CN117406429A - Desensitization design method for free-form surface optical system - Google Patents
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- 238000000586 desensitisation Methods 0.000 title claims abstract description 19
- 230000035945 sensitivity Effects 0.000 claims abstract description 74
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Abstract
The invention provides a desensitization design method of a free-form surface optical system, which comprises the following steps: s1, setting initial structural parameters of a target optical system according to index parameter requirements of the target optical system, and constructing a multi-target genetic algorithm cost function comprising an image quality evaluation function and an error sensitivity evaluation function. S2, solving the cost function of the multi-target genetic algorithm to obtain an optical system closest to the index parameter requirement of the target optical system, and obtaining the free-form surface optical system. S3, setting an image quality and error sensitivity judging threshold value of the free-form surface optical system. And S4, optimizing the image quality and the error sensitivity of the free-form surface optical system through an error sensitivity evaluation function until an optimization result meets the index parameter requirement of the target optical system. The method and the device quantify the error sensitivity of the optical system, reduce the calculated amount in the desensitization optimization process of the free-form surface optical system, and improve the error sensitivity optimization efficiency.
Description
Technical Field
The invention relates to the technical field of application optics, in particular to a desensitization design method of a free-form surface optical system.
Background
The error sensitivity of the optical system characterizes the degradation degree of the imaging quality of the optical system after the internal parameters of the optical system are interfered, specifically measures the difficulty from theoretical design to manufacturing realization of the optical system, reflects the resistance of the optical system to external interference, and plays an important role in realizing the optical system by performing desensitization design on the optical system.
The optical free-form surface system has strong aberration correction capability and is gradually applied to various optical systems. However, the surface equation of the free-form surface optical system is complex, and the manufacturing cost is high, so that the method has important significance for developing desensitization design of the free-form surface optical system.
At present, some desensitization design methods are provided for an optical system, and a global optimization algorithm and a multiple structure optimization method are mainly provided.
The global optimization algorithm is a method for directly obtaining the optical system with low error sensitivity by firstly carrying out aberration correction on the optical system in the design process, carrying out large sample optimization and iteration on the optical system with optimized image quality and selecting a system with better tolerance robustness from a large number of design samples.
The multiple structure optimization method is to build multiple structures with different error types based on the original optical system structure, simulate the error types and the error magnitudes possibly generated by the optical system in the production, processing and practical application processes, and synchronously optimize the original optical system structure and the multiple structures with error disturbance, so that the imaging quality of all the structures is still within an acceptable range, and the original optical system can be demonstrated to have better capability of resisting error interference. Although the design methods have strong universality, the design efficiency is low, and the desensitization design cannot be realized efficiently.
In 2012, bin Ma et al, rochester university, usa, applied a common optical aspheric surface to Q-type free-form surface contrast design a mobile phone photographic objective lens, and when eccentricity and thickness errors are applied to one of the lenses, the amount of change in wave aberration of the Q-type free-form surface optical system applied was small, indicating that in this design, the Q-type surface type was effective in reducing the error sensitivity of the optical system. But do not address the clear theoretical reasons and unique design methodologies.
In the existing optical system desensitization design method, a global optimization algorithm adopts a large sample optimization iteration method, and because of the lack of an error sensitivity theory as a guide, the image quality is optimized and the global search is required to find out an optical system design result meeting the requirement, so that the efficiency is lower and blindness is achieved; in practical applications, when disturbance is applied to structural errors (curvature and thickness) and positional errors (inclination and decentration) of an optical system, at least 64 configurations are needed for a 4-lens system, and the calculation amount brought by the optimal design is huge. The method is effective for the design of optical system desensitization, but the characteristic parameters of the optical system with deep mathematical relationship with the error sensitivity of the optical system are not explored, the error sensitivity theory is lacking as a strong guide, the quantitative design of the optical system is difficult, the design efficiency is low, and the design directivity is weak.
The free-form surface optical system has a plurality of design variables, and if the design method is adopted for desensitization design, the design efficiency is extremely low. However, in the prior art, there is no disclosed design method for desensitizing a free-form surface optical system.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for designing a free-form surface optical system, which uses a reference point sampling method to evaluate and optimize the error sensitivity of the free-form surface optical system by optimally controlling the slope of the mirror surface of the optical element at the intersection point of the light and the optical element, while ensuring the imaging quality of the optical system.
In order to achieve the above purpose, the present invention adopts the following specific technical scheme:
the invention provides a desensitization design method of a free-form surface optical system, which comprises the following steps:
s1, setting initial structural parameters of a target optical system according to index parameter requirements of the target optical system, and constructing a first error sensitivity evaluation function SEN including an image quality evaluation function System Is a multi-objective genetic algorithm cost function.
S2, solving a multi-target genetic algorithm cost function to obtain a group of optical systems, selecting one optical system closest to the index parameter requirement of the target optical system from the group of optical systems, and upgrading the surface type of the optical system into a free-form surface to obtain the free-form surface optical system.
S3, determining a threshold value RMS WFE for image quality of the free-form surface optical system V And error sensitivity determination threshold SENF V Setting is performed.
S4, evaluating a function SENF through the second error sensitivity System And evaluating and optimizing the image quality and the error sensitivity of the free-form surface optical system until the optimization result of the free-form surface optical system meets the index parameter requirement of the target optical system.
Preferably, step S4 comprises the sub-steps of:
s41, optimizing a free-form surface optical system by taking the distance between the reflecting mirrors, the curvature radius, the quadric surface coefficient and the free-form surface higher order term coefficient as variables;
s42, judging whether the image quality and the error sensitivity of the free-form surface optical system meet the index parameter requirements of the target optical system or not:
determining RMS WFE for freeform optical systems System Whether or not it is less than the image quality judgment threshold RMS WFE V ；
Judging a second error sensitivity evaluation function SENF of the free-form surface optical system System Whether or not it is smaller than the error sensitivity judgment threshold SENF V ；
If yes, ending the step S4, and outputting a design result meeting the requirements;
if not, the process returns to step S41.
Preferably, the first error sensitivity evaluation function SEN System The construction process of (2) is as follows:
inclination error sensitivity evaluation function SEN of first surface reflector in free-form surface optical system Surface The method comprises the following steps:
wherein k is the sequence number of the view fields of the free-form surface optical system, and NOF view fields are shared;
τ is the absolute value of the reciprocal of K, which is the tangential slope of the intersection of the incident ray and the first mirror.
First error sensitivity evaluation function SEN System The method comprises the following steps:
where i is a plane number, i=1, 2 … n, n denotes the number of optical surfaces in the free-form surface optical system.
Preferably, the mirror slope at the reference point of the freeform optical system is controlled and optimized using a "ring-arm" reference point sampling approach,
the "ring-arm" reference point sampling mode is to locate the reference point in each field of view of the freeform optical system by means of NOR rings and NOA arms that intersect each other.
Preferably, the ring and arm selection in the "ring-arm" sampling mode is as follows:
the ring is defined in the following manner: ring# is a Ring number, and Ring 1, ring 2, ring3, … and Ring NOR respectively extend outwards from the center of any mirror surface of the free-form surface optical system;
the arms are defined in the following manner: arm # Arm numbers, from meridian +90°, are sequentially ordered in a counterclockwise direction, arm 1,Arm 2,Arm 3,Arm …, arm NOA, respectively.
Preferably, at each reference point, the tangential slope of the intersection of the incident ray with the first mirror is Ku, v, where u is the ring number and v is the arm number; u=1, 2 … NOR; v=1, 2 … NOA.
Preferably, the second error sensitivity evaluation function SENF under full field of view System In the calculation process of (2):
firstly, calculating error sensitivity SENF of a first surface free-form surface reflecting mirror corresponding to a single field of view of a free-form surface optical system:
wherein τ u,v Absolute value of inverse Ku, v;
then calculating the average value of the error sensitivity of the rest free-form surface reflectors corresponding to each view field of the free-form surface optical system as a second error sensitivity evaluation function SENF under the full view field System ：
Compared with the prior art, the desensitization design method combines the reference point sampling mode of the ring-arm, and meets the requirement of reducing the error sensitivity of the optical system under the precondition of ensuring the imaging quality of the optical system by controlling and optimizing the mirror slope of the optical element at the reference point. The method takes the reflective free-form surface optical system as a model, takes the error sensitivity theoretical basis as a strong guide, obtains the mathematical relationship between the optical slope and the error sensitivity, and carries out the sensitivity-reducing optimization design on the optical system in a targeted manner.
Compared with the prior art, the method quantifies the error sensitivity of the optical system, and can remarkably reduce the calculated amount in the desensitization optimization process of the free-form surface optical system and improve the error sensitivity optimization efficiency.
Drawings
Fig. 1 is a flow chart of a desensitization design method of a free-form surface optical system according to an embodiment of the present invention.
Fig. 2 is a flow chart of a method for desensitizing a freeform optical system according to an embodiment of the present invention.
Fig. 3 is a schematic view illustrating light propagation of a freeform optical system according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of a "ring-arm" sampling mode of a freeform optical system according to an embodiment of the present invention.
Fig. 5 is a schematic layout diagram of a freeform optical system according to an embodiment of the present invention.
Fig. 6 is a wavefront diagram of a freeform optical system provided in accordance with an embodiment of the present invention.
FIG. 7 is a diagram of error sensitivity evaluation functions (SENF) before and after optimization of a free-form surface optical system according to an embodiment of the present invention System ) Value versus graph.
Fig. 8 is a graph showing wave aberration variation amounts before and after optimization of the free-form surface optical system according to the embodiment of the present invention.
Wherein reference numerals include: an incident light ray 1, a mirror normal 2, a reflected light ray 3, a mirror 4, a tangent 5 to the intersection of the incident light ray and the mirror, and an intersection 6 of the incident light ray and the mirror.
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 shows a flow chart of a desensitization design method of a free-form surface optical system according to an embodiment of the invention.
Fig. 2 shows a flow diagram of a method for desensitizing a freeform optical system provided according to an embodiment of the present invention.
As shown in fig. 1 and fig. 2, the desensitization design method of the free-form surface optical system provided by the embodiment of the invention includes the following steps:
s1, according to the index parameter requirement of the target optical system, carrying out initial structure parameter processing on the target optical systemSetting up lines and constructing a first error sensitivity evaluation function SEN including an image quality evaluation function System Is a multi-objective genetic algorithm cost function.
First error sensitivity evaluation function SEN System For screening the initial structure of the target optical system.
First error sensitivity evaluation function SEN System The construction process of (1) is as follows:
fig. 3 shows a schematic light propagation diagram of a freeform optical system according to an embodiment of the present invention.
As shown in fig. 3, an incident light ray 1 is incident on a reflector 4, reflected by the reflector 4 to obtain a reflected light ray 3, and a reflector normal 2 is formed, an intersection 6 of the incident light ray 1 and the reflector 4 is N, a tangent 5 of the reflector 4 is made at the N point, and a tangent slope is K.
However, K cannot be obtained as a tangent function, which results in that a suitable threshold cannot be set and from the viewpoint of the optimization function, the optimization process usually obtains the minimum value of the optimization function, so that in order to facilitate the setting of the error sensitivity threshold, the absolute value of the inverse K is defined as τ, and thus the first error sensitivity evaluation function SEN of the optical system System The following are provided:
the first mirror tilt error sensitivity evaluation function is SEN Surface ：
Where k is the field number and there are NOF fields of view.
First error sensitivity evaluation function SEN System The method comprises the following steps:
where i is a plane number, i=1, 2 … n. n refers to the number of optical surfaces in the optical system.
Fig. 4 shows a schematic diagram of a "ring-arm" sampling mode of a freeform optical system according to an embodiment of the present invention.
As shown in fig. 4, the "ring-arm" sampling method provided by the present invention defines: pupil sampling is performed for each field of view, ring3 in fig. 4 representing the pupil.
The sampling mode of NOR number of NOA arms is adopted, and the selection modes of the rings and the arms are as follows:
the ring is defined in the following manner: ring# represents the Ring number, ring 1,Ring 2,Ring 3,Ring … from the center outwards, respectively, represents the Ring that may be present, ring NOR;
the arms are defined in the following manner: arm# represents the number of rings, starting from the meridian +90°, arm 1, and sequentially ordered in the counterclockwise direction, arm2, arm 3, arm …, arm NOA, respectively.
For example, ring3 and Arm2 correspond to the sampling points shown by the red arrows.
At each sampling point, the tangential slope of the intersection of the ray and the mirror is defined as Ku, v, where u is the ring number and v is the arm number; u=1, 2 … NOR; v=1, 2 … NOA.
Firstly, calculating the error sensitivity of a free-form surface reflecting mirror corresponding to a single view field, and then calculating the average value of the error sensitivity of the three free-form surface reflecting mirrors corresponding to each view field as an integrated error sensitivity evaluation function.
In one field of view, the error sensitivity of a single free-form mirror is defined as SENF:
error sensitivity SENF of three-surface free-form surface reflecting mirror corresponding to all view fields System ：
S2, solving a cost function of the multi-target genetic algorithm to obtain a group of optical systems, selecting one optical system closest to the index parameter requirement of the target optical system, and upgrading the surface type of the optical system into a free-form surface to obtain the free-form surface optical system.
S3, determining a threshold value RMS WFE for image quality of the free-form surface optical system V And error sensitivity determination threshold SENF V Setting is performed.
S4, evaluating a function SENF through the second error sensitivity System And evaluating and optimizing the image quality and the error sensitivity of the free-form surface optical system until the optimization result of the free-form surface optical system meets the index parameter requirement of the target optical system.
Step S4 comprises the following sub-steps:
s41, optimizing a free-form surface optical system by taking the distance between the reflectors, the curvature radius, the quadric surface coefficient and the free-form surface shape parameter as variables;
in the optimization process, the structural parameters of the free-form surface optical system are ensured to meet the requirements, including the parameters of the total length of the system, the rear working distance and the like.
S42, judging whether the image quality and the error sensitivity of the free-form surface optical system meet the index parameter requirements of the target optical system or not:
determining RMS WFE for freeform optical systems System Whether or not it is less than the image quality judgment threshold RMS WFE V ；
Judging error sensitivity SENF of free-form surface optical system System Whether or not it is smaller than the error sensitivity judgment threshold SENF V ；
If yes, ending the step S4, and outputting a design result meeting the requirements;
if not, the process returns to step S41.
In one embodiment provided by the invention:
a square view field Cook type off-axis three-mirror optical system with a focal length of 100mm, an F number of 5, wavelength selection of 550nm,3 degrees multiplied by 3 degrees (meridian: -8.5 degrees to-10.5 degrees, sagittal: -1.5 degrees to 1.5 degrees) is taken as an example for design.
In step S1:
firstly, according to the index parameter requirement of a target optical system, setting the initial structural parameter of the target optical system:
and (5) setting initial structural parameters. Optical system parameter value range: all quadric coefficients: 5.0000-5.0000, a secondary mirror blocking ratio of 0.400-0.500, a three-mirror blocking ratio of 1.500-2.000, a secondary mirror magnification of 1.500-2.000 and a three-mirror magnification of 0.350-1.000.
Secondly, constructing a multi-objective genetic algorithm cost function comprising an image quality evaluation function and an error sensitivity evaluation function.
Parameter setting of a multi-objective genetic algorithm: population number 200, 500 iterations, genetic probability=0.9, mutation probability=0.1.
Setting a multi-objective genetic algorithm cost function: image quality evaluation function: a primary aberration; error sensitivity evaluation function: SEN (SEN-based optical fiber) System 。
In step S2:
and solving by adopting a multi-target genetic algorithm, and selecting an optical system with acceptable image quality and error sensitivity from the solution set, namely selecting one optical system closest to the index parameter requirement of the target optical system. The parameters of the final selected optical system are as follows:
| System | α 1 | α 2 | β 1 | β 2 | e 1 2 | e 2 2 | e 3 2 | F 1 | F 2 |
| 174 | 0.499 | 1.500 | 1.748 | 0.980 | -2.3071 | 0.0900 | 0.1430 | 1.0807 | 0.0728 |
the system RMS WFE is 0.0645λ, error sensitivity SENF system 0.0728, both image quality and error sensitivity are acceptable. And upgrading the surface model into a free-form surface, and performing the next-stage optimization.
In step S3:
the image quality judgment threshold of the free-form surface off-axis three-reflection optical system is set to be 0.0200lambda, and the error sensitivity judgment threshold is set to be 0.0700.
In step S4:
optimizing the free-form surface optical system by adopting the proposed second error sensitivity evaluation function SENF System 。
Fig. 5 shows a layout of a hook-type off-axis three-mirror optical system of a freeform optical system according to an embodiment of the present invention.
Fig. 6 shows a wavefront diagram of a Cook-off-axis three-mirror optical system of a freeform optical system provided in accordance with an embodiment of the present invention.
As shown in fig. 5 and 6, the optimization results of the Cook off-axis three-mirror optical system output are shown. Design result is that the main mirror adopts Chebyshev Polynomial, the secondary mirror adopts Zernike Fringe Sag, the three mirrors adopt Extended Polynomial, the system RMS WFE is 0.0026λ, and the error sensitivity SENF is adopted system 0.0266.
Error sensitivity analysis is performed on the free-form surface optical system and the quadric surface optical system. The two optical systems were each subjected to 500 monte carlo analyses, each mirror was subjected to a tilt error of ±0.01°, the error amount was subjected to normal distribution, and the average value of Δrms WFE was calculated.
FIG. 7 shows a free-form surface optical system error sensitivity evaluation function (SENF) of a Cook-type off-axis three-mirror optical system before and after optimization according to an embodiment of the invention system ) Comparison graph.
Fig. 8 shows a graph of wave aberration variation of a hook-type off-axis three-mirror optical system before and after optimization of a free-form surface optical system according to an embodiment of the present invention.
As shown in fig. 7 and 8, in the free-form surface optical system, compared with the quadric surface optical system, when the wave aberration is 1/25 of the original wave aberration and the tilt imbalance disturbance is the same, the change amount of the wave aberration is 51% of the original wave aberration, and it can be proved that the design method proposed by the present invention is correct and effective.
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 (7)
1. The desensitization design method of the free-form surface optical system is characterized by comprising the following steps of:
s1, setting initial structural parameters of a target optical system according to index parameter requirements of the target optical system, and constructing a first error sensitivity evaluation function SEN including an image quality evaluation function System Is a multi-objective genetic algorithm cost function;
s2, solving the multi-target genetic algorithm cost function to obtain a group of optical systems, selecting one optical system closest to the index parameter requirement of the target optical system from the group of optical systems, and upgrading the surface type of the optical system into a free-form surface to obtain a free-form surface optical system;
s3, judging a threshold value RMS WFE for the image quality of the free-form surface optical system V And error sensitivity determination threshold SENF V Setting;
s4, evaluating a function SENF through the second error sensitivity System And evaluating and optimizing the image quality and the error sensitivity of the free-form surface optical system until the optimization result of the free-form surface optical system meets the index parameter requirement of the target optical system.
2. The method for desensitizing a free-form surface optical system according to claim 1, wherein said step S4 comprises the sub-steps of:
s41, optimizing the free-form surface optical system by taking the distance between the reflecting mirrors, the curvature radius, the quadric surface coefficient and the free-form surface higher order term coefficient as variables;
s42, judging whether the image quality and the error sensitivity of the free-form surface optical system meet the index parameter requirements of the target optical system or not:
determining RMS WFE for freeform optical systems System Whether or not it is less than the image quality judgment threshold RMS WFE V ；
Judging a second error sensitivity evaluation function SENF of the free-form surface optical system System Whether or not it is smaller than the error sensitivity judgment threshold SENF V ；
If yes, ending the step S4, and outputting a design result meeting the requirements;
if not, the process returns to step S41.
3. The method for desensitizing a freeform optical system according to claim 1, wherein said first error sensitivity evaluation function SEN System The construction process of (2) is as follows:
the first surface reflector inclination error sensitivity evaluation function SEN in the free-form surface optical system Surface The method comprises the following steps:
wherein k is the sequence number of the fields of view of the free-form surface optical system, and NOF fields of view are shared;
τ is the absolute value of the reciprocal of K, K is the tangential slope of the intersection point of the incident light ray and the first surface reflector;
the first error sensitivity evaluation function SEN System The method comprises the following steps:
where i is a plane number, i=1, 2 … n, n denotes the number of optical surfaces in the free-form surface optical system.
4. The method for desensitizing a freeform optical system according to claim 1, wherein a "ring-arm" reference point sampling method is used to control and optimize the slope of the mirror surface at the reference point of the freeform optical system,
the "ring-arm" reference point sampling mode is to locate the reference point in each field of view of the freeform optical system by using NOR rings and NOA arms to intersect each other.
5. The method of claim 1, wherein the ring and arm selection in the "ring-arm" sampling mode is as follows:
the ring is defined in the following manner: ring# is a Ring number, and Ring 1, ring 2, ring3, … and Ring NOR respectively extend outwards from the center of any mirror surface of the free-form surface optical system;
the arm is defined in the following manner: arm # Arm numbers, from meridian +90°, are sequentially ordered in a counterclockwise direction, arm 1,Arm 2,Arm 3,Arm …, arm NOA, respectively.
6. The method of claim 5, wherein at each of the reference points, a tangential slope of an intersection of an incident ray and the first mirror is Ku, v, where u is a ring number and v is an arm number; u=1, 2 … NOR; v=1, 2 … NOA.
7. The method of designing a free-form surface optical system according to claim 6, wherein the second error sensitivity evaluation function SENF under the full view field System In the calculation process of (2):
firstly, calculating error sensitivity SENF of a first surface free-form surface reflecting mirror corresponding to a single field of view of the free-form surface optical system:
wherein, the tau u,v Absolute value of inverse Ku, v;
then calculating the average value of the error sensitivity of the rest free-form surface reflectors corresponding to each view field of the free-form surface optical system as a second error sensitivity evaluation function SENF under the whole view field System ：
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