is as follows:
Figure BDA00041014519200001110
wherein c is the curvature of the curved surface vertex, l is the quadric surface coefficient,
Figure BDA0004101451920000121
is a free-form surface polynomial A q Is a coefficient of each item.
S2, according to the first free-form surface omega 1 Calculating second free-form surface Ω 2 All characteristic data points P of (1) i,j,2 And performing least square fitting to obtain a second free-form surface omega 2 。
Step S2 comprises the following sub-steps:
s21, according to the optical line segment S i,j P i,j,1 T i,1 Is used for calculating characteristic light ray R i,j From the entrance pupil S i,j To ideal image point I i Is not equal to the optical path length of (2)
Figure BDA0004101451920000122
First characteristic ray R 1,1 Passes through the first target point T 1,1 And then continue to propagate through the second free-form surface omega 2 After reflection, converging to ideal image point I 1 Optical path length
Figure BDA0004101451920000123
The method comprises the following steps:
Figure BDA0004101451920000124
wherein ,n3 Is a first free-form surface omega 2 The refractive index of the medium at the spatial location of the outgoing light ray. Characteristic ray R emitted by ith view field i,j From a first free-form surface Ω 1 After reflection, converging to target point T i,1 . Under ideal conditions, characteristic ray R i,j Through point T i,1 From the second free-form surface Ω 2 At point P ij 2 After reflection, converging to ideal image point I i Optical path length
Figure BDA0004101451920000125
The following relationship exists: />
Figure BDA0004101451920000126
Figure BDA0004101451920000127
From the target point T according to Malus' law i,1 Starting to converge to an ideal image point I i All the characteristic light rays in the space have the same optical path;
thus from the target point T i,1 Starting to make a second free-form surface omega 2 Surface vertex O 2 Is finally intersected with the ideal image point I i There are:
Figure BDA0004101451920000128
then characteristic ray R i,j From the starting point S i,j To ideal image point I i Is not equal to the optical path length of (2)
Figure BDA0004101451920000129
Can be expressed as:
Figure BDA00041014519200001210
wherein ,
Figure BDA00041014519200001211
is the light ray section T i,1 O 2 I i Is provided).
In practical optical systems, characteristic rays of different apertures may be reflected and imaged via the same point of the free-form surface for different fields of view. However, for an oversized view field system, the free-form surface cannot collect light rays with different view fields and different apertures at ideal image points. Thus, the back surface is fitted from the entrance pupil S ij To target point T i1 Is different from the ideal optical path
Figure BDA0004101451920000131
S22, according to the optical path
Figure BDA0004101451920000132
And a first free-form surface omega 1 Solving the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 ；
Calculate the starting point S i,j Emitted characteristic ray R i,j And the fitted first free-form surface omega 1 Is the actual intersection point P of (2) i,j,1 a Light ray segment S i,j P i,j,1 a Is not equal to the optical path length of (a)
Figure BDA0004101451920000133
The method comprises the following steps:
Figure BDA0004101451920000134
thus, for solving the second free-form surface Ω 2 Is not equal to the optical path length of (a)
Figure BDA0004101451920000135
Figure BDA0004101451920000136
wherein ,Pi,j,1 a Is from the starting point S i,j Emitted characteristic ray R i,j And a first free-form surface omega 1 Is the actual intersection of (1);
for the first free-form surface omega after the least square fitting 1 The surface equation is arranged into an equation expressed in terms of F (x, y, z):
Figure BDA0004101451920000137
the first free-form surface equation F (x, y, z) is biased and then substituted into the characteristic data point P i,j,1 a To obtain the first free-form surface omega 1 Normal vector N of each point on 1 The method comprises the following steps:
Figure BDA0004101451920000138
according to the law of refraction/reflection:
n 1 (A 1 o ×N 1 o )＝n 2 (A 1 o′ ×N 1 o ) (20)
wherein ,
Figure BDA0004101451920000139
Figure BDA00041014519200001310
A 1 o ，A 1 o′ respectively characteristic ray R i,j Relative to the first free-form surface Ω 1 A unit vector of incident light and reflected light;
N 1 o for point P i,j,1 a Unit normal vector at.
Constructing an optical line segment P according to equation (22) i,j,1 a P i,j,2 The equation of the straight line can be combined with the formula (17) to calculate the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 。
S23, the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 Fitting a free-form surface characterized by an XY polynomial using a least squares method to obtain a second free-form surface Ω 2 。
The equation for the XY polynomial is:
Figure BDA0004101451920000141
wherein c is the curvature of the curved surface vertex, l is the quadric surface coefficient,
Figure BDA0004101451920000142
is a free-form surface polynomial A q Is a coefficient of each item.
S3, further performing iterative optimization on the initial structure through an optical path iterative method until the free-form surface light system meets imaging requirements. Fig. 6 shows a schematic diagram of a comparison of actual and ideal optical path lengths for each field of view imaging provided in accordance with an embodiment of the present invention.
As shown in fig. 6, the ideal optical system actually expands the imaging characteristics of the optical system in the paraxial region to an arbitrarily large space, so that the actual optical path length of each field imaging is deviated from the ideal optical path length for the actual optical system. The freeform surface system constructed according to the steps S1 and S2 can initially meet the system focal power requirement, but the imaging quality of the marginal view field is poor, and further iterative optimization is needed.
In the optical path iteration method provided by the invention, a current free-form surface system is used as a new initial structure, and then the optical path of characteristic data points for solving each free-form surface in the system is continuously corrected in sequence, and the specific process is as follows:
first, by setting the initial optical path correction amount Δopd 1 For the calculated optical path
Figure BDA0004101451920000143
Correction is performed to obtain the optical path length for recalculating the free-form surface feature data points>
Figure BDA0004101451920000149
Figure BDA0004101451920000145
wherein ,εi,1 For correction of
Figure BDA0004101451920000146
Is expressed as: />
Figure BDA0004101451920000147
wherein ,
Figure BDA0004101451920000148
as a basic iteration coefficient, delta epsilon i,1 (Δε i,1 Not less than 0) is epsilon i,1 When delta epsilon i,1 When=0,>
Figure BDA0004101451920000151
for the optical path
Figure BDA0004101451920000152
Its modified optical path per iteration +.>
Figure BDA0004101451920000153
Can be expressed as:
Figure BDA0004101451920000154
wherein ,
Figure BDA0004101451920000155
wherein ,
ε i,2 for correction of
Figure BDA0004101451920000156
Iteration coefficients of (a);
Figure BDA0004101451920000157
as a basic iteration coefficient;
Δε i,2 (Δε i,2 not less than 0) is epsilon i,2 Is an iteration number of (a);
when delta epsilon i,2 When the value of the sum is =0,
Figure BDA0004101451920000158
ΔOPD 2 is that
Figure BDA0004101451920000159
An optical path correction amount of (a). FIG. 7 illustrates an optical configuration of an off-axis two-mirror system in the XOZ plane using an aplanatic surface expansion approach in accordance with an embodiment of the present invention.
FIG. 8 shows an optical structure of an off-axis two-mirror system in the YOZ plane using an aplanatic surface expansion approach, according to an embodiment of the invention.
As shown in fig. 7-8, the super-large field off-axis reflective free-form surface optical system obtained by the design method provided by the invention has better imaging characteristics, and can obtain the optical system design result with high imaging quality and reasonable optical-mechanical structure through simple subsequent optimization.
S4, obtaining the initial structure of the optimized free-form surface optical system when the number of the reflecting mirrors N is more than 2 through repeating the step S1, the step S2 and the step S3.
For the off-axis multi-reflector free-form surface system (the number of the reflectors is N, N is more than 2), the design method is the same as that of the off-axis two-reflector free-form surface system.
Setting N-1 target points T in the preprocessing step S0 i,k And N data points P 1,1,k And (3) obtaining the product. Further repeating steps S1 and S2 may result in all the characteristic data points for the N unknown free-form surfaces. Fitting the characteristic data points into a free-form surface, constructing a free-form surface system, observing the quality of the system, and if the imaging of a part of view field of the free-form surface system does not meet the imaging quality requirement. And (3) performing optimization iteration on the free-form surface system by using the optical path iteration method in the step (S3) until the free-form surface system meets the imaging requirement, and outputting the free-form surface system.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
The above embodiments of the present invention do not limit the scope of the present invention. Any of various other corresponding changes and modifications made according to the technical idea of the present invention should be included in the scope of the claims of the present invention.

Claims (9)

1. The design method of the initial structure of the ultra-large visual field off-axis reflective free-form surface optical system is characterized by comprising the following steps of:
the preprocessing step S0 is to define system parameters:
the number of free-form surfaces of the free-form surface optical system is K, and the kth free-form surface is defined as omega k ，k＝1,2,…K；
Dividing the free-form surface optical system into M fields of view, uniformly sampling the full aperture light of each field of view by a grid method to obtain J characteristic light rays, and defining the J characteristic light rays of the i field of view as R i,j ，i＝1,2,…M；j＝1,2,…J；
Definition of characteristic ray R i,j The intersection point with the entrance pupil is the starting point S i,j Defining the characteristic ray R i,j And the kth free-form surface omega k Is the characteristic data point P i,j,k ；
Definition of the characteristic ray R i,j After being reflected by k free curved surfaces, the target point T is reached i,k When k=k, point T i,k I.e. ideal image point I i ；
In the free-form surface optical system, the free-form surface optical system is formed from a starting point S i,j Emitted characteristic ray R i,j At characteristic data point P i,j,k Free-form surface Ω of the surface k After reflection, reaches the target point T i,k Rear characteristic ray R i,j Continuing the propagation, at characteristic data point P i,j,K Free-form surface Ω of the surface K Reflection to ideal image point I i ；
S1, according to the starting point S i,j And target point T i,k Calculating a first free-form surface Ω 1 All characteristic data points P of (1) i,j,1 Fitting the free-form surface omega by a least square method to obtain a first free-form surface omega 1 ；
S2, according to the first free-form surface omega 1 Calculating second free-form surface Ω 2 Is formed by the following steps ofWith characteristic data points P i,j,2 Fitting the second free-form surface omega by a least square method 2 Constructing an initial structure of the free-form surface optical system of the two reflectors;
s3, further performing iterative optimization on the initial structure through an optical path iterative method until the free-form surface light system meets imaging requirements;
and S4, obtaining an initial structure of the optimized free-form surface optical system when the number N of the reflecting mirrors is more than 2 by repeating the step S1, the step S2 and the step S3.
2. The method for designing an initial structure of an off-axis reflective free-form surface optical system with an oversized view field as set forth in claim 1, wherein,
the characteristic data point P in the step S1 i,j,1 The solving step of (1) comprises:
s11, calculating a first characteristic ray R in the first view field 1,1 Through the first free-form surface omega 1 After reflection, reaches the first target point T 1,1 Solving the optical path length of the first free-form surface omega of the first view field 1 Characteristic data point P of (1) 1,j,1 ；
S12, calculating the free curved surface omega of the rest view field characteristic rays except the first view field 1 The ideal optical path reaching the target point after reflection, and then the coordinate positions of the characteristic data points of the rest fields of view are positioned;
s13, the first free-form surface omega 1 All characteristic data points P of (1) i,j,1 Fitting by a least square method to obtain the first free-form surface omega 1 。
3. The method for designing the initial structure of the super-large field off-axis reflective free-form surface optical system according to claim 2, wherein the step S11 comprises:
first characteristic light ray R under first view 1,1 Through the first free-form surface omega 1 After reflection reaching the first target point T 11 Is not equal to the optical path length of (2)
Figure FDA0004101451900000021
The method comprises the following steps:
Figure FDA0004101451900000022
wherein ,n1 and n2 For the first free-form surface Ω 1 Refractive index of medium where incident light and emergent light are located;
all characteristic rays R in the first field of view 1,j Through the first free-form surface omega 1 After reflection, converging to the first target point T 1,1 Is not equal to the optical path length of (2)
Figure FDA0004101451900000023
The method comprises the following steps:
Figure FDA0004101451900000024
according to Malus's law, under ideal conditions:
Figure FDA0004101451900000025
solving a first free-form surface Ω of the first field of view according to equation (3) 1 Characteristic data point P of (1) 1,j,1 。
4. The method for designing an initial structure of an oversized view-field off-axis reflective free-form surface optical system according to claim 3, wherein the step S12 comprises:
for the first free-form surface Ω 1 Knowing the characteristic ray R of the ith field of view i,j Is made parallel to the characteristic ray R i,j Is intersected with the first free-form surface omega 1 At the curved surface vertex O 1 Passing through the entrance pupil S i,j Making a vertical line to make S i,j S′ i,j Perpendicular to S' i,j O 1 ；
According to Malus' S law, ray segment S i,j P i,j,1 T i,1 and S′i,j O 1 T i,1 Is equal, namely:
Figure FDA0004101451900000026
Figure FDA0004101451900000027
Figure FDA0004101451900000028
wherein ,
Figure FDA0004101451900000031
is the light ray segment S i,j P i,j,1 T i,1 Is a light path length of (2);
Figure FDA0004101451900000032
is the light ray segment S' i,j O 1 T i,1 Is a light path length of (2);
in point S i,j Constructing a local coordinate system X 'Y' Z 'for an origin O'; the field angle of the i-th field of view is known as (ω X ,ω Y ) S is then i,j P i,j,1 (O′P i,j,1 ) The projection in the X ' OZ ' plane and the Y ' OZ ' plane has an included angle omega with the Z ' axis respectively X and ωY The method comprises the steps of carrying out a first treatment on the surface of the Let the incident vector S i,j P i,j,1 The projection length on the Z' axis is 1, and the incident vector S is based on the geometric relation i,j P i,j,1 Projection lengths on the X 'axis and the Y' axis are tan omega respectively X and tanωY Unit incident vector S i,j P i,j,1 o The presence is:
Figure FDA0004101451900000033
constructing an optical line segment S' according to equation (7) i,j O 1 The linear equation:
Figure FDA0004101451900000034
point S i,j Sum point S i,j Plane equation of the tangential plane:
Figure FDA0004101451900000035
combined type (7-9), solving point
Figure FDA0004101451900000036
To determine the first free-form surface Ω according to equation (4-6) 1 All characteristic data points P of (1) i,j,1 ；
The step S13 includes:
the calculated characteristic data point P of the first free-form surface i,j,1 Fitting to an expression of an XY polynomial, constructing the first free-form surface Ω 1 ；
The expression of the XY polynomial is:
Figure FDA0004101451900000037
wherein c is the curvature of the curved surface; l is a quadric coefficient;
Figure FDA0004101451900000038
is a free-form surface polynomial; a is that q Is a polynomial coefficient.
5. The method for designing an initial structure of an oversized view-field off-axis reflective free-form surface optical system according to claim 4, wherein the step S2 comprises the sub-steps of:
s21, according to the optical line segment S i,j P i,j,1 T i,1 Is not equal to the optical path length of (2)
Figure FDA0004101451900000039
Calculating the characteristic ray R i,j From the entrance pupil S i,j To the ideal image point I i Optical path of->
Figure FDA00041014519000000310
S22, according to the optical path
Figure FDA0004101451900000041
And a first free-form surface omega 1 Solving the second free-form surface Ω 2 All characteristic data points P of (1) i,j,2 ；
S23, the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 Fitting a free-form surface characterized by an XY polynomial using a least squares method to obtain the second free-form surface Ω 2 。
6. The method for designing an initial structure of an oversized view-field off-axis reflective free-form surface optical system according to claim 5, wherein the step S21 comprises:
the first characteristic ray R 1,1 Passes through the first target point T 1,1 And then continue to propagate through the second free-form surface omega 2 After reflection, converging to ideal image point I 1 Optical path length
Figure FDA0004101451900000042
The method comprises the following steps:
Figure FDA0004101451900000043
wherein ,n3 For the first free-form surface Ω 2 The refractive index of the medium in which the outgoing light rays are located;
the characteristic ray R emitted by the ith view field i,j From the first free-form surface Ω 1 After reflection, converging to the target point T i,1 The characteristic ray R i,j Through the target point T i,1 Incident on the second free-form surface Ω 2 At point P i,j,2 After reflection, converging to ideal image point I i Is not equal to the optical path length of (2)
Figure FDA0004101451900000044
The method comprises the following steps:
Figure FDA0004101451900000045
Figure FDA0004101451900000046
from point T according to Malus's law i,1 Starting to converge to an ideal image point I i All the characteristic light rays in the space have the same optical path;
thus from point T i,1 Starting to make a second free-form surface omega 2 Surface vertex O 2 Is finally intersected with the image point I i There are:
Figure FDA0004101451900000047
then characteristic ray R i,j From the entrance pupil S i,j To ideal image point I i Is not equal to the optical path length of (2)
Figure FDA0004101451900000048
The method comprises the following steps:
Figure FDA0004101451900000049
wherein ,
Figure FDA00041014519000000410
is the light ray section T i,1 O 2 I i Is provided).
7. The method for designing an initial structure of an oversized view-field off-axis reflective free-form surface optical system according to claim 6, wherein the step S22 comprises:
calculate the exit pupil S i,j Emitted characteristic ray R i,j And the fitted first free-form surface omega 1 Is the actual intersection point P of (2) i,j,1 a Light ray segment S i,j P i,j,1 a Is not equal to the optical path length of (a)
Figure FDA0004101451900000051
The method comprises the following steps:
Figure FDA0004101451900000052
obtaining a second free-form surface omega 2 Is not equal to the optical path length of (a)
Figure FDA0004101451900000053
The method comprises the following steps:
Figure FDA0004101451900000054
wherein the characteristic data point P i,j,1 a For passing through the entrance pupil S i,j Emitted characteristic ray R i,j And a first free-form surface omega 1 Is the actual intersection of (1);
for the first free-form surface omega after the least square fitting 1 The surface equation is arranged into F(x, y, z) expression:
Figure FDA0004101451900000055
the first free-form surface equation F (x, y, z) is biased and then substituted into the characteristic data point P i,j,1 a Further obtaining the coordinates of the first free-form surface Ω 1 Normal vector N of each point on 1 The method comprises the following steps:
Figure FDA0004101451900000056
according to the law of refraction/reflection:
n 1 (A 1 o ×N 1 o )＝n 2 (A 1 o′ ×N 1 o ) (20)
wherein ,
Figure FDA0004101451900000057
Figure FDA0004101451900000058
A 1 o ，A 1 o′ respectively the characteristic rays R i,j With respect to said first free-form surface Ω 1 A unit vector of incident light and reflected light;
N 1 o for the point P i,j,1 a Unit normal vector at the position;
constructing ray P according to equation (22) i,j,1 a P i,j,2 The equation of the straight line is combined with the formula (17) to calculate the second free-form surface omega 2 All characteristic data points P of (1) i,j,2 。
8. The method for designing the initial structure of the off-axis reflective free-form surface optical system with extra-large field of view according to claim 7, wherein in the optical path iteration method of step S3, the current free-form surface system is used as a new initial structure, and then the optical paths of the feature data points for solving each free-form surface in the free-form surface system are sequentially modified continuously, which comprises the following steps:
by setting an initial optical path correction amount ΔOPD 1 For the calculated optical path
Figure FDA0004101451900000061
Correction is performed to obtain the optical path length for recalculating the free-form surface feature data points>
Figure FDA0004101451900000062
Figure FDA0004101451900000063
wherein ,εi,1 For correction of
Figure FDA0004101451900000064
Is expressed as:
Figure FDA0004101451900000065
wherein ,
Figure FDA0004101451900000066
based on iteration coefficients, ++>
Figure FDA0004101451900000067
Δε i,1 Is epsilon i,1 Is a iteration quantity of Deltaε i,1 ≥0；
When deltaε i,1 When the value of the sum is =0,
Figure FDA0004101451900000068
for the optical path
Figure FDA0004101451900000069
Its modified optical path per iteration +.>
Figure FDA00041014519000000610
The method comprises the following steps:
Figure FDA00041014519000000611
wherein ,
Figure FDA00041014519000000612
wherein ,
ε i,2 for correction of
Figure FDA00041014519000000613
Iteration coefficients of (a);
Figure FDA00041014519000000614
based on iteration coefficients, ++>
Figure FDA00041014519000000615
Δε i,2 Is epsilon i,2 Is a iteration quantity of Deltaε i,2 ≥0；
When delta epsilon i,2 When the value of the sum is =0,
Figure FDA00041014519000000616
ΔOPD 2 is that
Figure FDA00041014519000000617
An optical path correction amount of (a).
9. The method for designing an initial structure of an off-axis reflective free-form surface optical system with an oversized view field according to claim 8,
when the number of the free-form surfaces is N, N is more than 2, the design method is the same as that of the free-form surface system of the off-axis reflector in the claim 1;
setting N-1 target points T in the preprocessing step S0 i,k And N data points P 1,1,k ；
Repeating the step S1 and the step S2 to obtain all characteristic data points of N unknown free-form surfaces;
fitting all characteristic data points into a free-form surface, constructing a free-form surface system, observing the quality of the system, and if the imaging of a part of view field of the free-form surface system does not meet the imaging quality requirement; and (3) performing optimization iteration on the free-form surface system by the optical path iteration method in the step (S3) until the free-form surface system meets imaging requirements, and outputting the free-form surface system.
CN202310177631.XA 2023-02-28 2023-02-28 Design method for initial structure of ultra-large visual field off-axis reflection type free-form surface optical system Pending CN116149050A (en)

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CN116661139A (en) * 2023-06-09 2023-08-29 中国科学院长春光学精密机械与物理研究所 Design method of free-form surface optical system
CN116661139B (en) * 2023-06-09 2024-05-10 中国科学院长春光学精密机械与物理研究所 Design method of free-form surface optical system

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116661139A (en) * 2023-06-09 2023-08-29 中国科学院长春光学精密机械与物理研究所 Design method of free-form surface optical system
CN116661139B (en) * 2023-06-09 2024-05-10 中国科学院长春光学精密机械与物理研究所 Design method of free-form surface optical system

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