A small space variation aberration optical design method

Abstract

The application discloses a small space variation aberration optical design method, comprising the following steps: determining the performance index and initial structure parameters of an optical system according to the imaging requirement of a target imaging system; calculating the point spread function vertical height variance, horizontal width variance, peak signal-to-noise ratio and structural similarity index of each field point diagram and the central field point diagram, and the point diagram peak signal-to-noise ratio and structural similarity difference caused by defocus of each different field sampling point based on the initial structure parameters; optimizing the performance of the optical system under defocus; calculating a comprehensive evaluation function for evaluating the space aberration variation of the optical system, and iteratively optimizing the lens structure parameters by the least square method; and outputting the finally optimized optical system structure when the iteration is completed. The optical system is optimized and designed by introducing the comprehensive evaluation function for aberration evaluation of different fields and defocus distances, and the uniformity and stability of the space aberration of the optical system are significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical design, and in particular to a small spatial variation aberration optical design method. BACKGROUND

[0002] In the design of optical systems, aberration is one of the key factors affecting the imaging quality. Aberration refers to the imaging distortion caused by the deviation of the light propagation path when the light passes through the optical elements. In order to improve the imaging quality of the optical system, the optical designer needs to control and minimize the aberration through reasonable design.

[0003] Traditional optical design methods usually rely on the adjustment of optical element parameters and structure and the selection of optical element materials to reduce aberration and improve the imaging quality of the system. However, in practical applications, especially in high-precision imaging and large field-of-view imaging optical systems, aberration often exhibits spatial variation characteristics, and the aberration difference at different field-of-view positions can be very significant. Especially in wide field-of-view or other complex application scenarios, the spatial variation of aberration within the field-of-view is difficult to effectively control, which will result in poor imaging quality in some areas and affect the performance of the entire system.

[0004] In addition, with the increasing requirements for optical systems, the defocus problem has also become an important factor affecting the imaging quality. The aberration variation caused by defocus is complex, and the spatial aberration variation at different defocus positions can be significant, which is often difficult to accurately control through traditional design methods. Therefore, how to effectively control the aberration caused by defocus in the design process and maintain the uniformity of the aberration of the entire system has become a major challenge in optical design.

[0005] At present, although the existing optical system optimization methods solve the problem of aberration control to some extent, in some application scenarios, they still face the problem of large variation of aberration with different fields of view and defocus distances. Especially in multi-field-of-view conditions, how to balance the difference in aberration between fields of view and the complex aberration caused by defocus is still a difficult problem to be solved. SUMMARY

[0006] In view of the deficiencies of the prior art, the present application provides a small spatial variation aberration optical design method, which comprehensively evaluates the point spread function uniformity at different field-of-view distributions and defocus positions, calculates the point spread function and its variation at each spatial position, quantifies the variation of aberration under different fields of view and defocus conditions, and thus realizes accurate control of aberration.

[0007] The purpose of the present application is achieved by the following technical solutions:

[0008] A small spatial variation aberration optical design method, comprising the following steps:

[0009] S1: determining performance indexes and initial structure parameters of the optical system according to imaging requirements of the target imaging system;

[0010] S2: calculating point spread function vertical height variance horizontal width variance peak signal-to-noise ratio (PSNR) of each field point diagram and that of the central field point diagram i and structural similarity index (SSIM) i , defocus-induced peak signal-to-noise ratio (PSNR) of the point diagram defocus and structural similarity difference (SSIM) defocus ;

[0011] S3: calculating a comprehensive evaluation function F according to the following formula:

[0012]

[0013] wherein, W1, W2 and W3 are preset weight coefficients and do not change with each iteration; subscript i represents the i-th field; N represents the number of defocus points selected; and F' is an evaluation function for constraining imaging indexes and imaging quality.

[0014] S4: if the current iteration is the first iteration or the current value of the comprehensive evaluation function F is smaller than the historical minimum value, then updating the final structure parameters of the lens to the lens structure parameters in the current iteration; otherwise, keeping the final structure parameters of the lens unchanged and not updating.

[0015] S5: judging whether the loop ending condition is met, if yes, stopping iteration and outputting the current final structure parameters of the lens; otherwise, updating the lens structure parameters in the current iteration by the least square method and repeating S2-S4 to optimize the lens structure.

[0016] Further, in S1, the performance indexes of the optical system include lens focal length, working wavelength and field of view angle; and the initial structure parameters include lens surface type, lens curvature radius and lens spacing.

[0017] Further, the calculation formulae of the point spread function vertical height variance horizontal width variance in each different field sampling point are as follows:

[0018]

[0019]

[0020] wherein, n v represents the number of vertical fields, n hThe average value of the height of the point spread function in the vertical direction of each field of view, The average value of the width of the point spread function in the horizontal direction of each field of view, The average value of the width of the point spread function in the horizontal direction of each field of view, The average value of the width of the point spread function in the horizontal direction of each field of view. The average value of the width of the point spread function in the horizontal direction of each field of view.

[0021] Further, in S2, the peak signal-to-noise ratio PSNR of the point spread function of each field of view and the point spread function of the central field of view i The calculation formula is as follows:

[0022]

[0023]

[0024] Where MAX I is the maximum pixel value of the point spread function of different fields of view and the point spread function of the central field of view, MSE is the mean of the pixel difference between images; I1(i,j) represents the pixel value of the i,j pixel position in the point spread function of each field of view, I2(i,j) represents the pixel value of the i,j pixel position in the point spread function of the central field of view; m and n are the length and width dimensions of the image, respectively.

[0025] Further, the structural similarity index SSIM of the point spread function of each field of view and the point spread function of the central field of view i The calculation formula is as follows:

[0026]

[0027] In the formula, μ i represents the mean of the point spread function of each field of view, μ0 represents the mean of the point spread function of the central field of view, σ i 2 represents the variance of the point spread function of each field of view, σ0 2 represents the variance of the point spread function of the central field of view, σ i0 is the covariance of the point spread function of each field of view and the point spread function of the central field of view; C1 and C2 are constants to ensure that the denominator is not zero, and are usually taken as C1=(K1L) 2 and C2=(K2L) 2 , where L is the dynamic range of the image.

[0028] Further, in S2, the peak signal-to-noise ratio PSNR of the point spread function of each field of view and the point spread function of the central field of view defocus The calculation method is as follows:

[0029] (1) Select a set of defocus distances Δf1, Δf2, …, Δf nEach defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus.

[0030] (2) For each out-of-focus distance, calculate the point spread function (PSF) at the current position, and then calculate the peak signal-to-noise ratio (PSR) between each out-of-focus PSF and the in-focus PSF.

[0031]

[0032] Where i represents different defocus numbers, MAX i This represents the maximum pixel value of the PSF at different out-of-focus and in-focus positions. The mean square error between the PSF at different out-of-focus positions and the PSF at the in-focus position;

[0033] (3) Based on the peak signal-to-noise ratio at multiple out-of-focus positions The peak signal-to-noise ratio (PSNR) of the dot plot caused by defocusing was obtained. defocus ;

[0034]

[0035] Furthermore, in S2, the structural similarity difference (SSIM) caused by defocusing defocus The calculation method is as follows:

[0036] (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n Each defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus.

[0037] (2) For each out-of-focus distance, calculate the point spread function (PSF) at the current position, and then calculate the structural similarity index between each out-of-focus PSF and the near-focus PSF.

[0038]

[0039] In the formula, μ Δfi The mean PSF value represents the point spread function at different out-of-focus positions, and μ0 represents the mean PSF value at the in-focus position. σ0 represents the variance of the point spread function (PSF) at different out-of-focus positions. 2 The variance of the point spread function (PSF) representing the focal position. C1 and C2 are the covariances of the point spread function (PSF) at different out-of-focus positions and the point spread function (PSF) at the near-focus position; C1 and C2 are constants, usually C1 = (K1L). 2 And C2=(K2L) 2 , where L is the dynamic range of the image;

[0040] (3) Based on the structural similarity index SSIM at multiple defocus positions Δfi The SSIM diagram shows the structural similarity differences in the dot matrix caused by defocusing. defocus :

[0041]

[0042] Furthermore, the loop termination condition in S5 is reaching a preset number of iterations or the comprehensive evaluation function F reaching a set threshold.

[0043] Furthermore, K1 = 0.01, K2 = 0.03.

[0044] The beneficial effects of this invention are as follows:

[0045] The small-space-variable aberration optical design method proposed in this invention comprehensively considers aberration variations under different fields of view and defocus conditions during the design process, and optimizes the optical structure by introducing a comprehensive evaluation function that assesses aberration uniformity. This effectively controls aberration non-uniformity between different fields of view and under defocus conditions, improves the imaging quality of the entire system, and avoids the decline in imaging performance caused by aberration non-uniformity in traditional designs. Attached Figure Description

[0046] Figure 1 This is a flowchart of the optical design method for small spatial variation aberrations in an embodiment of the present invention.

[0047] Figure 2 This is a schematic diagram of the structure of the double Gaussian objective lens according to an embodiment of the present invention.

[0048] Figure 3 This is a dot plot of the double Gaussian objective lens (before optimization) in the visible light range of 486-656nm according to an embodiment of the present invention.

[0049] Figure 4 This is the MTF curve of the dual Gaussian objective lens (before optimization) in the visible light range of 486-656nm in an embodiment of the present invention.

[0050] Figure 5 This is a dot plot of the double Gaussian objective lens (optimized) in the visible light range of 486-656nm according to an embodiment of the present invention.

[0051] Figure 6 The MTF curve of the dual Gaussian objective lens (optimized) in the visible light range of 486-656nm is shown in the embodiment of the present invention.

[0052] Figure 7 This is a defocusing diagram of the dual Gaussian objective lens (before optimization) in the visible light range of 486-656nm according to an embodiment of the present invention.

[0053] Figure 8 The image shows the defocusing array of the dual Gaussian objectives (optimized) in the visible light range of 486-656 nm according to an embodiment of the present invention.

[0054] Explanation of reference numerals in the attached diagram: G1 - first lens, G2 - second lens, STO - aperture stop, G3 - third lens, G4 - fourth lens. Detailed Implementation

[0055] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0056] like Figure 1 As shown in the flowchart of the small spatial variation aberration optical design method in this embodiment, the specific steps include:

[0057] Step 1: Determine the performance indicators and initial structural parameters of the optical system based on the imaging requirements of the target imaging system.

[0058] The system's performance indicators include lens focal length, operating wavelength, and field of view; the initial structural parameters include lens surface type, lens radius of curvature, and lens spacing.

[0059] In this embodiment, the working wavelength is the visible light 486-656nm band, the working field of view is 10°, and the lens aperture is 25mm.

[0060] In this embodiment, the initial optical structure is a double Gaussian lens structure, such as... Figure 2 As shown, the structure includes, in sequence, a front Gaussian lens group, an aperture stop STO, a rear Gaussian lens group, and a sensor arranged on the same optical axis.

[0061] The front Gaussian lens group includes: a meniscus lens G1 with positive optical power and a meniscus lens G2 with negative optical power arranged sequentially from the object side to the image side; wherein G1 and G2 both have concave surfaces located on the image side and convex surfaces located on the object side.

[0062] The rear Gaussian lens group includes: a meniscus lens G3 with negative optical power and a meniscus lens G4 with positive optical power arranged sequentially from the object side to the image side; wherein G3 and G4 both have concave surfaces on the object side and convex surfaces on the image side.

[0063] like Figure 3 , Figure 4 , Figure 7As shown, the initial double Gaussian lens before optimization exhibits significant aberration variations under different fields of view and defocus conditions, with the minimum RMS radius of the dot plot being 3.961 μm and the maximum being 21.293 μm. Sampling different feature field points on the image plane yielded a dot plot radius variance of 42.72 μm for each field of view. 2 The aberration distribution across the entire field of view is uneven.

[0064] Step 2: Based on the initial structural parameters from Step 1, calculate the vertical height variance of the point spread function at each sampling point in different fields of view. Horizontal width variance Peak signal-to-noise ratio (PSNR) of each field-of-view point map and the center field-of-view point map i and Structural Similarity Index (SSIM) i Peak Signal-to-Noise Ratio (PSNR) of the dot plot caused by defocus defocus SSIM and structural similarity differences defocus .

[0065] Among them, the vertical height variance s of the point spread function at each sampling point in different fields of view v 2 Horizontal width variance s h 2 The calculation expressions are as follows:

[0066]

[0067]

[0068] In the formula, n v n represents the number of fields of view in the vertical direction. h This indicates the number of fields of view in the horizontal direction. This represents the average height of the point map for each field of view in the vertical direction. This represents the average width of the dot plot for each field of view in the horizontal direction. The height of the dot plot representing different fields of view in the vertical direction. This indicates the width of the dot plot representing different fields of view in the horizontal direction.

[0069] Peak signal-to-noise ratio (PSNR) of each field-of-view point map and the center field-of-view point map i The calculation formula is as follows:

[0070]

[0071]

[0072] Among them, MAX IThe maximum pixel value is represented by the dot plot under different fields of view and the dot plot of the central field of view. MSE is the mean of the pixel difference between the images. I1(i,j) represents the pixel value at the i-th and j-th pixel positions in each field of view dot plot, and I2(i,j) represents the pixel value at the i-th and j-th pixel positions in the central field of view dot plot. m and n are the length and width dimensions of the image, respectively.

[0073] Structural Similarity Index (SSIM) between the point map of each field of view and the point map of the central field of view i The calculation formula is as follows:

[0074]

[0075] In the formula, μ i σ represents the mean of the point plots for each field of view, μ0 represents the mean of the point plot for the central field of view, and σ represents the mean of the point plots for each field of view. i 2 σ0 represents the variance of the spread function at each field of view point. 2 σ represents the variance of the spread function at the center field of view. i0 Let C1 and C2 be the covariances of the spread functions at each field of view and the spread function at the center field of view; C1 and C2 are constants to ensure that the denominator is not zero, and C1 is usually taken as (K1L). 2 And C2=(K2L) 2 Where L is the dynamic range of the image. K1 is preferably 0.01, and K2 is preferably 0.03.

[0076] Peak Signal-to-Noise Ratio (PSNR) of Dot Map Caused by Defocus defocus The calculation method is as follows:

[0077] (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n Each defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus.

[0078] (2) For each out-of-focus distance, calculate the point spread function (PSF) at the current position, and then calculate the peak signal-to-noise ratio (PSR) between each out-of-focus PSF and the in-focus PSF.

[0079]

[0080] Where i represents different defocus numbers, MAX i This represents the maximum pixel value of the PSF at different out-of-focus and in-focus positions. The mean square error between the PSF at different out-of-focus positions and the PSF at the in-focus position;

[0081] (3) Based on the peak signal-to-noise ratio at multiple out-of-focus positions The peak signal-to-noise ratio (PSNR) of the dot plot caused by defocusing was obtained.defocus ;

[0082]

[0083] SSIM (Structural Similarity Differences Caused by Defocus) defocus The calculation method is as follows:

[0084] (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n Each defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus.

[0085] (2) For each out-of-focus distance, calculate the point spread function (PSF) at the current position, and then calculate the structural similarity index (SSIM) between each out-of-focus PSF and the near-focus PSF. Δfi :

[0086]

[0087] In the formula, The mean PSF value represents the point spread function at different out-of-focus positions, and μ0 represents the mean PSF value at the in-focus position. σ0 represents the variance of the point spread function (PSF) at different out-of-focus positions. 2 The variance of the point spread function (PSF) representing the focal position. C1 and C2 are the covariances of the point spread function (PSF) at different out-of-focus positions and the point spread function (PSF) at the near-focus position; C1 and C2 are constants, usually C1 = (K1L). 2 And C2=(K2L) 2 Where L is the dynamic range of the image; K1 is preferably 0.01, and K2 is preferably 0.03.

[0088] (3) Based on the structural similarity index at multiple defocus positions SSIM yields the difference in point array structure similarity caused by defocusing. defocus :

[0089]

[0090] Step 3: Calculate the comprehensive evaluation function F according to the following formula:

[0091]

[0092] In the formula, W1, W2, and W3 are pre-set weighting coefficients that do not change with each iteration; the subscript i represents the i-th field of view; N represents the number of selected defocuses; and F' is the evaluation function for constraining imaging indices and imaging quality.

[0093] Step 4: If this is the first iteration, or if the current value of the comprehensive evaluation function F is less than its historical minimum value, then update the final structural parameters of the lens to the lens structural parameters under the current iteration; otherwise, keep the final structural parameters of the lens unchanged and do not update them.

[0094] Step 5: Determine whether the loop termination condition is met (reaching the preset number of iterations or the comprehensive evaluation function F reaching the set threshold). If it is met, stop the iteration and output the current final lens structure parameters; otherwise, update the lens structure parameters under the current iteration using the least squares method and repeat steps 2 to 4 to optimize the lens structure.

[0095] like Figure 5 , Figure 6 , Figure 8 As shown, after optimizing the initial structure of the double Gaussian objective lens using the method of this embodiment, aberration differences are significantly reduced under different fields of view and defocus conditions. The point spread function variation of the system is effectively controlled under different field angles, and the vertical height variance and horizontal width variance of each field of view are significantly reduced. The minimum RMS radius of the point map is 5.833 μm, and the maximum is 11.619 μm. Within a larger field of view, the uniformity of aberrations is significantly improved. Under defocus conditions, the variation in the point map is also reduced compared to before optimization. Sampling different characteristic field points on the image plane yields a point map radius variance of 3.055 μm for each field of view. 2 The value decreased significantly compared to before optimization, and the distribution of the point array in the entire field of view tended to be more uniform.

[0096] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for optical design with small spatial variation aberrations, characterized in that, Includes the following steps: S1: Determine the performance indicators and initial structural parameters of the optical system based on the imaging requirements of the target imaging system; S2: Based on the initial structural parameters, calculate the vertical height variance of the point spread function at each different field-of-view sampling point. Horizontal width variance Peak signal-to-noise ratio of each field-of-view point map and the central field-of-view point map and structural similarity index Peak signal-to-noise ratio of dot plot caused by defocus and structural similarity differences ; S3: Calculate the comprehensive evaluation function F according to the following formula: ； In the formula, , , These are pre-defined weighting coefficients that do not change with each iteration; subscripts Indicates the i-th field of view; Indicates the number of selected defocus points; This is an evaluation function that constrains imaging parameters and imaging quality. S4: If this iteration is the first iteration, or if the current value of the comprehensive evaluation function F is less than its historical minimum value, then update the final structural parameters of the lens to the lens structural parameters under the current iteration. Conversely, the final structural parameters of the lens remain unchanged and are not updated. S5: Determine if the loop termination condition is met. If it is met, stop the iteration and output the current final lens structure parameters. Conversely, the lens structure parameters under the current iteration are updated using the least squares method, and S2~S4 are repeated to optimize the lens structure.

2. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, In S1, the performance indicators of the optical system include lens focal length, working wavelength, and field of view; the initial structural parameters include lens surface type, lens radius of curvature, and lens spacing.

3. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, Vertical height variance of point spread function at different field-of-view sampling points Horizontal width variance The calculation formula is as follows: ； ； In the formula, This indicates the number of fields of view in the vertical direction. Indicates the number of fields of view in the horizontal direction. This represents the average height of the point map for each field of view in the vertical direction. This represents the average width of the dot plot for each field of view in the horizontal direction. The height of the dot plot representing different fields of view in the vertical direction. This indicates the width of the dot plot representing different fields of view in the horizontal direction.

4. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, In S2, the peak signal-to-noise ratio of each field-of-view point map to the central field-of-view point map The calculation formula is as follows: ； ； in, This represents the maximum pixel value of the dot plot under different fields of view and the dot plot of the central field of view. This represents the mean of pixel differences between images; In the diagram of each field of view point, the first... , The pixel value at the pixel location. Represented as the number in the central field-of-view point list diagram , The pixel value at the pixel location; and These are the length and width dimensions of the image, respectively.

5. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, Structural similarity index between the point map of each field of view and the point map of the central field of view The calculation formula is as follows: ； In the formula, This represents the mean of the plot of points in each field of view. This represents the mean of the center field-of-view point plot. This represents the variance of the spread function at each field of view point. The variance of the spread function at the center field of view is represented by . Let be the covariance of the spread function at each field of view and the spread function at the center field of view; and To ensure that the constant in the denominator is not zero, it is usually taken as... and ,in It is the dynamic range of the image.

6. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, In S2, the peak signal-to-noise ratio of the dot plot caused by defocusing The calculation method is as follows: (1) Select a set of defocus distances , , ..., Each defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus. (2) For each out-of-focus distance, calculate the point spread function (PSF) at the current position, and then calculate the peak signal-to-noise ratio (PSR) between each out-of-focus PSF and the in-focus PSF. : ； Where t represents different defocal numbers. This represents the maximum pixel value of the PSF at different out-of-focus and in-focus positions. The mean square error between the PSF at different out-of-focus positions and the PSF at the in-focus position; (3) Based on the peak signal-to-noise ratio at multiple out-of-focus positions The peak signal-to-noise ratio of the dot plot caused by defocus was obtained. ; 。 7. The optical design method for small spatial variation aberrations according to claim 6, characterized in that, In S2, the structural similarity difference caused by defocusing The calculation method is as follows: (1) Select a set of defocus distances , , ..., Each defocus distance corresponds to a different focal position, covering slight defocusing situations, including positive and negative focus. (2) For each defocus distance, calculate the point spread function (PSF) at the current position, and then calculate the structural similarity index between each defocus PSF and the near-focus PSF. : ； In the formula, This represents the mean of the point spread function (PSF) at different out-of-focus positions. The mean of the point spread function (PSF) representing the focal position. The variance of the point spread function (PSF) at different out-of-focus positions. The variance of the point spread function (PSF) representing the focal position. The covariance of the point spread function (PSF) at different out-of-focus positions and the point spread function (PSF) at the near-focus position; and It is a constant, usually taken as and ,in It is the dynamic range of the image; (3) Based on the structural similarity index at multiple out-of-focus positions The differences in the similarity of the point array structure caused by defocusing were obtained. : 。 8. The optical design method for small spatial variation aberrations according to claim 1, characterized in that, The loop termination condition in S5 is reaching a preset number of iterations or the comprehensive evaluation function F reaching a set threshold.

9. The optical design method for small spatial variation aberrations according to claim 5 or 7, characterized in that, K1=0.01, K2=0.03.

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