Optical design method for small spatial variation aberration

Abstract

The invention discloses a small spatial variation aberration optical design method, which comprises the following steps of: determining a performance index and an initial structure parameter of an optical system according to an imaging requirement of a target imaging system; based on the initial structure parameters, calculating vertical height variances and horizontal width variances of point spread functions under different view field sampling points, peak signal-to-noise ratios and structural similarity indexes of view field point sequence diagrams and center view field point sequence diagrams, and peak signal-to-noise ratios and structural similarity differences of the point sequence diagrams caused by defocus; the performance of the optical system under the defocusing condition is optimized; and calculating a comprehensive evaluation function used for evaluating the spatial aberration change condition of the optical system, iteratively optimizing lens structure parameters through a least square method, and when iteration is finished, outputting a final optimized optical system structure. According to the invention, by introducing the comprehensive evaluation function for carrying out aberration evaluation on different view fields and out-of-focus distances, optimization design is carried out on the optical system, and the uniformity and the stability of the spatial aberration of the optical system are remarkably improved.

Description

Technical Field

[0001] The invention relates to the field of optical design, and in particular to an optical design method for small spatial variation aberrations. Background Art

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

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

[0004] In addition, as the requirements for optical systems increase, defocus has also become an important factor affecting imaging quality. Since the aberration changes caused by defocus are more complex, and the spatial aberration changes at different defocus positions may be more significant, it is often difficult to accurately control them through traditional design methods. Therefore, how to effectively control the aberration caused by defocus during the design process and maintain the aberration uniformity of the entire system has become a major challenge in optical design.

[0005] Although the existing optical system optimization methods have solved the problem of aberration control to a certain extent, in some application scenarios, they still face the problem that aberrations vary greatly with different fields of view and defocus distances. Especially under multi-field conditions, how to balance the differences in aberrations between fields of view and the complex aberrations caused by defocus is still a difficult problem that needs to be solved urgently. Summary of the invention

[0006] In view of the shortcomings of the prior art, the present invention proposes an optical design method for small spatial variation aberrations. The method comprehensively evaluates the uniformity of the point spread function under different field of view distributions and defocus positions, and quantifies the changes of aberrations between different fields of view and defocus conditions by calculating the point spread function and its changes at each spatial position, thereby achieving precise control of the aberrations.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] An optical design method for small spatial variation aberrations comprises the following steps:

[0009] S1: Determine the performance indicators and initial structural parameters of the optical system according to the imaging requirements of the target imaging system;

[0010] 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 (PSNR) of each field of view spot diagram and the center field of view spot diagram i and structural similarity index SSIM i , Peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus and Structural Similarity Difference SSIM defocus ;

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

[0012]

[0013] Wherein, W1, W2, and W3 are pre-set weight coefficients and do not change with each iteration; subscript i represents the i-th field of view; N represents the number of selected defocus points; and F' is the evaluation function of constrained imaging indicators and imaging quality.

[0014] S4: If this iteration is the first iteration, or the current value of the comprehensive evaluation function F is less than its historical minimum value, the final structural parameters of the lens are updated to the lens structural parameters of the current iteration; otherwise, the final structural parameters of the lens are kept unchanged and are not updated;

[0015] S5: Determine whether the conditions for loop termination are met. If so, stop the iteration and output the final structural parameters of the current lens. Otherwise, update the structural parameters of the lens in the current iteration by the least squares method, and repeat S2 to S4 to optimize the lens structure.

[0016] Furthermore, in S1, the performance indicators of the optical system include lens focal length, operating wavelength, and field of view angle; and the initial structural parameters include lens surface type, lens curvature radius, and lens spacing.

[0017] Furthermore, the vertical height variance of the point spread function at different field of view sampling points is Horizontal Width Variance The calculation formula is as follows:

[0018]

[0019]

[0020] Where n v Indicates the vertical field of view, n hIndicates the horizontal field of view. It represents the average height of the spot diagram of each field of view in the vertical direction. Represents the average width of the spot diagram of each field of view in the horizontal direction, Indicates the spot diagram height of different fields of view in the vertical direction, Indicates the spot diagram width for different fields of view in the horizontal direction.

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

[0022]

[0023]

[0024] Among them, MAX I is the maximum pixel value of the spot diagram under different fields of view and the spot diagram of the central field of view, MSE is the mean of the pixel differences between images; I1(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of each field of view, and I2(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of the central field of view; m and n are the length and width of the image, respectively.

[0025] Furthermore, the structural similarity index SSIM of each field of view spot diagram and the central field of view spot diagram is i The calculation formula is as follows:

[0026]

[0027] In the formula, μ i represents the mean of the spot diagrams of each field of view, μ0 represents the mean of the spot diagram 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 under 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, usually C1=(K1L) 2 and C2=(K2L) 2 , where L is the dynamic range of the image.

[0028] Furthermore, in S2, the peak signal-to-noise ratio PSNR of the spot diagram caused by defocus is defocus The calculation method is as follows:

[0029] (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n, where each defocus distance corresponds to a different focus position, covering slight defocus situations of positive focus and negative focus;

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

[0031]

[0032] Among them, i represents different defocus point numbers, MAX i is the maximum pixel value of the PSF at different defocus positions and the PSF at the in-focus position, is the mean square error between the PSF at different defocus positions and the PSF at the in-focus position;

[0033] (3) Based on the peak signal-to-noise ratio at multiple defocus positions Get the peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus ;

[0034]

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

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

[0037] (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 in-focus PSF

[0038]

[0039] In the formula, μ Δfi represents the mean value of the point spread function PSF at different defocus positions, μ0 represents the mean value of the point spread function PSF at the quasi-focus position, The variance of the point spread function PSF at different defocus positions, σ0 2 The variance of the point spread function PSF at the in-focus position is represented by is the covariance of the point spread function PSF at different defocus positions and the point spread function PSF at the quasi-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) SSIM based on the structural similarity index at multiple defocus positions Δfi , and obtain the structural similarity difference SSIM of the spot diagram caused by defocus defocus :

[0041]

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

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

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

[0045] The optical design method for small spatial variation aberration proposed in the present invention comprehensively considers the aberration changes in different fields of view and under defocus conditions during the design process, and adopts a comprehensive evaluation function for introducing aberration uniformity evaluation to optimize the optical structure. It can effectively control the aberration non-uniformity between different fields of view and under defocus conditions, improve the imaging quality of the entire system, and avoid the degradation of imaging performance due to aberration non-uniformity in traditional designs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flow chart of the optical design method for small spatial variation aberration in an embodiment of the present invention.

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

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

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

[0050] Figure 5 This is a point diagram of the double Gaussian objective lens (after optimization) according to an embodiment of the present invention under visible light of 486-656 nm.

[0051] Figure 6 This is an MTF curve diagram of the double Gaussian objective lens (after optimization) in the embodiment of the present invention under visible light 486-656nm.

[0052] Figure 7 1 is a diagram of the defocusing points of the double Gaussian objective lens (before optimization) according to an embodiment of the present invention under visible light of 486-656 nm.

[0053] Figure 8 1 is a diagram of the defocusing points of the double Gaussian objective lens (after optimization) according to an embodiment of the present invention under visible light of 486-656 nm.

[0054] Description of reference numerals: G1 - first lens, G2 - second lens, STO - aperture stop, G3 - third lens, G4 - fourth lens. DETAILED DESCRIPTION

[0055] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become more clear. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0056] like Figure 1 As shown in FIG. 1 , the flowchart of the optical design method for small spatial variation aberration of this embodiment specifically includes the following steps:

[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] Among them, the system's performance indicators include lens focal length, working wavelength, field of view angle, etc.; the initial structural parameters include lens surface type, lens curvature radius, lens spacing, etc.

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

[0060] The optical initial structure in this embodiment uses a double Gauss lens structure, such as Figure 2 As shown, the structure includes 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 Gauss lens group includes: a meniscus lens G1 with positive focal length and a meniscus lens G2 with negative focal length, which are arranged in sequence from the object side to the image side; wherein both G1 and G2 have concave surfaces on the image side and convex surfaces on the object side.

[0062] The rear Gauss lens group includes: a meniscus lens G3 with negative optical power and a meniscus lens G4 with positive optical power, which are arranged in sequence 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 in the figure, the initial double Gauss lens before optimization has significant aberration changes under different fields of view and defocus conditions. The minimum RMS radius of the point diagram is 3.961μm and the maximum is 21.293μm. Sampling different characteristic field points on the image plane, the variance of the point diagram radius under each field of view is 42.72μm 2 , the aberration distribution of the whole field of view is uneven.

[0064] Step 2: Based on the initial structural parameters of step 1, calculate the vertical height variance of the point spread function at different field of view sampling points Horizontal Width Variance Peak signal-to-noise ratio (PSNR) of each field of view spot diagram and the center field of view spot diagram i and structural similarity index SSIM i , Peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus and Structural Similarity Difference SSIM defocus .

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

[0066]

[0067]

[0068] Where n v Indicates the vertical field of view, n h Indicates the horizontal field of view. It represents the average height of the spot diagram of each field of view in the vertical direction. Represents the average width of the spot diagram of each field of view in the horizontal direction, Indicates the spot diagram height of different fields of view in the vertical direction, Indicates the spot diagram width for different fields of view in the horizontal direction.

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

[0070]

[0071]

[0072] Among them, MAX Iis the maximum pixel value of the spot diagram under different fields of view and the spot diagram of the central field of view, MSE is the mean of the pixel differences between images; I1(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of each field of view, and I2(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of the central field of view; m and n are the length and width of the image, respectively.

[0073] Structural similarity index SSIM of each field of view spot diagram and the central field of view spot diagram i The calculation formula is as follows:

[0074]

[0075] In the formula, μ i represents the mean of the spot diagrams of each field of view, μ0 represents the mean of the spot diagram 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 under 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, 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.

[0076] Peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus The calculation method is as follows:

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

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

[0079]

[0080] Among them, i represents different defocus point numbers, MAX i is the maximum pixel value of the PSF at different defocus positions and the PSF at the in-focus position, is the mean square error between the PSF at different defocus positions and the PSF at the in-focus position;

[0081] (3) Based on the peak signal-to-noise ratio at multiple defocus positions Get the peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocusdefocus ;

[0082]

[0083] Defocus-induced structural similarity difference SSIM defocus The calculation method is as follows:

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

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

[0086]

[0087] In the formula, represents the mean value of the point spread function PSF at different defocus positions, μ0 represents the mean value of the point spread function PSF at the quasi-focus position, The variance of the point spread function PSF at different defocus positions, σ0 2 The variance of the point spread function PSF at the in-focus position is represented by is the covariance of the point spread function PSF at different defocus positions and the point spread function PSF at the quasi-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) Structural similarity index at multiple defocus positions Get the structural similarity difference SSIM of the spot diagram caused by defocus defocus :

[0089]

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

[0091]

[0092] Wherein, W1, W2, W3 are pre-set weight coefficients and do not change with each iteration; subscript i represents the i-th field of view; N represents the number of selected defocus points; and F' is the evaluation function of constrained imaging index and imaging quality.

[0095] Step 4: If this iteration is the first iteration, or the current value of the comprehensive evaluation function F is less than its historical minimum value, the final structural parameters of the lens are updated to the lens structural parameters of the current iteration; otherwise, the final structural parameters of the lens are kept unchanged and are not updated;

[0096] Step 5: Determine whether the conditions for ending the loop are met (reaching the preset number of iterations or the comprehensive evaluation function F reaches the set threshold). If so, stop the iteration and output the final structural parameters of the current lens; otherwise, update the lens structural parameters under the current iteration through the least squares method, and repeat steps 2 to 4 to optimize the lens structure.

[0097] like Figure 5 , Figure 6 , Figure 8 As shown, after the initial structure of the double Gaussian objective lens is optimized and designed using the method of this embodiment, the difference in aberrations under different fields of view and defocus conditions is significantly reduced. Under different field angles, the change in the point spread function of the system is effectively controlled, and the vertical height variance and horizontal width variance of each field of view are significantly reduced. The minimum RMS radius of the point diagram is 5.833μm, and the maximum is 11.619μm. In a larger field of view, the uniformity of the aberration is significantly improved. In the case of defocus, the change in the point diagram is also reduced compared to before optimization. Sampling different characteristic field points on the image plane, it is found that the variance of the radius of the point diagram under each field of view is 3.055μm 2 , which is significantly lower than before optimization, and the distribution of the full-field point diagram tends to be uniform.

[0098] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention shall be included in the protection scope of the invention.

Claims

1. A method for designing optical systems with small spatially varying aberrations, characterized in that: The following steps are involved: S1: Determine the performance indicators and initial structural parameters of the optical system according to 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 (PSNR) of each field of view spot diagram and the center field of view spot diagram i and structural similarity index SSIM i , Peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus and Structural Similarity Difference SSIM defocus ; S3: Calculate the comprehensive evaluation function F according to the following formula: Where W1, W2, and W3 are pre-set weight coefficients that do not change with each iteration; the subscript i represents the first, i fields of view; N represents the number of selected out-of-focus points; F' is the evaluation function of constrained imaging index and imaging quality. S4: If this iteration is the first iteration, or the current value of the comprehensive evaluation function F is less than its historical minimum value, the final structural parameters of the lens are updated to be the lens structural parameters under the current iteration; Otherwise, the final structural parameters of the lens are kept unchanged and not updated; S5: Determine whether the loop end condition is met, if so, stop the iteration and output the final structural parameters of the current lens; Otherwise, the lens structure parameters of the current iteration are updated by the least square method, and S2 to 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, operating wavelength, and field of view angle; and the initial structural parameters include lens surface type, lens curvature radius, and lens spacing.

3. The optical design method for small spatial variation aberrations according to claim 1, characterized in that: Vertical height variance of the point spread function at different field of view sampling points Horizontal Width Variance The calculation formula is as follows: Where n v Indicates the vertical field of view, n h Indicates the horizontal field of view. It represents the average height of the spot diagram of each field of view in the vertical direction. Represents the average width of the spot diagram of each field of view in the horizontal direction, Indicates the spot diagram height of different fields of view in the vertical direction, Indicates the spot diagram width for 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 PSNR of each field of view point diagram and the central field of view point diagram i The calculation formula is as follows: Among them, MAX I is the maximum pixel value of the spot diagram under different fields of view and the spot diagram of the central field of view, MSE is the mean of the pixel differences between images; I1(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of each field of view, and I2(i,j) represents the pixel values ​​of the i-th and j-th pixel positions in the spot diagram of the central field of view; m and n are the length and width of the image, respectively.

5. The optical design method for small spatial variation aberration according to claim 1, characterized in that: Structural similarity index SSIM of each field of view spot diagram and the central field of view spot diagram i The calculation formula is as follows: In the formula, μ i represents the mean of the spot diagrams of each field of view, μ0 represents the mean of the spot diagram 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 central field point spread function, σ i0 is the covariance of the point spread function under 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, usually C1=(K1L) 2 and C2=(K2L) 2 , where L is the dynamic range of the image.

6. The optical design method for small spatial variation aberration according to claim 1, characterized in that: In S2, the peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus The calculation method is as follows: (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n , where each defocus distance corresponds to a different focus position, covering slight defocus situations of positive focus and negative focus; (2) For each defocus distance, calculate the point spread function PSF at the current position, and then calculate the peak signal-to-noise ratio between each defocus PSF and the in-focus PSF Among them, i represents different defocus point numbers, MAX i is the maximum pixel value of the PSF at different defocus positions and the PSF at the in-focus position, is the mean square error between the PSF at different defocus positions and the PSF at the in-focus position; (3) Based on the peak signal-to-noise ratio at multiple defocus positions Get the peak signal-to-noise ratio (PSNR) of the spot diagram caused by defocus defocus ; 7. The optical design method for small spatial variation aberrations according to claim 1, characterized in that: S2, defocus-induced structural similarity difference SSIM defocus The calculation method is as follows: (1) Select a set of defocus distances Δf1, Δf2, ..., Δf n , where each defocus distance corresponds to a different focus position, covering slight defocus situations of positive focus 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 in-focus PSF In the formula, represents the mean value of the point spread function PSF at different defocus positions, μ0 represents the mean value of the point spread function PSF at the quasi-focus position, The variance of the point spread function PSF at different defocus positions, σ0 2 The variance of the point spread function PSF at the in-focus position is represented by is the covariance of the point spread function PSF at different defocus positions and the point spread function PSF at the quasi-focus position; C1 and C2 are constants, usually C1=(K1L) 2 and C2=(K2L) 2 , where L is the dynamic range of the image; (3) Structural similarity index at multiple defocus positions Get the structural similarity difference SSIM of the spot diagram caused by defocus defocus :

8. The optical design method for small spatial variation aberration according to claim 1, characterized in that: The loop termination condition in S5 is that a preset number of iterations is reached or the comprehensive evaluation function F reaches a set threshold.

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

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