CN107219626A - The freeform optics system optimization method of faying face shape and visual field optimisation strategy - Google Patents

Abstract

The invention discloses a method for optimizing a free-form surface optical system combined with surface shape and field of view optimization strategies. In this method, the coefficients of the Zernike standard polynomial that characterize the wave aberration of the optical system are used as the evaluation basis, and the optimization process is carried out by a stepwise approximation strategy combining surface shape optimization and field of view optimization. The steps are as follows: firstly, select the initial small field of view, XY polynomial and polynomial relationship model, each step of optimization is targeted to find out the largest item of system aberration, select the corresponding XY polynomial item in the free-form surface as a new variable to optimize and balance the aberration, and at the same time, according to each field of view of the system Synchronously adjust the weights of each field of view based on the rms value of the wave aberration; after optimizing and obtaining a structure that meets the performance index within a small field of view, gradually expand the field of view and repeat the above optimization steps until the structural parameters of the optical system within the entire field of view are obtained . The invention has the advantages of large field of view, fast optimization speed, pertinence and guidance of aberrations.

Description

Optimization method of free-form surface optical system combining surface shape and field of view optimization strategy

technical field

The invention belongs to the field of optical design, and in particular relates to a free-form surface optical system optimization method combined with surface shape and field of view optimization strategies.

Background technique

The free-form surface off-axis reflective optical system design method is widely used to design off-axis reflective optical systems with free-form surfaces. In recent years, freeform off-axis reflective optical system design methods have made great progress. In order to realize an optical system with a large aperture and a large field of view, some freeform surface optical system design methods have been proposed, such as Zhu Jun et al., in "Design method of freeform off-axis reflective imaging systems with adirect construction process". The direct design method of curved surface off-axis reflective imaging system, and the correction of aberrations and aberrations proposed by Meng Qingyu in the article "Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror" relationship, using XY polynomials to correct system aberrations, these methods can realize the design of off-axis reflective optical systems with large field of view and large aperture. The free-form surface off-axis reflective optical system design method is a method to obtain a system that meets the requirements by optimizing variables. In the article "Design of Three-mirror Optical System for Space", Chang Jun et al. The method has been successfully applied to the design and processing of space cameras.

The free-form surface off-axis reflective optical system design method is to solve the initial structure of the coaxial reflective system, and then perform off-axis processing on the optical system on the basis of the coaxial initial structure. The free-form surface of the optical system obtained after off-axis processing is characterized by polynomials, and then optimization variables are added to the free-form surface to optimize the system, and finally an off-axis reflective optical system that meets the technical specifications is obtained. Due to the imperfect description methods of free-form surfaces, few examples for reference, difficulty in image quality balance, and complex control of boundary conditions, it is difficult to design and optimize free-form surface optical systems. The sampling number of the field of view of the free-form surface off-axis system is large, the number of ray tracing is large, and it takes a long time. The balance of aberrations in the optical system is complicated, and the difficulty of optimization also becomes greater.

In order to better characterize free-form surfaces, researchers have proposed methods such as Zernike polynomials, XY polynomials, Gaussian radial basis functions, and non-uniform rational B-splines to characterize free-form surfaces. These methods can get the correct representation, but require a lot of computation. In order to reduce the optimization difficulty and improve the optimization efficiency at the same time, Zhang Xin et al. proposed a free-form surface design method based on vector aberration in the article "Aberration Characteristics of Free-form Surface Optical System Based on Vector Aberration". Through vector aberration analysis, the aberration characteristics of the optical system can be analyzed. This method mainly analyzes the aberration characteristics, but in the optimization process, the aberration correction is not targeted.

Contents of the invention

The purpose of the present invention is to provide a free-form surface optical system optimization method that combines the surface shape and field of view optimization strategy, which can correct the aberration of the off-axis reflective optical system containing the free-form surface in a targeted manner, and improve the efficiency of optical system design optimization.

The technical solution to realize the object of the present invention is: a method for optimizing a free-form surface optical system combining surface shape and field of view optimization strategy, the method steps are as follows:

Step 1. Establish the initial structure of off-axis three counters:

Referring to the example of the off-axis three-mirror optical system, select an initial structure of the coaxial three-mirror optical system;

Step 2. Structural constraints on the initial structure of the off-axis three-inverter:

On the basis of the coaxial reflective optical system, the off-axis processing is carried out, and the macro language corresponding to the optical system that limits light occlusion is used to call it in the evaluation function to control the structure of the system, and the initial structure and initial structure of the off-axis system are obtained. field of view;

Step 3. Combining the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization, the system is optimized for surface shape and field of view;

Step 4. Determine whether the optimization result meets the requirements of the technical indicators. If it does not meet the requirements of the current field of view, go to step 3 to continue to optimize the surface shape and field of view of the system; Expand the field, and then go to step 3 to optimize the system in combination with the field of view and surface shape; if the current field of view index requirements are met and the field of view range meets the index requirements, the optimization will end.

Further, the method steps of surface shape optimization described in step 3 are as follows:

1) After deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation, calculate the sum of the squares of the Zernike coefficients for all fields of view where 4≤j≤37;

2) Find the maximum term of the sum of squares of Zernike coefficients, denoted as P _m ;

3) Find the free term x ^m y ⁿ of the XY polynomial corresponding to the maximum term P _m ;

4) Determine whether m in the free term x ^m y ⁿ of the XY polynomial corresponding to the largest term P _m is an even number, and has not been used as an optimization variable. If these two conditions are met, then go to step 6), if not, go to to step 5);

5) Remove the Zernike term P _m , find out the maximum term of the square sum of coefficients in the remaining items, and denote it as P _m ;

6) Set x ^m y ⁿ as optimization variable.

Further, the method steps of field of view optimization described in step 3 are as follows:

1) Optimizing the field of view of the system, deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation, and calculating the sum of the squares of the Zernike standard polynomial coefficients of a single field of view

2) Calculate the average value of the RMS value of each field of view

3) Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Compared with the prior art, the present invention has significant advantages in that:

(1) Large field of view: Compared with other free-form surface off-axis reflective optical system design methods, this method can expand the field of view during the optimization process, so a larger field of view can be obtained;

(2) Fast optimization speed: This method combines surface shape optimization and field of view optimization to optimize the system, which can greatly increase the optimization speed and improve the optimization efficiency;

(3) Aberration targeting: This method combines the relationship between Zernike polynomials and XY polynomials to correct specific aberration items, and the optimization process is aberration-specific;

(4) Guidance: Since other free-form surface off-axis reflective optical system design methods do not disclose specific operation steps, this paper discloses specific operation steps, which are instructive for optical system design.

Description of drawings

Fig. 1 is a schematic diagram of the structural limitations of the present invention.

Fig. 2 is a schematic diagram of the field of view expansion of the present invention.

FIG. 3 is a system structure diagram showing the simulation results of Embodiment 1 of the present invention.

FIG. 4 is a graph of the modulation transfer function during the system optimization process of the simulation results of Embodiment 1 of the present invention.

FIG. 5 is a flow chart of the design method of the free-form surface off-axis reflective optical system combining surface shape optimization and field of view optimization strategies according to the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

With reference to Figures 1 to 5, the present invention combines the surface shape and field of view optimization strategy for the free-form surface optical system optimization method, the method steps are as follows:

Step 1. Establish the initial structure of off-axis three counters:

Referring to the example of the off-axis three-mirror optical system, select an initial structure of the coaxial three-mirror optical system;

Step 2. Combining with Figure 1, carry out structural restrictions on the initial structure of the off-axis three counters:

On the basis of the coaxial reflective optical system, the off-axis processing is carried out, and the macro language corresponding to the optical system that limits light occlusion is used to call it in the evaluation function to control the structure of the system, and the initial structure and initial structure of the off-axis system are obtained. field of view;

Step 3. Combining the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization, the system is optimized for surface shape and field of view;

Step 4. Determine whether the optimization result meets the requirements of the technical indicators. If it does not meet the requirements of the current field of view, go to step 3 to continue to optimize the surface shape and field of view of the system; Field expansion, as shown in Figure 2, and then go to step 3 to optimize the system in combination with the field of view and surface shape; if the current field of view index requirements are met and the field of view range meets the index requirements, then the optimization ends.

Further, the method steps of surface shape optimization described in step 3 are as follows:

1) After deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation, calculate the sum of the squares of the Zernike coefficients for all fields of view where 4≤j≤37;

2) Find the maximum term of the sum of squares of Zernike coefficients, denoted as P _m ;

3) Find the free term x ^m y ⁿ of the XY polynomial corresponding to the maximum term P _m ;

4) Determine whether m in the free term x ^m y ⁿ of the XY polynomial corresponding to the largest term P _m is an even number, and has not been used as an optimization variable. If these two conditions are met, then go to step 6), if not, go to to step 5);

5) Remove the Zernike term P _m , find out the maximum term of the square sum of coefficients in the remaining items, and denote it as P _m ;

6) Set x ^m y ⁿ as optimization variable.

Further, the method steps of field of view optimization described in step 3 are as follows:

1) Optimizing the field of view of the system, deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation, and calculating the sum of the squares of the Zernike standard polynomial coefficients of a single field of view

2) Calculate the average value of the RMS value of each field of view

3) Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

FIG. 3 is a system structure diagram showing the simulation results of Embodiment 1 of the present invention. FIG. 4 is a graph of the modulation transfer function during the system optimization process of the simulation results of Embodiment 1 of the present invention.

Referring to Figure 5, a method for designing a free-form off-axis reflective optical system that combines surface shape optimization and field of view optimization strategies, the steps of the method are as follows:

Step 1. Establish the initial structure of off-axis three counters:

Referring to the example of the off-axis three-mirror optical system, the initial structure is obtained by off-axis processing on the basis of the coaxial three-mirror optical system. It is an even-order aspheric surface, the secondary mirror is a spherical mirror, and the third mirror is a free-form surface characterized by XY polynomials.

Step 2. Structural constraints on the initial structure of the off-axis three-inverter:

Using the macro language that is written to limit light occlusion corresponding to the optical system, call it in the evaluation function, control the structure of the system, and obtain the initial structure and initial field of view.

Step 3. Under the structure of the initial field of view, derive the Zernike standard polynomial coefficient C _ij of the sub-item representation, and calculate the sum of the squares of Zernike coefficients for all fields of view Find the maximum term of the sum of the squares of Zernike coefficients according to the flow chart in Figure 5; find the free term of the XY polynomial corresponding to the maximum term; m in the free term of the corresponding XY polynomial is an even number, and has not been used as an optimization variable, satisfying these two condition, set the free term as the optimization variable.

Step 4. Optimize the field of view of the current system, derive the Zernike standard polynomial coefficient C _ij of sub-item representation, and calculate the square sum of each Zernike standard polynomial coefficient of a single field of view according to the field of view optimization strategy in the flow chart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 5. Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system. The result of the optimization is shown in Figure 4(a), which meets the requirements of the current technical indicators;

Step 6. At this time, the field of view of the system does not meet the requirements of the index, and the field of view of the system needs to be expanded;

Step 7, expand the field of view of the system;

Step 8. Deriving the Zernike standard polynomial coefficients C _ij of sub-item representations for the system after the field of view is expanded, and calculating the sum of the squares of Zernike coefficients for all fields of view Find the maximum term of the sum of the squares of Zernike coefficients according to the flow chart in Figure 5; find the free term of the XY polynomial corresponding to the maximum term; m in the free term of the corresponding XY polynomial is an even number, and has not been used as an optimization variable, satisfying these two A condition, the XY polynomial free term is set as the optimization variable;

Step 9. Optimize the field of view of the system after the field of view is expanded, derive the Zernike standard polynomial coefficient C _ij of the sub-item representation, and calculate the square sum of the Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flow chart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 10. Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system. The result of the optimization is shown in Figure 4(b), which meets the requirements of the current technical indicators

Step 11. At this time, the field of view of the system does not meet the requirements of the index, and the field of view of the system needs to be expanded;

Step 12, expanding the field of view of the system;

Step 13. Deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation for the system after the field of view is expanded, and calculating the sum of the squares of Zernike coefficients for all fields of view Find the maximum term of the sum of the squares of Zernike coefficients according to the flow chart in Figure 5; find the free term of the XY polynomial corresponding to the maximum term; m in the free term of the corresponding XY polynomial is an even number, and has not been used as an optimization variable, satisfying these two A condition, the XY polynomial free term is set as the optimization variable;

Step 14: Optimizing the field of view of the system after expanding the field of view, deriving Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flow chart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 15. Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system. The result of the optimization is shown in Figure 4(c), which does not meet the requirements of the current technical indicators and needs to be combined with the system The surface shape and field of view optimization strategy further optimizes the system;

Step 16. Deriving the Zernike standard polynomial coefficient C _ij of the sub-item representation for the system after the field of view is expanded, and calculating the sum of the squares of Zernike coefficients for all fields of view Find the maximum term of the sum of the squares of Zernike coefficients according to the flow chart in Figure 5; find the free term of the XY polynomial corresponding to the maximum term; m in the free term of the corresponding XY polynomial is an even number, and has not been used as an optimization variable, satisfying these two A condition, the XY polynomial free term is set as the optimization variable;

Step 17: Optimizing the field of view of the system after the field of view is expanded, deriving Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flowchart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 18. Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system. The result of the optimization is shown in Figure 4(d), which does not meet the requirements of the current technical indicators and needs to be combined with the system The surface shape and field of view optimization strategy further optimizes the system;

Step 19: Deriving Zernike standard polynomial coefficients C _ij for sub-item representations of the expanded field of view system, and calculating the sum of the squares of Zernike coefficients for all fields of view Find the maximum term of the sum of the squares of Zernike coefficients according to the flow chart in Figure 5; find the free term of the XY polynomial corresponding to the maximum term; m in the free term of the corresponding XY polynomial is an even number, and has not been used as an optimization variable, satisfying these two A condition, the XY polynomial free term is set as the optimization variable;

Step 20: Optimizing the field of view of the system after expanding the field of view, deriving the Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of the Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flowchart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 21, optimize the system by combining the optimization variable added by the surface shape optimization and the field of view weight of the field of view optimization, and the result of the optimization is shown in Figure 4(e), which meets the requirements of the current technical indicators;

Step 22. At this time, the field of view of the system meets the index requirements, and the optimization ends.

Example 1

A free-form surface off-axis reflective optical system design method combining surface shape optimization and field of view optimization strategies, the method steps are as follows:

Step 1. Establish the initial structure of off-axis three counters:

Referring to the example of the off-axis three-mirror optical system, the initial structure is obtained by off-axis processing on the basis of the coaxial three-mirror optical system. It is an even-order aspheric surface, the secondary mirror is a spherical mirror, and the third mirror is a free-form surface characterized by XY polynomials.

Step 2. Structural constraints on the initial structure of the off-axis three-inverter:

Using the written macro language corresponding to the optical system to limit light occlusion, call it in the evaluation function, control the structure of the system, and obtain the initial structure and initial field of view 0°×3°.

Step 3. Under the structure of the initial field of view, derive the Zernike standard polynomial coefficient C _ij of the sub-item representation, and calculate the sum of the squares of Zernike coefficients for all fields of view According to the field of view optimization strategy in the flow chart of Figure 5, find out the maximum term of the square sum of Zernike coefficients, at this time P _m =P ₄ ; find the free term of the XY polynomial corresponding to the maximum term P ₄ as x ² and y ² items; P ₄ corresponds to In the free term ^x2 and y2 of the XY polynomial, m is an even number and has not been used as an optimization variable. If these ^two conditions are met, the ^x2 and ^y2 items are set as optimization variables.

Step 4. Optimizing the field of view of the system, deriving the Zernike standard polynomial coefficient C _ij of sub-item representation, and calculating the square sum of each Zernike standard polynomial coefficient of a single field of view according to the field of view optimization strategy in the flow chart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 5. Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system, and the results obtained from the optimization meet the requirements of the current technical indicators as shown in Figure 4(a);

Step 6. Determine whether the field of view of the system meets the index requirements at this time. At this time, the field of view does not meet the requirements, and the field of view of the system needs to be expanded;

Step 7, expand the field of view of the system;

Step 8. Under the structure of expanding the field of view, derive the Zernike standard polynomial coefficient C _ij of sub-item representation, and calculate the square sum of Zernike coefficients of all fields of view Find out the maximum term of the sum of the squares of Zernike coefficients according to the flowchart in Figure 5, at this time P _m =P ₆ ; find the free term of the XY polynomial corresponding to the maximum term P ₆ to be x ² and y ² items; P ₆ items correspond to Among the free terms x ² and y ² of the XY polynomial, m is an even number, but it has been used as an optimization variable, so it is necessary to discard the P ₆ term, and continue to derive the Zernike coefficients of all fields of view according to the steps of graphic optimization in the flow chart of Figure 5 sum of square Find the maximum term of the square sum of Zernike coefficients. At this time, P _m = P ₄ , which is similar to the P ₆ term. In the free term x ² and y ² of the corresponding XY polynomial, m is an even number, but it has already been used as an optimization variable, so it needs to be discarded P ₄ items, continue to export the sum of the squares of Zernike coefficients in all fields of view Find the maximum term of the square sum of Zernike coefficients, at this time P _m =P ₅ , m in the free term xy term of the corresponding XY polynomial is an odd number, which does not meet the conditions for becoming an optimization variable, and the P ₅ term is discarded; therefore, it is necessary to continue to derive all visual Sum of Squares of Zernike Coefficients in Field Find the maximum term of the sum of squares of Zernike coefficients, at this time P _m =P ₇ , the free term x ² y, y and y ^of the XY polynomial corresponding to P ₇ , m is an even number, and has not been used as an optimization variable. Therefore, x ² y, y and y ³ items as optimization variables;

Step 9. Optimizing the field of view of the system, deriving the Zernike standard polynomial coefficient C _ij of sub-item representation, and calculating the sum of the squares of each Zernike standard polynomial coefficient of a single field of view According to the flow chart in Figure 5, the field of view optimization strategy is calculated to obtain the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 10, optimize the system by combining the optimization variable added by the surface shape optimization and the field of view weight of the field of view optimization, and the result of the optimization is shown in Figure 4(b) and meets the requirements of the current technical indicators;

Step 11. Determine whether the field of view of the system meets the index requirements at this time, and the field of view does not meet the requirements at this time, and the field of view of the system needs to be expanded;

Step 12, expanding the field of view of the system;

Step 13, deriving the wave aberration coefficients characterized by the system Zernike of the optical system at this time, and calculating the sum of the squares of the individual aberration coefficients of each field of view according to the graphic optimization strategy of the flowchart in Fig. 5 . Derive the Zernike standard polynomial coefficient C _ij of sub-item characterization, and calculate the sum of the squares of Zernike coefficients for all fields of view According to the surface shape optimization strategy in the flow chart in Figure 5, the items of the XY polynomials corresponding to P ₄ , P ₆ , P ₅ , P ₈ , P ₇ , and P ₉ do not meet the two conditions for becoming optimization variables, and these six items need to be discarded , according to the field of view optimization strategy in the flow chart of Figure 5, find out the maximum term of the square sum of Zernike coefficients, at this time P _m =P ₁₁ ; find the free terms of the XY polynomial corresponding to the maximum term P ₁₁ to be x ⁴ , x ² y ² and y ⁴ item; the free term x ⁴ , x ² y ² and y ⁴ of the XY polynomial corresponding to P ₁₁ is an even number, and has not been used as an optimization variable. If these two conditions are met, x ⁴ , x ² y ² and y ⁴ These three items are set as optimization variables.

Step 14: Optimizing the field of view of the system, deriving Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flowchart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 16. Combine the optimization variables added by surface shape optimization and the field of view weight of field of view optimization to optimize the system. At this time, the result obtained from the optimization does not meet the requirements of the current technical indicators as shown in Figure 4(c), so it is necessary to continue Optimize the surface shape and field of view of the system;

Step 17, deriving the wave aberration coefficients characterized by the system Zernike of the optical system at this time, and calculating the sum of the squares of the individual aberration coefficients of each field of view according to the graphic optimization strategy of the flowchart in Fig. 5 . Derive the Zernike standard polynomial coefficient C _ij of sub-item characterization, and calculate the sum of the squares of Zernike coefficients for all fields of view According to the surface shape optimization strategy in the flow chart in Figure 5, the items of the XY polynomials corresponding to items P ₄ to P ₁₆ do not meet the two conditions for becoming optimization variables, and these items need to be discarded, and find out according to the field of view optimization strategy in the flow chart in Figure 5 Zernike coefficient square sum maximum term, at this time P _m =P ₁₇ ; find the free term of the XY polynomial corresponding to the maximum term P ₁₇ to be x ⁴ y, x ² y ³ and y ⁵ items; the free term of the XY polynomial corresponding to P ₁₇ m in x ⁴ y, x ² y ³ and y ⁵ items is an even number, and has not been used as an optimization variable. If these two conditions are met, the three items of x ⁴ y, x ² y ³ and y ⁵ are set as optimization variables.

Step 18: Optimizing the field of view of the system, deriving Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flowchart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 19: Combine the optimization variables added by the surface shape optimization and the field of view weight of the field of view optimization to optimize the system. At this time, the result obtained by the optimization does not meet the requirements of the current technical indicators as shown in Figure 4(d), so it is necessary to continue Optimize the surface shape and field of view of the system;

Step 20, deriving the wave aberration coefficient characterized by the system Zernike of the optical system at this time, and calculating the sum of the squares of the individual aberration coefficients of each field of view according to the graphic optimization strategy of the flowchart in FIG. 5 . Derive the Zernike standard polynomial coefficient C _ij of sub-item characterization, and calculate the sum of the squares of Zernike coefficients for all fields of view According to the surface shape optimization strategy in the flow chart in Figure 5, the XY polynomial items corresponding to items P ₄ to P ₂₁ do not meet the two conditions for becoming optimization variables and need to be discarded. Find the Zernike coefficient according to the field of view optimization strategy in the flow chart in Figure 5 The square sum of the maximum term, at this time P _m =P ₂₂ ; the free term of the XY polynomial corresponding to the maximum term P ₂₂ is found to be x ⁶ , x ² y ⁴ , x ⁴ y ² and y ⁶ items; the corresponding XY polynomial of P ₂₂ m in the free items x ⁶ , x ² y ⁴ , x ⁴ y ² and y ⁶ items is an even number, and has not been used as an optimization variable. If these two conditions are met, x ⁶ , x ² y ⁴ , x ⁴ y ² and y ⁶ items These four items are set as optimization variables.

Step 21: Optimizing the field of view of the system, deriving Zernike standard polynomial coefficients C _ij represented by sub-items, and calculating the sum of the squares of Zernike standard polynomial coefficients of a single field of view according to the field of view optimization strategy in the flowchart in Figure 5 Calculate the average value of the RMS value of each field of view Calculate the square sum Q _i of each Zernike standard polynomial coefficient of a single field of view and divide it by the average value A of the square sum to obtain W _i =Q _i /A _, and take Wi as the optimization weight of each field of view.

Step 22, optimize the system by combining the optimization variable added by the surface shape optimization and the field of view weight of the field of view optimization, and the result of the optimization is shown in Figure 4(e), which meets the requirements of the current technical indicators;

Step 23, judging that the field of view of the system meets the index requirements at this time, and ending the optimization.

Compared with other off-axis reflective optical systems containing free-form surfaces, the present invention can correct the aberration in the optical system in a targeted manner. Therefore, the optimization is targeted, the optimization speed is improved, and the optimization efficiency is increased. At the same time, the field of view is gradually expanded during the optimization process, and a larger field of view can be obtained. The invention discloses the steps of a specific design method, and has guiding significance for the design of off-axis reflective optical systems containing free-form surfaces.

Claims (3)

1. the freeform optics system optimization method of a kind of faying face shape and visual field optimisation strategy, it is characterised in that method is walked It is rapid as follows：

Step 1, set up off-axis three anti-initial configurations：

With reference to the example of off-axis three reflecting optical system, a three-mirror reflection optical system initial configuration is chosen；

Step 2, structure limitations are carried out to off-axis three anti-initial configurations：

Off-axisization processing is carried out on the basis of axis reflector formula optical system, the limitation light of the corresponding optical system write is utilized The macrolanguage that line is blocked, is called in evaluation function, the structure of control system, obtains off-axis system initial configuration and initial Visual field；

Step 3, faying face shape optimize the visual field weight of increased optimized variable and visual field optimization, system is carried out the optimization of face shape and Visual field optimizes；

Step 4, judge whether optimum results meet the technical requirements, if being unsatisfactory for current field requirement, go to step 3 pair System proceeds face shape and visual field optimization；If being unsatisfactory for requiring field range requirement, visual field expansion is carried out to system, then Go to step 3 combination visual field and face shape is optimized to system；If meeting current field index request and field range meeting Index request, then terminate optimization.

2. the freeform optics system optimization method of faying face shape according to claim 1 and visual field optimisation strategy, its It is characterised by, the method and step that face shape described in step 3 optimizes is as follows：

1) the Zernike standard polynomial coefficients C that export subitem is characterized_ijAfterwards, entire field items Zernike coefficients are calculated to put down Fang HeWherein 4≤j≤37；

2) Zernike coefficient quadratic sum maximal terms are found out, P is denoted as_m；

3) maximal term P is found_mThe corresponding polynomial free term x of XY^myⁿ；

4) maximal term P is judged_mThe corresponding polynomial free term x of XY^myⁿWhether middle m is even number, and is not become as optimization Amount, if meeting the two conditions, goes to step 6), if it is not satisfied, then going to step 5)；

5) Zernike P is removed_m, coefficient quadratic sum maximal term in residual term is found out, P is denoted as_m；

6) by x^myⁿIt is set to optimized variable.

3. the freeform optics system optimization method of faying face shape according to claim 1 and visual field optimisation strategy, its It is characterised by, the method and step that visual field described in step 3 optimizes is as follows：

1) visual field optimization, the Zernike standard polynomial coefficients C that export subitem is characterized are carried out to system_ij, calculate and obtain single regard Every Zernike standard polynomials coefficient quadratic sum of field

2) calculate and obtain each visual field RMS value average value

3) every Zernike standard polynomials coefficient quadratic sum Q of single visual field is calculated_iDivided by quadratic sum average value A, obtain W_i =Q_i/ A, by W_iIt is used as the optimization weight of each visual field.