Wide-spectrum optical system initial structure design method based on particle swarm optimization

Abstract

The invention discloses a method for designing an initial structure of a wide-spectrum optical system based on a particle swarm algorithm, and solves the problems that the initial structure of a traditional wide-spectrum optical system is low in construction efficiency and long in design period, and the imaging quality is affected due to the fact that the difficulty of correcting a secondary spectrum is increased in a wide-band range. According to the method, particle swarm optimization design is adopted, the focal length, chromatic aberration and the minimum deviation angle serve as objective functions, the focal length, the lens interval and the optical glass material serve as particles, the optimal parameters of the wide-spectrum optical system are calculated, and the curvature radius of each lens is calculated by further combining the optimal parameters; the optimal initial structure of the wide-spectrum optical system can be quickly constructed, so that the design efficiency is remarkably improved, and the design period is shortened.

Description

Technical Field

[0001] This invention relates to a design method for broadband optical systems, specifically to a method for initial structure design of broadband optical systems based on particle swarm optimization algorithm. Background Technology

[0002] Broadband imaging technology offers unique advantages in optical detection under complex environments. Studies have shown that under atmospheric attenuation conditions such as fog and smoke, the short-wave infrared band exhibits atmospheric penetration characteristics similar to the thermal infrared band. Compared to traditional visible light imaging technology, short-wave infrared offers significant advantages in imaging quality under adverse weather conditions and battlefield smoke interference. Combining short-wave infrared with visible light imaging technology can create a multispectral detection system capable of all-weather operation, a characteristic that makes it valuable for military reconnaissance applications such as laser eavesdropping.

[0003] Broadband optical systems possess excellent performance, but their design is often complex, primarily due to the challenge of correcting secondary spectra across the wide wavelength range. Traditional methods for obtaining initial structures are mainly suitable for shortband optical system design and are inefficient in broadband system design. Summary of the Invention

[0004] The purpose of this invention is to address the problems of low construction efficiency and long design cycle of the initial structure of traditional broadband optical systems, and the increased difficulty in correcting the secondary spectrum due to the wide spectral range, which in turn affects the imaging quality. The invention provides a method for designing the initial structure of broadband optical systems based on the particle swarm optimization algorithm.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for initial structure design of a broadband optical system based on particle swarm optimization, characterized by the following steps: Step 1: Take the focal length, chromatic aberration, and total deviation angle of the two characteristic rays of each lens in the broadband optical system as optimization objectives, and construct an evaluation function based on the optimization objectives. ; Step 2: Set the focal length search range, the interval range between two adjacent lenses, and the range of Abbe number of each lens material in the broadband optical system, and use them as constraints. Step 3: Use the particle swarm algorithm to randomly create individual particles within the constraints. Each individual particle represents the focal length of each lens in a broadband optical system, the distance between two adjacent lenses, and the Abbe number of each lens material. Step 4: Evaluate the function As the fitness function of the particle swarm algorithm, the fitness value of each particle in step 3 is calculated. Step 5: Select individuals with low fitness values ​​as superior individuals, and obtain the focal length of each lens, the distance between two adjacent lenses, and the Abbe number of each lens material in a set of broadband optical systems corresponding to the superior individuals; Step 6: In a broadband optical system, the focal length difference caused by the change in the radius of curvature of the two surfaces of each lens As the optimization target, focal length difference As the objective function, and setting the search range of the curvature radii of the two surfaces of each lens as curvature radius constraints, the particle swarm optimization algorithm is used to calculate the optimal curvature radii of the two surfaces of each lens. Step 7: Input the focal length of each lens, the distance between two adjacent lenses, the Abbe number of each lens material, and the optimal radius of curvature obtained in Step 6 into the optical design software to obtain the initial structure of the broadband optical system.

[0006] Further, in step 1, the evaluation function The expression is: ; In the formula: N represents the number of lenses, For two characteristic rays in the first The total deflection angle of the image from each lens. Let be the total object-side deflection angle of the two characteristic rays on the i-th lens. For the first Chromatic aberration of individual lenses Let be the optical power of the i-th lens. , Let be the focal length of the i-th lens. For the target optical power of a broadband optical system, , For the focal length of a broadband optical system, It is the weight of the total deflection angle difference. It is the weight of color difference correction. It is the weight of the lens power deviation.

[0007] Furthermore, step 2 specifically involves: Step 2.1: Set the focal length search range of each lens in the broadband optical system, i.e. ; These represent the upper and lower limits of the focal length search for each lens, respectively. This represents the focal length of the j-th lens; Step 2.2: Set the range of the interval between two adjacent lenses in the broadband optical system, i.e. , These represent the minimum and maximum values ​​of the range between two adjacent lenses, respectively. This represents the distance between the j-th lens and the (j+1)-th lens; Step 2.3: Set the range of Abbe number for each lens material in the broadband optical system, i.e. , Let represent the possible values ​​of the Abbe number for the lens material, and m represent the number of possible values. This represents the Abbe number of the j-th lens material; Step 2.4: Use the focal length search range of each lens, the range of the interval between two adjacent lenses, and the range of the Abbe number of each lens material as constraints.

[0008] Furthermore, in step 3, the number of individual particles randomly created within the constraints using the particle swarm optimization algorithm is n, and the expression for the k-th individual particle is: ; Where k takes values ​​from 1, 2, 3, ..., n.

[0009] Furthermore, in step 4, the formula for calculating the fitness value of each individual particle in step 3 is: ; in, The fitness function representing the mapping from the kth particle swarm individual to the kth particle swarm individual. The mapping relationship, where k takes values ​​from 1, 2, 3, ..., n.

[0010] Furthermore, in step 5, the expression for selecting individuals with smaller fitness values ​​as superior individuals is: ; in, Indicates selection corresponding The value of c ranges from 1 to n.

[0011] Furthermore, in step 6, the focal length difference The expression is: ; ; in, Let represent the radii of curvature of the first and second surfaces of the i-th lens in the superior individual determined in step 5, respectively. The radii of curvature of the two surfaces of the i-th lens are denoted as . The optical power calculated in time, To determine the optical power of the i-th lens based on the focal length of the i-th lens in step 5, This represents the refractive index of the i-th lens; The search range for the curvature radii of each lens's two surfaces is set as follows: .

[0012] Further, in step 6, the calculation of the optimal radius of curvature of the two surfaces of each lens using the particle swarm optimization algorithm specifically involves: The objective function is used as the fitness function of the particle swarm algorithm. Each particle represents a set of curvature radii of the two surfaces of each lens. Combining the curvature radius constraint, the set of curvature radii of the two surfaces of each lens corresponding to the individual with the smaller fitness value is selected as the optimal curvature radius of the two surfaces of each lens.

[0013] The beneficial effects of this invention are: This invention discloses an initial structure design method for a broadband optical system based on particle swarm optimization. The method uses particle swarm optimization design, taking focal length, chromatic aberration, and the total deviation angle of two characteristic rays as objective functions, and treating focal length, lens spacing, and Abbe number of optical glass material as particles to calculate the optimal parameters of the broadband optical system. Furthermore, by combining the optimal parameters, the radius of curvature of each lens is calculated, which can quickly construct the optimal initial structure of the broadband optical system, thereby significantly improving design efficiency and shortening the design cycle. Attached Figure Description

[0014] Figure 1 This is a convergence curve obtained from an embodiment of the initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to the present invention. Figure 2 This is an initial structure diagram of a broadband optical system obtained from an embodiment of the initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to the present invention. Figure 3 for Figure 2 A graph showing the change in focal length as a function of wavelength for a medium-broadband spectral optical system; Figure 4 In an embodiment of the initial structure design method for a broadband optical system based on particle swarm optimization algorithm of the present invention, the initial structure of the broadband optical system is optimized to obtain the structure diagram of the broadband optical system; Figure 5 for Figure 4 MTF plot of the modulation transfer function of a medium-broadband spectral optical system in the 0.4–1.1 μm band; Figure 6 for Figure 4 Point plot of a medium-broadband spectral optical system in the 0.4-1.1µm band; Figure 7 for Figure 4 A graph showing the change in focal length as a function of wavelength for a medium-broadband spectral optical system. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] This embodiment presents an initial structure design method for a broadband optical system based on particle swarm optimization (PSO). Based on the PSO framework, the focal length, lens spacing, and optical material properties of each lens in the optical system are defined as individual parameter vectors. A uniform distribution initialization strategy is adopted, randomly generating several populations within a preset focal length range, spacing constraints, and material Abbe number in space. By constructing a multi-objective fitness function H, key optical performance indicators such as effective focal length deviation, chromatic aberration characteristics, and total offset are comprehensively considered to achieve fitness evaluation and optimization of individual populations. Specifically, the method includes the following steps: Step 1: Take the focal length, chromatic aberration, and total deviation angle of the two characteristic rays of each lens in the broadband optical system as optimization objectives, and construct an evaluation function based on the optimization objectives. In this embodiment, a particle swarm optimization algorithm is used to optimize the wideband optical system, thereby obtaining a set of optimal solutions. This set of optimal solutions covers the Abbe number of each lens material, focal length (optical power), and the spacing between lenses.

[0017] Evaluation function The expression is: , ; ; In the formula: N represents the number of lenses, For two characteristic rays in the first The total deflection angle of the image from each lens. Let be the total object-side deflection angle of the two characteristic rays on the i-th lens. For the first Chromatic aberration of individual lenses Let be the optical power of the i-th lens. Let be the focal length of the i-th lens. For the focal length of a broadband optical system, For the target optical power of a broadband optical system, It is the weight of the total deflection angle difference. It is the weight of color difference correction. It is the weight of the lens power deviation.

[0018] Step 2: Set the focal length search range for each lens in the broadband optical system, the range of the interval between two adjacent lenses, and the range of the Abbe number V for each lens material, and use these as constraints; specifically: Step 2.1: Set the focal length search range of each lens in the broadband optical system, i.e. ; These represent the upper and lower limits of the focal length search for each lens, respectively. This represents the focal length of the j-th lens; Step 2.2: Set the range of the interval between two adjacent lenses in the broadband optical system, i.e. , These represent the minimum and maximum values ​​of the range between two adjacent lenses, respectively. This represents the distance between the j-th lens and the (j+1)-th lens; Step 2.3: Set the range of Abbe number for each lens material in the broadband optical system, i.e. , Let represent the possible values ​​of the Abbe number for the lens material, and m represent the number of possible values. This represents the Abbe number of the j-th lens material; Step 2.4: Use the focal length search range of each lens, the range of the interval between two adjacent lenses, and the range of the Abbe number of each lens material as constraints.

[0019] Step 3: Use the particle swarm algorithm to randomly create n individual particles within the constraints. Each individual particle represents the focal length of each lens in a broadband optical system, the distance between two adjacent lenses, and the Abbe number of each lens material. The expression for the kth particle swarm individual is: ; Where k takes values ​​from 1, 2, 3, ..., n.

[0020] Step 4: Evaluate the function As the fitness function of the particle swarm optimization algorithm, the fitness value of each particle in step 3 is calculated; the fitness value of each particle in step 3 is calculated. The formula is: ; in, The fitness function representing the mapping from the k-th particle swarm individual to the k-th particle swarm individual. The mapping relationship, where k takes values ​​from 1, 2, 3, ..., n.

[0021] Step 5: Select individuals with lower fitness values ​​as superior individuals, expressed as: ; in, Indicates selection corresponding The value of i ranges from 1 to n.

[0022] Step 6: In a broadband optical system, the focal length difference caused by the change in the radius of curvature of the two surfaces of each lens As the optimization target, focal length difference The expression is: ; ; in, Let represent the radii of curvature of the first and second surfaces of the i-th lens in the superior individual determined in step 5, respectively. The radii of curvature of the two surfaces of the i-th lens are denoted as . The optical power calculated in time, To determine the optical power of the i-th lens based on the focal length of the i-th lens in step 5, Let represent the refractive index of the i-th lens.

[0023] focal length difference As the objective function, the search range of the curvature radii for the two surfaces of each lens is set as the curvature radius constraint. The objective function is used as the fitness function of the particle swarm algorithm. Each particle represents a set of curvature radii of the two surfaces of each lens. Combined with the curvature radius constraint, the set of curvature radii of the two surfaces of each lens corresponding to the individual with the smaller fitness value is selected as the optimal curvature radius of the two surfaces of each lens.

[0024] Step 7: Input the focal length of each lens, the distance between two adjacent lenses, the Abbe number of each lens material, and the optimal radius of curvature obtained in Step 6 into the optical design software to obtain the initial structure of the broadband optical system.

[0025] In this embodiment, the design specifications of the broadband optical system are shown in Table 1. Based on the design specifications in Table 1, key parameters are constrained, including: optical power (…). Abbe number () The constraints on lens spacing (d), number of lenses, population size, random step size coefficient, and total system focal length are shown in Table 2. The objective function is optimized by comprehensively considering aberration correction and system performance. The system operates in the 0.4–1.1 μm band, covering the visible to near-infrared region to meet the requirements of wide-spectrum imaging.

[0026] Table 1 Table 2 The particle swarm optimization algorithm used in this embodiment, with a population size of 50 and a maximum number of iterations of 150, can meet the system performance requirements and obtain multiple excellent initial structures through iteration. Figure 1 To obtain the convergence curve of the particle swarm optimization algorithm after 150 iterations, as the objective value of the fitness function decreases, the particle swarm optimization algorithm continues to optimize the initial structure parameters until the objective value no longer changes, and then outputs a set of wideband system parameters. The radius of curvature, lens thickness, and material are then obtained as shown in Table 3. Table 3 The data shown in Table 3 was input into the optical design software to obtain the following results: Figure 2 The initial structure of the optical system shown is given. This initial optical system has a focal shift of -0.0254 to 0.0675 mm within the required wavelength range. The resulting curve showing the focal length versus wavelength is shown below. Figure 3 As shown.

[0027] The calculated initial structures for the visible and near-infrared broadband spectra are input into optical design software, and after simple optimization, the final broadband optical system structure is obtained as follows: Figure 4 As shown, it can simultaneously receive information from the visible to near-infrared bands. The focal length is 45mm for different wavelengths, the image plane position is the same, and the system has the advantages of compact structure and lightweight design while ensuring broadband imaging performance.

[0028] The modulation transfer function (MTF) of the broadband optical system obtained in this embodiment is as follows: Figure 5 As shown, in the 0.4–1.1 μm band, at the Nyquist frequency of 100 lp / mm, the MTF for both low and mid frequencies reaches above 0.7, and the MTF for high frequencies is also above 0.4. This indicates that the objective lens has good performance in transmitting image information. The dot plot of this optical system is shown below. Figure 6 As shown, according to Figure 6 As can be seen, the root mean square is smaller than the Airy disk diameter, indicating that the optical design of this lens achieves good image quality.

[0029] The focal shift curve of the broadband optical system obtained in this embodiment is as follows: Figure 7 As shown, the curve reflects the change of the system's focal length with wavelength. The design results indicate that the focal shift within this wavelength range is -0.0256 to 0.0139 mm, less than 0.045 mm. This demonstrates that the lens can achieve co-image plane imaging at different wavelengths over a wide wavelength range.

[0030] This embodiment employs a particle swarm optimization algorithm-based initial structure design method for broadband optical systems to design a broadband optical system with a focal length of 45mm and a field of view of ±3°, covering the working band from visible light to near-infrared. The effectiveness and computational efficiency of the system are verified by simulation. The simulation results show that the optimization algorithm can obtain a large number of locally optimal solutions with engineering application value through an iterative process in a short convergence time, significantly improving the design efficiency of broadband optical systems compared with traditional design methods.

[0031] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present invention should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for initial structure design of a broadband optical system based on particle swarm optimization algorithm, characterized in that, Includes the following steps: Step 1: Take the focal length, chromatic aberration, and total deviation angle of the two characteristic rays of each lens in the broadband optical system as optimization objectives, and construct an evaluation function based on the optimization objectives. ; Step 2: Set the focal length search range, the interval range between two adjacent lenses, and the range of Abbe number of each lens material in the broadband optical system, and use them as constraints. Step 3: Use the particle swarm algorithm to randomly create individual particles within the constraints. Each individual particle represents the focal length of each lens in a broadband optical system, the distance between two adjacent lenses, and the Abbe number of each lens material. Step 4: Evaluate the function As the fitness function of the particle swarm algorithm, the fitness value of each particle in step 3 is calculated. Step 5: Select individuals with low fitness values ​​as superior individuals, and obtain the focal length of each lens, the distance between two adjacent lenses, and the Abbe number of each lens material in a set of broadband optical systems corresponding to the superior individuals; Step 6: In a broadband optical system, the focal length difference caused by the change in the radius of curvature of the two surfaces of each lens As the optimization target, focal length difference As the objective function, and setting the search range of the curvature radii of the two surfaces of each lens as curvature radius constraints, the particle swarm optimization algorithm is used to calculate the optimal curvature radii of the two surfaces of each lens. Step 7: Input the focal length of each lens, the distance between two adjacent lenses, the Abbe number of each lens material, and the optimal radius of curvature obtained in Step 6 into the optical design software to obtain the initial structure of the broadband optical system.

2. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 1, characterized in that, In step 1, the evaluation function The expression is: ； In the formula: N represents the number of lenses, For two characteristic rays in the first The total deflection angle of the image from each lens. Let be the total object-side deflection angle of the two characteristic rays at the i-th lens. For the first Chromatic aberration of individual lenses Let be the optical power of the i-th lens. , Let be the focal length of the i-th lens. For the target optical power of a broadband optical system, , For the focal length of a broadband optical system, It is the weight of the total deflection angle difference. It is the weight of color difference correction. It is the weight of the lens power deviation.

3. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 1, characterized in that, Step 2 is as follows: Step 2.1: Set the focal length search range of each lens in the broadband optical system, i.e. ; These represent the upper and lower limits of the focal length search for each lens, respectively. This represents the focal length of the j-th lens; Step 2.2: Set the range of the interval between two adjacent lenses in the broadband optical system, i.e. , These represent the minimum and maximum values ​​of the range between two adjacent lenses, respectively. This represents the distance between the j-th lens and the (j+1)-th lens; Step 2.3: Set the range of Abbe number for each lens material in the broadband optical system, i.e. , Let represent the possible values ​​of the Abbe number for the lens material, and m represent the number of possible values. This represents the Abbe number of the j-th lens material; Step 2.4: Use the focal length search range of each lens, the range of the interval between two adjacent lenses, and the range of the Abbe number of each lens material as constraints.

4. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 2, characterized in that, In step 3, the particle swarm algorithm is used to randomly create n individual particles within the constraints. The expression for the k-th individual particle is: ； Where k takes values ​​from 1, 2, 3, ..., n.

5. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 4, characterized in that, In step 4, the formula for calculating the fitness value of each individual particle in step 3 is: ； in, The fitness function representing the mapping from the kth particle swarm individual to the kth particle swarm individual. The mapping relationship, where k takes values ​​from 1, 2, 3, ..., n.

6. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 5, characterized in that, In step 5, the expression for selecting individuals with smaller fitness values ​​as superior individuals is: ； in, Indicates selection corresponding The value of c ranges from 1 to n.

7. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 2, characterized in that, In step 6, the focal length difference The expression is: ； ； in, Let represent the radii of curvature of the first and second surfaces of the i-th lens in the superior individual determined in step 5, respectively. The radii of curvature of the two surfaces of the i-th lens are denoted as . The optical power calculated in time, To determine the optical power of the i-th lens based on the focal length of the i-th lens in step 5, This represents the refractive index of the i-th lens; The search range for the curvature radii of each lens's two surfaces is set as follows: 。 8. The initial structure design method for a broadband optical system based on particle swarm optimization algorithm according to claim 2, characterized in that, In step 6, the calculation of the optimal radius of curvature of the two surfaces of each lens using the particle swarm optimization algorithm specifically involves: The objective function is used as the fitness function of the particle swarm algorithm. Each particle represents a set of curvature radii of the two surfaces of each lens. Combining the curvature radius constraint, the set of curvature radii of the two surfaces of each lens corresponding to the individual with the smaller fitness value is selected as the optimal curvature radius of the two surfaces of each lens.

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