CN116090193A - Method for rapidly optimizing glass material in optical optimization design - Google Patents

Method for rapidly optimizing glass material in optical optimization design Download PDF

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CN116090193A
CN116090193A CN202211642862.5A CN202211642862A CN116090193A CN 116090193 A CN116090193 A CN 116090193A CN 202211642862 A CN202211642862 A CN 202211642862A CN 116090193 A CN116090193 A CN 116090193A
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陈巧
宋菲君
唐熊忻
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Institute of Software of CAS
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Abstract

The invention discloses a method for rapidly optimizing glass materials in optical optimization design, which comprises the following steps: 1) Generating n of optical glass according to parameters of each glass in glass library d ‑v d ‑dP g,F Space and determining a boundary curved surface of the space; 2) Recording an evaluation function value m.f. (n) of the optical system before optimization; 3) Determining the quantity of glass materials participating in optimization through pseudo random numbers; 4) Reading parameters of glass materials participating in optimization as continuous variables, and optimizing by a damping least square method; 5) Judging the closest glass material according to the optimized glass parameters, and replacing the optimized parameters with actual parameters of the corresponding glass materials in the glass library; 6) Replacing the glass parameters in the model with corresponding specific glass parameters and optimizing; recording the updated function value m.f. (n+1); 7) When m.f. (n+1) is greater than m.f. (n), discarding the current model parameters; otherwise, the current model parameters are reserved.

Description

Method for rapidly optimizing glass material in optical optimization design
Technical Field
The invention belongs to the technical field of optical system design, and particularly relates to a method for rapidly optimizing glass materials in optical optimization design.
Background
The refractive index means that the ratio of the sine of the angle of incidence gamma to the sine of the angle of refraction beta is a function of wavelength when monochromatic light is incident on the glass from vacuum.
n＝sinγ/sinβ
The Abbe number (Abbe number) is often used to characterize the "mid-dispersion" of a glass, the larger the Abbe number, the smaller the dispersion
Figure BDA0004008406210000011
Relative partial dispersion: in the apochromatic lens design, it is often necessary to consider relative partial dispersion, and after the chromatic aberration of the two colors is eliminated, the residual chromatic aberration (secondary spectrum) with respect to the third color becomes the main chromatic aberration.
According to the abbe's formula, most "normal glass" satisfies the following linear relationship:
P x,y ＝m x,y ·ν d +b x,y
in v d And P x,y Respectively is a transverse coordinate variable m and a longitudinal coordinate variable m x,y Is a slope, b x,y Is the intercept.
For the correction of the secondary spectrum, at least one "abnormal glass", i.e. P ' deviating from the Abbe's straight line formula, is required ' x,y . The deviation can be delta P' x,y And (3) representing. For example, ΔP g,F The characteristic of the deviation of the specific dispersion of the "abnormal glass" from the abbe straight line is quantitatively shown.
Figure BDA0004008406210000012
ΔP g,F ＝P g,F -0.6457+0.001703·ν d
The traditional optical system design is that the initial structure of the system is calculated from the ideal optical formula calculation, the optical structure system is calculated by the aberration theory, and the advanced aberration is estimated and compensated by the ray tracing. In the optimal design process of the optical lens, the curvature radius R and the thickness T are used as continuous variables, and the minimum value of the evaluation function, namely the local optimal solution, is obtained by using a damping least square method under the constraint of the evaluation function. In addition to radius of curvature and thickness, glass materials are also important optimization variables, often requiring replacement of glass or glass combinations when optical system aberrations do not meet design requirements.
Optical designs have been developed over the years, and optical designers have designed various types of lens systems of different parameters, and have undergone production and use to verify that they meet the specification requirements. In modern optical system design, an optical designer usually searches a lens design program close to the index according to the design index, and performs local optimization adjustment to achieve an optimal solution based on the program, wherein the lens for reference is mostly from a book handbook or an optical lens patent. In recent years, the development of the ZLAF glass with extremely high refractive index and low medium dispersion is successful, and more choices are provided for the selection of glass materials in optical design. When the prior patent or case is used as a reference design, the system glass material is optimized, and the imaging quality of the lens can be further improved.
Refractive index n of main parameter of optical glass d And Abbe number v d The interval is larger, belongs to discrete variables, and is not suitable for damping least square method. Hammer optimization (Hammer optimization) of the optical design software ZEMAX can realize the function of glass optimization replacement, but the algorithm process is not disclosed.
The selection of glass materials in the optical design process is a complex and difficult process, the optical glass belongs to discrete variables, what type of glass should be used for different types of optical systems, what type of glass should be replaced for compensating different aberrations, and the process provides preliminary estimation by using a dispersion formula, but the calculation process is complex and has quite high requirements on the experience of optical design.
When ZEMAX is adopted to conduct glass optimization design, the glass is usually set to be replaced after the initial design of the system is completed based on an initial structure, and the hammer optimization (Hammer Optimization) in global optimization often needs a long time, so that the system can converge to reach a lower evaluation function result. However, the optimization result does not always meet the requirement, and at this time, a different initial structure needs to be further replaced to carry out the optimization design again. At this time, the evaluation function setting and Hammer glass-changing optimization process is repeated.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a method for rapidly optimizing glass materials in optical optimization design. The invention is mainly aimed at optimizing parameters such as curvature radius, thickness interval, glass material and the like. Wherein the main parameters of the glass material are refractive index, abbe number and relative partial dispersion deviation value.
The invention relates to a fast descent path method for simultaneously optimizing continuous variables and discrete variables. The invention optimizes discrete material variables as quasi-continuous variables through boundary constraint; not all materials are always used as variables in the optimization, but the decision is made to participate in the optimization of the materials in the round by generating pseudo random numbers.
The technical scheme of the invention is as follows:
a method for rapidly optimizing glass materials in optical optimization design comprises the following steps:
1) Based on refractive index, abbe number parameter and relative partial dispersion deviation value dP of each glass in glass library g,F N for producing optical glass d -v d -dP g,F Space, and determine the n d -v d -dP g,F Boundary surface of space;
2) Setting an evaluation function according to the index requirement of the optical system; recording an evaluation function value m.f. (n) of the optical system before optimization;
3) Generating a group of 1/0 pseudo random numbers according to the quantity of glass materials participating in optimization in the optical system, wherein the pseudo random numbers correspond to the materials to be optimized one by one; the pseudo-random number of 1 indicates that the corresponding material is used as a variable of the round of optimization, and the pseudo-random number of 0 indicates that the corresponding material does not participate in the round of optimization;
4) Reading the refractive index n of the glass material involved in the optimization d Abbe number v d And a relative dispersion deviation value dP g,F As a continuous variable, optimizing the continuous variable and other parameters in the optical system by a damping least square method;
5) Reading parameters of each glass in the glass library, judging the closest glass material according to the optimized glass parameters, and replacing the optimized parameters with actual glass parameters of the corresponding glass materials in the glass library;
6) Replacing the glass parameters in the system model corresponding to the optical system with the corresponding actual glass parameters in the material library one by one;
randomly generating a replacement sequence; after each replacement, carrying out one-time damping least square method optimization on the updated system model; recording the evaluation function value m.f. (n+1) of the optical system updated at this time after the complete replacement and optimization;
7) Comparing m.f. (n) with m.f. (n+1), and discarding the current system model parameters when the optimized m.f. (n+1) is greater than the m.f. (n) value before the optimization starts; otherwise, keeping the current system model parameters, returning to the step 3) and generating a new 1/0 pseudo-random number;
8) Repeating steps 3) through 7), wherein each repetition generates a new 1/0 pseudo random number in step 3) and a new replacement sequence in step 6); when the set times are reached, the current optimal system model parameters are selected from the reserved system model parameters to be output.
Further, the method for determining the boundary curved surface comprises the following steps: reading refractive index, abbe number and relative partial dispersion deviation value parameters of each glass in the glass library participating in optimization; according to n d -v d -dP g,F And fitting a plurality of boundary function curved surfaces to the scattered point distribution under the three-dimensional coordinate system of the space.
Further, the closest glass judgment method: calculating a distance between an unmatched glass and each glass in the glass library
Figure BDA0004008406210000031
Determining a replacement for each unmatched glass as a function of distance d; wherein N is dm 、V dm 、ΔP g,Fm Refractive index, abbe number and relative partial dispersion deviation value of unmatched glass in the system model; n (N) dg 、V dg 、ΔP g,Fg Refractive index, abbe number and relative partial dispersion deviation value of glass in the glass library; w (W) n 、W v 、W p The refractive index, abbe number and the relative partial dispersion deviation value.
Further, the information used in calculating the evaluation function includes focal length, amount of constraint on lens thickness, RMS value of the point map or wavefront, PTV value.
A server comprising a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program comprising instructions for performing the steps of the above method.
A computer readable storage medium having stored thereon a computer program, characterized in that the computer program when executed by a processor realizes the steps of the above method.
The invention has the following advantages:
the design experience of a designer is low, the performance of each optical glass material is not required to be known, and the design index of the optical system can be improved by replacing glass;
and optimizing the discrete variable by deriving a damping least square method to obtain a more proper glass combination.
The damping least square method in the model replacement method can be replaced by other optimization algorithms, such as an orthogonal descent method, an adaptation method, a simulated annealing method, a global search method, a variable scale method, a damping least square method added with an escape function and the like in a global optimization algorithm.
Glass boundary determination method: besides fitting a plurality of boundary curved surfaces, grids with proper density can be divided in a three-dimensional space, and whether the space three-dimensional grid belongs to an optimized interval is judged by judging whether glass exists in the cubic grid or not.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings, which are given by way of illustration only and are not intended to limit the scope of the invention.
FIG. 1 is a main flow chart of the technical scheme of the invention, and the processing flow of the optimizing method of the invention comprises the following steps.
Step one: plotting n of the optical glass according to refractive index, abbe number parameter and relative partial dispersion deviation value in glass library d -v d -dP g,F Space, and determining a boundary surface of the glass space. By fitting the glass boundary, the optimization range of the refractive index and the Abbe number can be reduced, and the problem that the optimized result parameters cannot search for proper glass is avoided.
The boundary curved surface determining method comprises the following steps: reading refractive index, abbe number and relative partial dispersion deviation value parameters of each glass in the glass library participating in optimization; according to the scattered point distribution under the three-dimensional coordinate system, a plurality of boundary function curved surfaces are fitted, the limiting range of the curved surfaces is slightly larger than the range of the actual glass, and the expansion of the optimizing range is favorable for searching more proper glass. The three-dimensional coordinate system here is n of the optical glass d -v d -dP g,F And drawing the three-dimensional coordinates of the space and the scattered point distribution according to the parameters of each glass in the glass library.
Step two: according to the index requirements of an actual optical system, proper evaluation functions are written, including focal length, constraint quantity on lens thickness, RMS value of a point diagram or wavefront, PTV value and the like. The curvature, thickness and material in the optical system are respectively used as optimization variables, wherein the independent variables of the material variables are refractive index, abbe number and relative partial dispersion deviation value. Recording the system evaluation function value m.f. (n) before optimization. Setting an evaluation function according to a program, wherein the constraint of focal length and lens thickness is performed according to the design index requirement, and the constraint mode can give an upper boundary and a lower boundary or fix a certain quantity as a target value; the RMS and PTV values of the point map and wavefront are the results obtained at the image plane by ray tracing the optical system.
Step three: according to the quantity of materials participating in optimization in the system, a group of 1/0 pseudo-random numbers are generated, and the pseudo-random numbers correspond to the materials to be optimized one by one. A pseudorandom number of 1 indicates that the corresponding material is used as a variable for the current round of optimization, and a pseudorandom number of 0 indicates that the corresponding material does not participate in the current round of optimization.
Step four: reading the refractive index n of the material involved in the optimization d Abbe number v d Relative partial colorCoefficient of dispersion deviation dP g,F The parameters are optimized as continuous variables with other parameters in the system by a damped least squares method. If the initial design is proper, the evaluation function is reasonably set, and the evaluation function can be quickly reduced to a minimum value.
Step five: the refractive index and Abbe number calculated by the damped least squares method are probably not completely corresponding to the glass, and therefore are determined by determining the distance to the model material n d ,v d ，dP g,F The closest glass material is replaced. And randomly sequencing according to the number of glass models which are required to be replaced, and replacing the material models with specific glass one by one.
The closest glass determination method:
Figure BDA0004008406210000051
wherein d represents the distance between the model material and the actual glass; n (N) dm 、V dm 、ΔP g,Fm Refractive index, abbe number and relative partial dispersion of the model material; n (N) dg 、V dg 、ΔP g,Fg Refractive index, abbe number and relative partial dispersion of the actual glass material; w (W) n 、W v 、W p For weight, the model glass was replaced with the "nearest" actual glass by comparing the distances of the model material from the respective glass materials.
Step six: when the three parameters are replaced to the actual glass, the system is not at the optimized minimum value due to the discrete characteristics of the glass, and the evaluation function is often increased, so that after each replacement, the curvature radius, the thickness and the glass material parameters which are not replaced to the specific glass are optimized by a damping least square method. After complete glass replacement, optimization, the m.f. (n+1) at this time was recorded.
Step seven: comparing m.f. (n) with m.f. (n+1), and discarding the model optimization and replacement when the optimized m.f. (n+1) is larger than the m.f. (n) value before the optimization starts. And (3) restarting the operation from the third step to the sixth step.
And when the optimized m.f. (n+1) is smaller than or equal to the m.f. (n) value before the optimization starts, reserving the model optimization and glass replacement, updating system parameters, and repeating the operations of the third step and the sixth step.
By adopting the material optimization algorithm provided by the patent, a better output result can be obtained after a plurality of groups of optimization substitutions are performed.
Once a lower rating function value m.f. (n+1) < m.f. (n), the entire system will be replaced with a new glass combination, with subsequent m.f. (n+2) and the last set of m.f. (n+1) comparisons. The evaluation function value can be updated in real time, and the system is updated to the latest state every time a group of lower evaluation function values are calculated.
Although specific embodiments of the invention have been disclosed for illustrative purposes, it will be appreciated by those skilled in the art that the invention may be implemented with the help of a variety of examples: various alternatives, variations and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will have the scope indicated by the scope of the appended claims.

Claims (6)

1. A method for rapidly optimizing glass materials in optical optimization design comprises the following steps:
1) Based on refractive index, abbe number and relative partial dispersion deviation value dP of each glass in glass library g,F N for producing optical glass d -v d -dP g,F Space, and determine the n d -v d -dP g,F Boundary surface of space;
2) Setting an evaluation function according to the index requirement of the optical system; recording an evaluation function value m.f. (n) of the optical system before optimization;
3) Generating a group of 1/0 pseudo random numbers according to the quantity of glass materials participating in optimization in the optical system, wherein the pseudo random numbers correspond to the materials to be optimized one by one; the pseudo-random number of 1 indicates that the corresponding material is used as a variable of the round of optimization, and the pseudo-random number of 0 indicates that the corresponding material does not participate in the round of optimization;
4) Reading refractive index of glass material participating in optimizationn d Abbe number v d And a relative dispersion deviation value dP g,F As a continuous variable, optimizing the continuous variable and other parameters in the optical system by a damping least square method;
5) Reading parameters of each glass in the glass library, judging the closest glass material according to the optimized glass parameters, and replacing the optimized parameters with actual glass parameters of the corresponding glass materials in the glass library;
6) Replacing the glass parameters in the system model corresponding to the optical system with the corresponding actual glass parameters in the material library one by one; randomly generating a replacement sequence; after each replacement, carrying out one-time damping least square method optimization on the updated system model; recording the evaluation function value m.f. (n+1) of the optical system updated at this time after the complete replacement and optimization;
7) Comparing m.f. (n) with m.f. (n+1), and discarding the current system model parameters when the optimized m.f. (n+1) is greater than the m.f. (n) value before the optimization starts; otherwise, keeping the current system model parameters, returning to the step 3) and generating a new 1/0 pseudo-random number;
8) Repeating steps 3) through 7), wherein each repetition generates a new 1/0 pseudo random number in step 3) and a new replacement sequence in step 6); when the set times are reached, the current optimal system model parameters are selected from the reserved system model parameters to be output.
2. The method according to claim 1, wherein the boundary surface determining method comprises: reading refractive index, abbe number and relative partial dispersion deviation value parameters of each glass in the glass library participating in optimization; according to n d -v d -dP g,F And fitting a plurality of boundary function curved surfaces to the scattered point distribution under the three-dimensional coordinate system of the space.
3. The method of claim 1, wherein the closest glass determination method: calculating a distance d= [ W ] between an unmatched glass and each glass in the glass library n (N dm -N dg ) 2 +W v (V dm -V dg ) 2 +W p (ΔP g,Fm -ΔP g,Fg ) 2 ] 12 The method comprises the steps of carrying out a first treatment on the surface of the Determining a replacement for each unmatched glass as a function of distance d; wherein N is dm 、V dm 、ΔP g,Fm Refractive index, abbe number and relative partial dispersion deviation value of unmatched glass in the system model; n (N) dg 、V dg 、ΔP g,Fg Refractive index, abbe number and relative partial dispersion deviation value of glass in the glass library; w (W) n 、W v 、W p The refractive index, abbe number and the relative partial dispersion deviation value.
4. A method according to claim 1 or 2 or 3, characterized in that the information used in calculating the evaluation function comprises focal length, amount of constraint on lens thickness, RMS value of the point map or wavefront, PTV value.
5. A server comprising a memory and a processor, the memory storing a computer program configured to be executed by the processor, the computer program comprising instructions for performing the steps of the method of any of claims 1 to 4.
6. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 4.
CN202211642862.5A 2022-12-20 2022-12-20 Method for rapidly optimizing glass material in optical optimization design Pending CN116090193A (en)

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