A computer-aided assembly method based on adaptive neighborhood algorithm

Abstract

The present invention discloses a computer-aided alignment method based on an adaptive neighborhood algorithm, which converts the alignment problem of an optical system into an optimal solution problem for solving an objective function, and introduces an adaptive neighborhood algorithm for solving the problem. The adjustment amount can be adaptively and iteratively calculated, and has the advantages of a large dynamic range and high solution accuracy. In each iteration, a neighborhood is first determined, and then the maximum value of the second-order approximate function of the objective function is calculated within the neighborhood. If the maximum value makes the objective function sufficiently increase, the next iteration is entered and the neighborhood radius is expanded; if the maximum value cannot make the objective function sufficiently increase, it means that the second-order approximate function within the current neighborhood is not reliable enough, and the neighborhood needs to be narrowed and the maximum value recalculated. The iteration is continued until the conditions required for convergence are met. The method of the present invention uses the integral of the image in the frequency domain as the evaluation function, eliminating the need for a wavefront aberration measuring instrument to detect the wavefront, thereby reducing complexity.

Description

Technical Field

[0001] The present invention relates to the field of optical technology, and in particular to a computer-aided assembly and adjustment method based on an adaptive neighborhood algorithm. Background Art

[0002] After machining, the optical system deviates from its ideal design state. Adjusting the relative positions of the optical components is necessary to improve the system's imaging quality. However, randomly adjusting components results in very low assembly efficiency, leading to the emergence of computer-aided assembly methods.

[0003] Traditional computer-aided methods mainly include the sensitivity matrix method, inverse optimization method, nodal aberration method, and neural network method. The sensitivity matrix method establishes a linear model between aberration and compensation, and then calculates the compensation of the optical element through the aberration measured by instruments such as interferometers; the inverse optimization method uses the optimization function of optical design software to reversely optimize the misalignment aberration as an optimization indicator to obtain the compensation; the nodal aberration method establishes the relationship between aberration and compensation based on nodal aberration theory; the neural network method is based on a large amount of data training, allowing the network to learn the relationship between aberration and compensation, thereby completing the correction.

[0004] Because the sensitivity matrix method approximates the relationship between aberration and compensation amount to a linear model, its applicable dynamic range is limited and it is not applicable to systems with large aberrations. The inverse optimization rule is limited by the optimization capabilities of the software itself and has uncertainty in the calculation of the compensation amount. The node aberration method can theoretically obtain an analytical solution to the compensation amount, but the calculation amount is large. The calculation accuracy and dynamic range of the neural network method are limited by the accuracy of the data set establishment. Once the aberration exceeds the range of the data set, the algorithm fails and the robustness is poor. Moreover, traditional computer-aided methods usually require measuring instruments such as interferometers to accurately measure the system wavefront, which increases the complexity of the assembly system and increases the assembly cost.

[0005] Therefore, a new computer-aided assembly and adjustment method is currently needed to overcome the shortcomings of existing methods, including limited dynamic range, poor robustness, large computational complexity, high uncertainty, and the need for additional measuring instruments such as interferometers, to complete the debugging and correction process of the optical system. Summary of the Invention

[0006] In view of this, the present invention provides a computer-aided adjustment method based on an adaptive neighborhood algorithm, which can adaptively adjust compensation elements without the need for additional measuring instruments. It has the advantages of a large dynamic range, good robustness, and high solution accuracy, reducing the complexity of adjustment.

[0007] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is:

[0008] A computer-aided alignment method based on an adaptive neighborhood algorithm is provided for performing computer-aided alignment on a compensation element of an optical system to be aligned. The specific steps include:

[0009] Step 1: Obtain an image captured by the optical system to be adjusted on the image plane, and use the integral of the image in the frequency domain as the current image quality evaluation function.

[0010] Step 2: Starting from the first iteration, at the kth iteration, the compensation vector x of the kth iteration is k As the center, Δ k For the neighborhood radius, make the neighborhood of the kth iteration; in the neighborhood of the kth iteration, construct the second-order approximate function of the evaluation function and determine the second-order approximate model.

[0011] Step 3: Derivative the second-order approximate function to obtain the second-order approximate maximum value of the evaluation function as the evaluation function value; according to the second-order approximate function, the maximum iteration step length p is obtained. max And determine the iteration step size p.

[0012] Step 4: The compensation vector x of the kth iteration k Substitute the evaluation function into the evaluation function to obtain the evaluation function value of the kth iteration and determine whether it is greater than the evaluation function value of the previous iteration. If so, adjust the compensation element according to the kth iteration step size and execute step 5; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 <Δ k And x k+1 =x k , and return to step 3 to continue.

[0013] Step 5: Perform virtual imaging on the adjusted optical system to obtain the adjusted image on the image plane; calculate the adjusted evaluation function value based on the adjusted image, and determine whether the adjusted evaluation function value meets the evaluation function value required for the adjustment. If so, end this process; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 ≥Δ k And x k+1 =x k +p and return to step 2 to continue.

[0014] Furthermore, the formula of the evaluation function F is expressed as:

[0015]

[0016] Where ρ is the radius in polar coordinates, σ is the angle in polar coordinates, I(ρ,σ) is the Fourier transform of the image, a1 is the lower limit of the angular integral of ρ, a2 is the upper limit of the angular integral of ρ, dρ is the radius differential in polar coordinates, and dσ is the angle differential in polar coordinates.

[0017] Furthermore, the lower limit of integration a1 is The upper limit of points a2 is

[0018] Furthermore, in the neighborhood of the kth iteration, a second-order approximate function of the evaluation function is constructed, and a second-order approximate model is determined. The specific method is:

[0019] The second-order approximate function m of the kth iteration k (p) is:

[0020]

[0021] Where k is the number of iterations, c is the fitting constant term, g represents the first-order gradient of function F, G represents the second-order gradient of function F, and p is the iteration step size;

[0022] In x k Collect l data points Y in the neighborhood k ,in n is the number of compensation elements; data points

[0023] Let x k +p k =Y k , where p k is the iteration step length of the kth iteration; according to Y k Adjust the compensation element and obtain F(Y k ); let m k (p) = F(Y k ), determine the second-order approximate model m k .

[0024] Furthermore, according to the second-order approximate function, the maximum iteration step length p is obtained max , the specific method is:

[0025]

[0026] Among them, g represents the first-order gradient of function F, τ k To adjust the parameters.

[0027] Furthermore, we adjust the parameter τ k The formula is:

[0028]

[0029] Where G represents the second-order gradient of function F.

[0030] Furthermore, the neighborhood radius Δ k The initial value of is 0.1.

[0031] Beneficial effects:

[0032] 1. The present invention proposes a computer-aided adjustment method based on an adaptive neighborhood algorithm, which calculates the adjustment amount of the compensation element through the adaptive neighborhood algorithm. In each iteration, a neighborhood is first determined, and then the maximum value of the second-order approximate function of the objective function is calculated in the neighborhood. If the maximum value makes the objective function sufficiently increase, the next iteration is entered and the neighborhood radius is expanded; if the extreme value cannot make the objective function sufficiently increase, it means that the second-order approximate function in the current neighborhood is not reliable enough, and the neighborhood needs to be narrowed and the maximum value recalculated. It is iterated in this way until the conditions required for convergence are met. This method transforms the adjustment problem of the optical system into a problem of solving the optimal solution of the objective function, and introduces an adaptive neighborhood algorithm for solution. It does not require additional measuring instruments, and can adaptively and iteratively calculate the adjustment amount. It has the advantages of a large dynamic range, good robustness and high solution accuracy.

[0033] 2. The method of the present invention uses the frequency domain integration of the image collected by the image plane as the evaluation function, eliminating the need for additional wavefront aberration measuring instruments to detect the wavefront and reducing the complexity of the assembly and adjustment system. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flow chart of the method of the present invention.

[0035] Figure 2 It is a schematic diagram of the installation of the present invention. DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0037] The system of the present invention is as follows Figure 2 As shown, the optical system to be assembled is located between the light source and the detector, which is used to obtain an image of the image plane and is used in step 1. In step 1, the integral of the image in the frequency domain is used as the current image quality evaluation function value.

[0038] like Figure 1 As shown, the present invention proposes a computer-aided alignment method based on an adaptive neighborhood algorithm, which performs computer-aided alignment on a compensation element of an optical system to be aligned. The specific steps include:

[0039] Step 1: Obtain the image captured by the optical system to be adjusted on the image plane, and use the integral of the image in the frequency domain as the current image quality evaluation function value. The imaging quality of the optical system is determined by its structural parameters. If the imaging quality of the system is measured by the evaluation function F, the structural parameters of each compensation element are expressed as x. i(i=1,2,3,...,n), then the relationship between the imaging quality of the system and the compensation element can be expressed as:

[0040] F=f(x1,x2,…,x n )

[0041] Where f represents the complex multivariate nonlinear relationship between the system imaging quality and the compensation element, but this relationship is difficult to solve. Therefore, in the embodiment of the present invention, the integral of the image captured by the image plane in the frequency domain is used as the evaluation function F. The formula of the evaluation function F is expressed as:

[0042]

[0043] Wherein, ρ is the radius in polar coordinates, σ is the angle in polar coordinates, I(ρ,σ) is the Fourier transform of the image, a1 is the lower limit of the angle integral of ρ, a2 is the upper limit of the angle integral of ρ, dρ is the radius differential in polar coordinates, and dσ is the angle differential in polar coordinates. In the embodiment of the present invention, the lower limit of the integral a1 is The upper limit of points a2 is

[0044] Therefore, the computer-aided assembly and adjustment problem is modeled as the problem of finding the optimal solution to the above multivariate nonlinear equations.

[0045] Step 2: Next, use the adaptive neighborhood algorithm to solve the equation. The idea of ​​the adaptive neighborhood algorithm is: in each iteration, first determine a neighborhood radius Δ k , then in Δ k Calculate the maximum value of the second-order approximation function of the objective function. If the objective function F is sufficiently increased, enter the next iteration and expand Δ k If the maximum value cannot make F increase sufficiently, it means that the current Δ k The second-order approximation function within is not reliable enough and needs to be reduced. k , recalculate the maximum value. The specific steps are: starting from the first iteration, at the kth iteration, the compensation vector x of the kth iteration is used k As the center, Δ k The neighborhood radius is the neighborhood of the kth iteration, and the neighborhood of the kth iteration is constructed; in the neighborhood of the kth iteration, the second-order approximation function of the evaluation function is constructed, and the second-order approximation model is determined. In the embodiment of the present invention, the neighborhood radius Δ k The initial value of is 0.1.

[0046] In the neighborhood, a second-order approximate function of the evaluation function is constructed and a second-order approximate model is determined. The specific method is:

[0047] The second-order approximate function m of the kth iteration k (p) is:

[0048]

[0049] Where k is the number of iterations, c is the fitting constant, g represents the first-order gradient of function F, G represents the second-order gradient of function F, and p is the iteration step size.

[0050] In x k Collect l data points Y in the neighborhood k ,in n is the number of compensation elements; data points

[0051] Let x k +p k =Y k , where p k is the iteration step length of the kth iteration; according to Y k Adjust the compensation element and obtain F(Y k ); let m k (p) = F(Y k ), determine the second-order approximate model m k .

[0052] Step 3: Second-order approximate function m k (p) is derived to obtain the second-order approximate maximum value of the evaluation function, as the evaluation function value; according to the second-order approximate function, the maximum iteration step length p is obtained max .

[0053] According to the second-order approximation function, the maximum iteration step length p is obtained max , the specific method is:

[0054]

[0055] Among them, g represents the first-order gradient of function F, τ k To adjust the parameters.

[0056] Adjustment parameter τ k The formula is:

[0057]

[0058] Where G represents the second-order gradient of function F.

[0059] Step 4: The compensation vector x of the kth iteration k Substitute the evaluation function and determine whether the evaluation function value of the kth iteration is greater than the evaluation function value of the previous iteration. If so, adjust the compensation element according to the current iteration step size and execute step 5; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 <Δ k And x k+1 =xk , and return to step 3 to continue.

[0060] The specific method of adjusting the compensation element according to the current iteration step size is: the compensation vector x k is the initial misalignment state of the optical system to be adjusted, x k Each element in can be set as the eccentricity in the x / y / z direction, the tilt in the x / y direction and the movement in the optical axis direction of each compensation element according to the requirements. The iteration step size p is x k The adjustment amount is , where each element corresponds to an adjustment amount of a compensation element. Therefore, after obtaining the iteration step, the tilt amount, eccentricity amount, and movement amount along the optical axis of the corresponding compensation element are adjusted accordingly according to each element.

[0061] Step 5: Virtually image the adjusted optical system and obtain the adjusted image on the image plane; calculate the adjusted evaluation function value based on the adjusted image, and judge whether the adjusted evaluation function value meets the evaluation function value required for the adjustment. If so, the process ends; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 ≥Δ k And x k+1 =x k +p and return to step 2 to continue.

[0062] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A computer-aided assembly method based on an adaptive neighborhood algorithm, characterized in that: Computer-aided adjustment of the compensation components of the optical system to be adjusted is performed. The specific steps include: Step 1: Obtain an image captured by the optical system to be adjusted on the image plane, and use the integral of the image in the frequency domain as the current image quality evaluation function F; Step 2: Starting from the first iteration, at the kth iteration, the compensation vector x of the kth iteration is k As the center, Δ k For the neighborhood radius, make the neighborhood of the kth iteration; in the neighborhood of the kth iteration, construct the second-order approximate function of the evaluation function F and determine the second-order approximate model; Step 3: Derivative the second-order approximate function to obtain the second-order approximate maximum value of the evaluation function F as the evaluation function value; according to the second-order approximate function, the maximum iteration step length p is obtained. max And determine the iteration step length p; Step 4: The compensation vector x of the kth iteration k Substitute the evaluation function F into the evaluation function, obtain the evaluation function value of the kth iteration, and determine whether it is greater than the evaluation function value of the previous iteration. If so, adjust the compensation element according to the kth iteration step size and execute step 5; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 <Δ k And x k+1 =x k , and return to step 3 to continue; Step 5: Perform virtual imaging on the adjusted optical system to obtain the adjusted image on the image plane; calculate the adjusted evaluation function value based on the adjusted image, and determine whether the adjusted evaluation function value meets the evaluation function value required for the adjustment. If so, end this process; otherwise, set the neighborhood radius Δ of the k+1th iteration k+1 ≥Δ k And x k+1 =x k +p and return to step 2 to continue.

2. The method according to claim 1, wherein The evaluation function F is expressed as follows: Where ρ is the radius in polar coordinates, σ is the angle in polar coordinates, I(ρ,σ) is the Fourier transform of the image, a1 is the lower limit of the angular integral of ρ, a2 is the upper limit of the angular integral of ρ, dρ is the radius differential in polar coordinates, and dσ is the angle differential in polar coordinates.

3. The method according to claim 2, wherein The lower limit of integration a1 is The upper limit of points a2 is 4. The method according to claim 1, wherein In the neighborhood of the kth iteration, a second-order approximate function of the evaluation function F is constructed, and a second-order approximate model is determined. The specific method is: The second-order approximation function of the k-th iteration is m k (p): Where k is the number of iterations, c is the fitting constant term, g represents the first-order gradient of the evaluation function F, G represents the second-order gradient of the evaluation function F, and p is the iteration step size; In x k Collect l data points Y in the neighborhood k ,in n is the number of compensation elements; data points Let x k +p k =Y k , where p k is the iteration step length of the kth iteration; according to Y k Adjust the compensation element and obtain F(Y k ); let m k (p) = F(Y k ), determine the second-order approximate model m k .

5. The method according to claim 1, wherein According to the second-order approximate function, the maximum iteration step length p is obtained max , the specific method is: Among them, g represents the first-order gradient of the evaluation function F, τ k To adjust the parameters.

6. The method according to claim 5, wherein The adjustment parameter τ k The formula is: Where G represents the second-order gradient of the evaluation function F.

7. The method according to claim 1, wherein The neighborhood radius Δ k The initial value of is 0.1.

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