Method for calculating tolerance analysis of imaging system based on restored image performance

Abstract

The invention relates to an analysis method for calculating the tolerance of an imaging system based on restored image performance. The method comprises the following steps: constructing a general optical element processing error model; determining a parameter boundary of an error model and generating a processing error parameter based on a given root-mean-square value of a processing surface shape error, importing the parameter into optical design software for ray tracing, acquiring wave aberration of each field of view of the system to obtain point spread functions of each field of view, and superposing a noise image to obtain a degraded image so as to construct a restored image; evaluating the MTF value of each field of view of the system to obtain the machining tolerance limit of each optical element; and multiplying the machining tolerance limit of each optical element by the proportionality coefficient Ra, circularly executing the steps, and gradually increasing the proportionality coefficient until the machining error boundary of each optical element of the system is obtained. Compared with the prior art, the tolerance analysis of the imaging system can be calculated, the machining tolerance boundary of the optical element is determined, and the method has important guiding significance on machining of the optical element in the system.

Description

Technical Field

[0001] The present invention relates to the field of computational imaging technology, and in particular to a computational imaging system tolerance analysis method based on restored image performance. Background Art

[0002] Computational imaging is an emerging research field that realizes specific imaging functions by combining optical systems and image processing. It breaks the traditional point-to-point mapping relationship and adopts a more flexible indirect imaging mode. It realizes the final required imaging function by combining optical systems and image processing. It has important applications in improving system performance, function and system simplification. This flexible design mode can change the mode of optical imaging information acquisition and balance the resources relied on by the optical hardware space and the image processing algorithm software space, thereby giving it many revolutionary advantages that are difficult to obtain in traditional imaging systems, such as simplifying the difficulty of optical system processing. However, this simplification is not endless and has a limit. Traditional tolerance analysis methods, such as sensitivity-based tolerance analysis methods, optomechanical-based tolerance analysis methods, and multi-evaluation criteria-based tolerance analysis methods, do not consider the performance of image restoration, and therefore cannot be applied to the tolerance analysis of computational imaging systems. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a tolerance analysis method for a computational imaging system based on restored image performance, so as to realize the use of the image quality of the restored image as an evaluation criterion, establish a digital model of the processing error, repeatedly iterate and update the processing error, and find the precise processing error boundary.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A tolerance analysis method for a computational imaging system based on restored image performance comprises the following steps:

[0006] Model building steps: building a general optical component processing error model;

[0007] System imaging performance evaluation steps: based on the given root mean square value of the processing surface shape error, determine the parameter boundary of the general optical element processing error model, and randomly generate multiple sets of processing error parameters; import the processing error parameters into the optical design software for ray tracing, obtain the wave aberration of each field of view of the system, thereby obtaining the point spread function of each field of view of the system, and superimpose the noise image to obtain the degraded image; based on the degraded image and the point spread function of each field of view of the system, process to obtain a restored image, and evaluate the MTF value of each field of view of the system of the restored image;

[0008] Processing surface shape error adjustment step: determine whether the minimum MTF value among the system field MTF values ​​obtained in the system imaging performance evaluation step is greater than a preset system index, and if so, increase the root mean square value of the processing surface shape error, and repeat the system imaging performance evaluation step until the minimum MTF value among the system field MTF values ​​obtained is less than the system index;

[0009] Overall analysis step: executing the system imaging performance evaluation step and the processing surface shape error adjustment step for each optical element of the computational imaging system separately to obtain the processing tolerance limit of each optical element; multiplying the processing tolerance limit of each optical element by the proportional coefficient Ra to obtain the processing tolerance of each optical element, cyclically executing the system imaging performance evaluation step and the processing surface shape error adjustment step, and gradually increasing the proportional coefficient until the processing error boundary of each optical element of the system is obtained.

[0010] Furthermore, the expression of the general optical element processing error model is:

[0011] Δz(x,y)=αΔz irr (x,y)+(1-α)Δz rot (x,y)

[0012] Where Δz(x,y) is the general optical element processing error image, Δz irr (x,y) is the rotational symmetric component, Δz rot (x,y) is the non-rotated heap component weight, α is the weight factor;

[0013]

[0014] In the formula, A i is the coefficient of the i-th order XY extended polynomial, E i (x, y) is the i-th order XY extended polynomial, N is the number of XY extended polynomials;

[0015]

[0016] In the formula, B i is the coefficient of the i-th order Fourier expansion polynomial, i is the order, w0 is the periodic coefficient of the Fourier polynomial, and M is the number of Fourier polynomials.

[0017] Furthermore, the calculation expression of the parameter boundary of the general optical element processing error model is:

[0018]

[0019] Where Err is the root mean square value of the machined surface error.

[0020] Furthermore, the calculation expression of the point spread function of each field of view of the system is:

[0021]

[0022] Where h(x,y) is the point spread function of the system field of view, k = 2π / λ, λ is the wavelength, Λ(s,t) is the circular function with an aperture of D, and W(s,t) is the system wave aberration. is the Fourier transform.

[0023] Furthermore, the acquisition process of the degraded image includes: convolving the strip target image at the Nyquist frequency with the field of view point spread function of each system, and then adding it to the noise image to obtain the final degraded image. The corresponding calculation expression is:

[0024]

[0025] Where g(x,y) is the degraded image, is Gaussian noise, is Poisson noise, and f(x,y) is the strip target image.

[0026] Furthermore, the calculation expression of the restored image is:

[0027]

[0028] Where f(x,y) is the restored image, is the inverse Fourier transform, H(u,v) is the point spread function of the system field of view, is the conjugate of the complex number, G(u,v) is the Fourier transform of the degraded image, and σ is the noise factor.

[0029] Furthermore, the calculation expression of the MTF value of each field of view of the restored image evaluation system is:

[0030]

[0031] Where SDN1 is the average DN value of the bright target band in the center of the restored image, SDN2 is the average DN value of the dark stripe on the left side of the bright target in the center of the restored image, and SDN3 is the average DN value of the dark stripe on the right side of the bright target in the center of the restored image.

[0032] Furthermore, the expression of the processing error boundary of each optical element of the system finally obtained in the overall analysis step is:

[0033] Err i =Ra*Err limi

[0034] In the formula, Err iis the processing error boundary of optical element i, Ra is the proportionality coefficient, Err limi is the processing tolerance limit of optical element i.

[0035] Furthermore, the method also includes a system adjustment tolerance analysis step: setting the system adjustment tolerance, the system adjustment tolerance including the eccentricity, tilt and spacing of the optical element; performing Monte Carlo sampling and ray tracing in the optical design software, and recording the ray tracing results; using the system full-field comprehensive modulation transfer function or the full-field comprehensive diffuse spot radius as an evaluation index, selecting the worst tolerance group of the system adjustment tolerance, and performing the system imaging performance evaluation step, the processing surface error adjustment step and the overall analysis step on the basis of the worst tolerance group.

[0036] Furthermore, the method also includes guiding the processing of optical elements in the system according to the determined processing error boundaries of each optical element.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] (1) The present invention constructs a universal optical element processing error model. By first giving a processing surface error, the parameter boundary of the error model is determined, error parameters are randomly generated, and the field wave aberration is obtained by using optical design software. The field point spread function and the degraded image are constructed to obtain a restoration function. The performance of the restored image is used as an evaluation index, and the processing tolerance limits of each optical element are continuously adjusted and obtained. Finally, the processing error boundaries of each optical element in the overall computational imaging system are obtained, which can accurately guide the actual processing of the optical elements in the system.

[0039] (2) The present invention is a universal processing error simulation analysis method, which can be applied to various optical element processing methods, such as single-point diamond turning, ion beam polishing, magnetorheological precision shaping, small grinding head precision shaping, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A schematic flow chart of a method for computing imaging system tolerance analysis based on restored image performance provided in an embodiment of the present invention;

[0041] Figure 2 A schematic diagram of a system assembly tolerance analysis process in a computational imaging system tolerance analysis method based on restored image performance provided in an embodiment of the present invention;

[0042] Figure 3 A schematic diagram of a process for generating optical element processing errors in a computational imaging system tolerance analysis method based on restored image performance provided in an embodiment of the present invention;

[0043] Figure 4A schematic diagram of a rendering process of system imaging performance in a method for computing imaging system tolerance analysis based on restored image performance provided in an embodiment of the present invention;

[0044] Figure 5 A schematic diagram of an image restoration and performance evaluation process in a computational imaging system tolerance analysis method based on restored image performance provided in an embodiment of the present invention;

[0045] Figure 6 The schematic diagram of the off-axis three-mirror system and the image quality evaluation diagram in the tolerance analysis method of the computational imaging system based on restored image performance provided in an embodiment of the present invention;

[0046] Figure 7 It is a schematic diagram of three free-form surface machining error limit results in the tolerance analysis method of the computational imaging system based on restored image performance provided in an embodiment of the present invention;

[0047] Figure 8 Schematic diagram of three free-form surface machining error boundary results in the tolerance analysis method of a computational imaging system based on restored image performance provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0049] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0051] Example 1

[0052] This embodiment provides a method for tolerance analysis of a computational imaging system based on restored image performance, comprising the following steps:

[0053] Model building steps: building a general optical component processing error model;

[0054] System imaging performance evaluation steps: based on the given root mean square value of the processing surface shape error, determine the parameter boundary of the general optical element processing error model, and randomly generate multiple sets of processing error parameters; import the processing error parameters into the optical design software for ray tracing, obtain the wave aberration of each field of view of the system, thereby obtaining the point spread function of each field of view of the system, and superimpose the noise image to obtain the degraded image; based on the degraded image and the point spread function of each field of view of the system, process to obtain a restored image, and evaluate the MTF value of each field of view of the system of the restored image;

[0055] Processing surface shape error adjustment step: determine whether the minimum MTF value among the system field MTF values ​​obtained in the system imaging performance evaluation step is greater than a preset system index, and if so, increase the root mean square value of the processing surface shape error, and repeat the system imaging performance evaluation step until the minimum MTF value among the system field MTF values ​​obtained is less than the system index;

[0056] Overall analysis step: executing the system imaging performance evaluation step and the processing surface shape error adjustment step for each optical element of the computational imaging system separately to obtain the processing tolerance limit of each optical element; multiplying the processing tolerance limit of each optical element by the proportional coefficient Ra to obtain the processing tolerance of each optical element, cyclically executing the system imaging performance evaluation step and the processing surface shape error adjustment step, and gradually increasing the proportional coefficient until the processing error boundary of each optical element of the system is obtained.

[0057] Preferably, the method further includes a system adjustment tolerance analysis step: setting the system adjustment tolerance, which includes the eccentricity, tilt and spacing of the optical element; performing Monte Carlo sampling and ray tracing in the optical design software, and recording the ray tracing results; using the system full-field integrated modulation transfer function or the full-field integrated diffuse spot radius as an evaluation index, selecting the worst tolerance group of the system adjustment tolerance, and performing the system imaging performance evaluation step, the processing surface error adjustment step and the overall analysis step on the basis of the worst tolerance group.

[0058] Preferably, the method further comprises guiding the processing of optical elements in the system according to the determined processing error boundaries of each optical element.

[0059] The following is an off-axis three-mirror system as an implementation example. The circuit and performance evaluation of the off-axis three-mirror system are as follows: Figure 6As shown, it contains three free-form surfaces, the field of view of the system is 8.0°×6.4°, the F number is 2.8, the wavelength range covers from 400nm to 1050nm, and the detector used is a CMOS detector with a pixel size of 6.9μm and a detector array size of 1224×1024 pixels. The maximum RMS spot diameter of the system's full field of view is 0.988μm, and the MTF of the system is greater than 0.78 at the Nyquist frequency (72lp / mm).

[0060] Process-based Figure 1 A computational imaging tolerance analysis method based on restored image performance evaluation is presented, comprising the following steps:

[0061] S1: System installation tolerance analysis;

[0062] S2: Generate optical element processing errors;

[0063] S3: system imaging performance rendering;

[0064] S4: Image restoration and performance evaluation;

[0065] S5: Adjust the machining error parameters;

[0066] S6: Output machining error boundary;

[0067] Step S1 specifically includes:

[0068] (1) System calibration tolerances include the following parameters: optical element eccentricity, tilt, spacing, etc. These tolerance boundaries are set based on existing precision calibration technology;

[0069] (2) Perform Monte Carlo sampling and ray tracing in the optical design software and record the ray tracing results;

[0070] (3) Using the system's full-field comprehensive modulation transfer function (MTF) or full-field comprehensive diffuse spot radius as the evaluation index, select the worst tolerance group for subsequent analysis. Figure 2 The system assembly tolerance analysis process is demonstrated.

[0071] Step S2 specifically includes:

[0072] (1) The established general optical element processing error model expression is shown in the following formula, which is composed of the rotational symmetric component Δz irr (x,y) and the non-rotating stack component Δz rot (x, y) composition, the weight factor α is adjusted according to the optical element processing technology;

[0073] Δz(x,y)=αΔz irr (x,y)+(1-α)Δz rot (x,y)

[0074] The non-rotationally symmetric component is in the form of an XY extended polynomial, and its expression is shown in the following formula:

[0075]

[0076] In the formula, f i is the coefficient of the i-th order XY extended polynomial, E i (x, y) is the i-th order XY extended polynomial, whose polynomial is in the order of x, y, x 2 ,xy,y 2 、x 3 、x 2 y、xy 2 ,y 3 …arranged in sequence, N is the number of XY extended polynomials.

[0077] The rotational symmetric component is expressed in the form of Fourier series expansion, as shown in the following formula:

[0078]

[0079] In the formula, B i is the coefficient of the Fourier expansion polynomial, w0 is the periodic coefficient of the Fourier polynomial, and M is the number of Fourier polynomials.

[0080] (2) Based on the given root mean square (RMS) value of the machining surface error Err, the parameter boundaries of the rotationally symmetric component and the non-rotationally symmetric component in the machining error model are determined, as shown in formulas (4) and (5):

[0081]

[0082] (3) n groups of machining errors are randomly generated, and the parameters of the machining error model satisfy the parameter boundaries in (2), and the deviation between the RMS of the machining error and the given RMS of the machining error is better than 10%. Figure 3 The process of generating optical component processing errors is demonstrated.

[0083] In the actual experiment process, this embodiment sets N to 14, M to 8, and n to 1000.

[0084] Step S3 also includes:

[0085] (1) Importing the processing error parameters generated in step S2 into the optical design software, performing ray tracing, and obtaining the wave aberration of each field of view of the system;

[0086] (2) Based on the Fourier transform of the generalized pupil function, the point spread function (PSF) of each field of view of the system is obtained, and its expression is as follows:

[0087]

[0088] Where k = 2π / λ, Λ(s, t) is a circular function with an aperture of D, W(s, t) is the system wave aberration, represents Fourier transform.

[0089] (3) The strip target image at the Nyquist frequency is convolved with each field of view PSF, and then added with the noise (Gaussian and Poisson noise) image to obtain the actual degraded image, which is expressed as follows:

[0090]

[0091] in, is Gaussian noise, is Poisson noise, g(x,y) is the degraded image, and x(x,y) is the target image. In this embodiment, the noise parameters are set to σ and g =1.1×10 -3 , σ p =8.8×10 -5 .

[0092] Figure 4 The rendering process of the system imaging performance is demonstrated.

[0093] Step S4 also includes:

[0094] (1) The degraded image and PSF are passed through the Wiener filtering algorithm to obtain the restored image, the formula of which is as follows:

[0095]

[0096] in, represents the inverse Fourier transform, H(u,v) is the Fourier transform of PSF, is the conjugate of the complex number, G(u,v) is the Fourier transform of the degraded image, σ is the noise factor, and in the actual operation, the embodiment sets it to σ=0.0088;

[0097] (2) Calculate the MTF of each field of view of the system based on the system strip target MTF calculation formula. The formula is as follows:

[0098]

[0099] Among them, SDN1 refers to the average DN value of the central bright target band, SDN2 refers to the average DN value of the dark stripe on the left side of the central bright target, and SDN3 refers to the average DN value of the dark stripe on the right side of the central bright target.

[0100] Figure 5 The image restoration and performance evaluation process are demonstrated.

[0101] Then, based on the measured system performance data, we Figure 1 The process is to adjust the processing error parameters and determine the minimum MTF value of the full field of view at this time. If the minimum MTF of the full field of view is greater than the system index, the processing error RMS value is increased and steps S2 to S5 are repeated until the minimum MTF of the full field of view of the system is less than the system index.

[0102] After the cycle is completed, the processing error boundary is output, and the RMS value of the processing error obtained in the above steps is output. The overall analysis method of the processing tolerance of multiple optical components can be summarized as follows:

[0103] (1) First, according to the above steps S1 to S6, analyze the processing tolerance limit Err of each optical element separately limi ;

[0104] (2) Then, the processing tolerance limit of each optical element is multiplied by the same proportionality factor Ra to obtain the processing tolerance of each optical element, and the proportionality factor Ra is gradually increased according to Figure 1 The process shown in the figure obtains the processing error boundary of each optical element in the system, and its expression is as follows:

[0105] Err i =Ra*Err limi

[0106] Finally, the boundary results of each mirror are: 1.80λ for the primary mirror, 2.80λ for the secondary mirror, and 1.25λ for the third mirror; the boundary results when the three mirrors have errors at the same time are: ratio Ra = 0.36, then the tolerance limits of the three mirrors are: 0.648λ for the primary mirror, 1.008λ for the secondary mirror, and 0.450λ for the third mirror. The results are as follows: Figure 7 , Figure 8 shown.

[0107] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A tolerance analysis method for a computational imaging system based on restored image performance, characterized in that: The following steps are involved: Model building steps: building a general optical component processing error model; System imaging performance evaluation step: based on a given root mean square value of a machining surface shape error, determining a parameter boundary of the universal optical element machining error model, and randomly generating multiple sets of machining error parameters; The processing error parameters are imported into the optical design software for ray tracing to obtain the wave aberration of each field of view of the system, thereby obtaining the point spread function of each field of view of the system, and superimposing the noise image to obtain the degraded image; Based on the degraded image and the point spread function of each field of view of the system, a restored image is obtained, and the MTF value of each field of view of the system of the restored image is evaluated; Processing surface shape error adjustment step: determine whether the minimum MTF value among the system field MTF values ​​obtained in the system imaging performance evaluation step is greater than a preset system index, and if so, increase the root mean square value of the processing surface shape error, and repeat the system imaging performance evaluation step until the minimum MTF value among the system field MTF values ​​obtained is less than the system index; Overall analysis step: executing the system imaging performance evaluation step and the processing surface shape error adjustment step for each optical element of the computational imaging system separately to obtain the processing tolerance limit of each optical element; multiplying the processing tolerance limit of each optical element by the proportional coefficient Ra to obtain the processing tolerance of each optical element, cyclically executing the system imaging performance evaluation step and the processing surface shape error adjustment step, and gradually increasing the proportional coefficient until the processing error boundary of each optical element of the system is obtained.

2. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The expression of the general optical element processing error model is: Δz(x,y)=αΔz irr (x,y)+(1-α)Δz rot (x, y) Where Δz(x, y) is the general optical element processing error image, Δz irr (x, y) is the rotational symmetric component, Δz rot (x, y) is the non-rotated heap component weight, α is the weight factor; In the formula, A i is the coefficient of the i-th order XY extended polynomial, E i (x, y) is the i-th order XY extended polynomial, N is the number of XY extended polynomials; In the formula, B i is the coefficient of the i-th order Fourier expansion polynomial, i is the order, w0 is the periodic coefficient of the Fourier polynomial, and M is the number of Fourier polynomials.

3. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 2, characterized in that: The calculation expression of the parameter boundary of the general optical element processing error model is: Where Err is the root mean square value of the machined surface error.

4. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The calculation expression of the point spread function of each field of view of the system is: Where h(x, y) is the point spread function of the system field of view, k = 2π / λ, λ is the wavelength, Λ(s, t) is the circular function with an aperture of D, and W(s, t) is the system wave aberration. is the Fourier transform.

5. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The acquisition process of the degraded image includes: convolving the strip target image at the Nyquist frequency with the field of view point spread function of each system, and then adding it to the noise image to obtain the final degraded image. The corresponding calculation expression is: Where g(x, y) is the degraded image, is Gaussian noise, is Poisson noise, and f(x, y) is the strip target image.

6. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The calculation expression of the restored image is: Where f(x, y) is the restored image, is the inverse Fourier transform, H(u, v) is the point spread function of the system field of view, * is the conjugate of the complex number, G(u, v) is the Fourier transform of the degraded image, and σ is the noise factor.

7. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The calculation expression of the MTF value of each field of view of the restored image evaluation system is: Where SDN1 is the average DN value of the bright target band in the center of the restored image, SDN2 is the average DN value of the dark stripe on the left side of the bright target in the center of the restored image, and SDN3 is the average DN value of the dark stripe on the right side of the bright target in the center of the restored image.

8. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The expression of the processing error boundary of each optical element of the system finally obtained in the overall analysis step is: Err i =Ra*Err limi In the formula, Err i is the processing error boundary of optical element i, Ra is the proportionality coefficient, Err limi is the processing tolerance limit of optical element i.

9. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The method further comprises a system adjustment tolerance analysis step: setting a system adjustment tolerance, wherein the system adjustment tolerance includes eccentricity, tilt and spacing of optical elements; performing Monte Carlo sampling and ray tracing in optical design software, and recording ray tracing results; Taking the system's full-field comprehensive modulation transfer function or the full-field comprehensive diffuse spot radius as an evaluation index, the worst tolerance group of the system's installation tolerance is selected, and the system imaging performance evaluation step, the processing surface error adjustment step and the overall analysis step are performed based on the worst tolerance group.

10. The tolerance analysis method of a computational imaging system based on restored image performance according to claim 1, characterized in that: The method further includes guiding the processing of optical elements in the system according to the determined processing error boundaries of each optical element.

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