A tolerance analysis method for computational imaging systems based on restored image performance

Abstract

The present invention relates to a tolerance analysis method for a computational imaging system based on restored image performance, comprising: constructing a universal optical element machining error model; determining the parameter boundaries of the error model based on a given root mean square value of the machining surface shape error, generating machining error parameters, and importing them into optical design software for ray tracing. The system obtains wave aberrations of each field of view to obtain point spread functions of each field of view, superimposes a noise image to obtain a degraded image, thereby constructing a restored image, and evaluating the MTF values ​​of each field of view of the system, using the machining tolerance limits of each optical element; multiplying the machining tolerance limits of each optical element by a proportionality coefficient Ra, and repeatedly executing the above steps, gradually increasing the proportionality coefficient until the machining error boundaries of each optical element in the system are obtained. Compared with the prior art, the present invention can implement tolerance analysis of computational imaging systems and determine the machining tolerance boundaries of optical elements, which has important guiding significance for the machining of optical elements 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 achieves specific imaging functions by combining optical systems and image processing. Breaking away from traditional point-to-point mapping, it adopts a more flexible indirect imaging model. By combining optical systems and image processing to achieve the desired imaging function, it has important applications in improving system performance, functionality, and simplification. This flexible design model can change the way optical imaging acquires information and balance the resources required by optical hardware and image processing algorithm software, thereby endowing it with revolutionary advantages that are difficult to achieve with traditional imaging systems, such as simplifying optical system processing. However, this simplification is not endless; it also has a limit. Traditional tolerance analysis methods, such as those based on sensitivity, optomechanical integration, and multiple evaluation criteria, do not consider image restoration performance and are therefore not applicable to 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 provide a tolerance analysis method for a computational imaging system based on the performance of restored images, so as to use the image quality of the restored image as the evaluation standard, establish a digital model of the processing error, repeatedly iteratively 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 construction steps: Construct a general optical component processing error model;

[0007] System imaging performance evaluation steps: Based on a given root mean square value of the machining surface error, determining the parameter boundaries of the universal optical element machining error model, and randomly generating multiple sets of machining error parameters; importing the machining error parameters into 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 a noise image to obtain a degraded image; processing the degraded image and the point spread function of each field of view of the system to obtain a restored image, and evaluating the MTF value of each field of view of the system of the restored image;

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

[0009] Overall analysis step: performing the system imaging performance evaluation step and the processing surface error adjustment step on 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 performing the system imaging performance evaluation step and the processing surface 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] Where 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] Where 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 universal 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 of the aperture D, W(s,t) is the system wave aberration, is the Fourier transform.

[0023] Furthermore, the degraded image acquisition process includes: convolving the strip target image at the Nyquist frequency with the point spread function of each system field of view, and then adding it with 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 to the left of the bright target in the center of the restored image, and SDN3 is the average DN value of the dark stripe to the right 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] Where Err iis the processing error boundary of optical element i, Ra is the proportional 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, which includes the eccentricity, tilt and spacing of the optical elements; 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 based on 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 the processing surface error, determining the parameter boundary of the error model, randomly generating error parameters, using optical design software to obtain the field wave aberration, constructing the field point spread function and the degenerate image, thereby obtaining the restoration function. Taking the performance of the restored image as the evaluation index, the processing tolerance limit of each optical element is continuously adjusted and obtained, and finally the processing error boundary of each optical element in the overall computational imaging system is 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 Schematic diagram of a flow chart of a tolerance analysis method for a computational imaging system based on restored image performance provided in an embodiment of the present invention;

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

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

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

[0046] Figure 7 Schematic diagram of three free-form surface machining error limit results in the tolerance analysis method of a 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] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only 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 herein 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 as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall 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, it does not need to be further defined or explained 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 construction steps: Construct a general optical component processing error model;

[0054] System imaging performance evaluation steps: Based on a given root mean square value of the machining surface error, determining the parameter boundaries of the universal optical element machining error model, and randomly generating multiple sets of machining error parameters; importing the machining error parameters into 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 a noise image to obtain a degraded image; processing the degraded image and the point spread function of each field of view of the system to obtain a restored image, and evaluating the MTF value of each field of view of the system of the restored image;

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

[0056] Overall analysis step: performing the system imaging performance evaluation step and the processing surface error adjustment step on 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 performing the system imaging performance evaluation step and the processing surface 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 elements; 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 in the figure, it contains three free-form surfaces, the system field of view is 8.0°×6.4°, the F number is 2.8, the wavelength range is 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 system's MTF 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, which includes 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 integrated modulation transfer function (MTF) or the full-field integrated diffuse spot radius as the evaluation index, the worst tolerance group is selected 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 expressed in the form of an XY extended polynomial, as shown in the following formula:

[0075]

[0076] Where, 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, and its polynomial is expressed in terms of x, y, x 2 ,xy,y 2 、x 3 、x 2 y, xy 2 、y 3 ...are arranged in sequence, where 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] Where 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 and non-rotationally symmetric components in the machining error model are determined, as shown in formulas (4) and (5):

[0081]

[0082] (3) Randomly generate n groups of machining errors, whose machining error model parameters meet the parameter boundaries in (2), and the deviation of the machining error RMS from the given machining error RMS 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 further 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, which is expressed 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 the 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 further includes:

[0094] (1) The degraded image and PSF are passed through the Wiener filtering algorithm to obtain the restored image, 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, and σ is the noise factor. 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 to the left of the central bright target, and SDN3 refers to the average DN value of the dark stripe to the right 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 repeated, and the machining error parameters are adjusted to determine the minimum MTF value of the full field of view. If the minimum MTF of the full field of view is greater than the system specification, the machining 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 specification.

[0102] After the cycle is completed, the machining error boundary is output, and the machining error RMS value obtained in the above steps is output. The overall analysis method for the machining tolerances 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 proportional coefficient Ra to obtain the processing tolerance of each optical element, and the proportional coefficient Ra is gradually increased according to Figure 1 The process shown in the figure can obtain the machining error boundary of each optical element in the system, which is expressed as follows:

[0105] Err i =Ra*Err limi

[0106] Finally, the boundary results of each mirror surface 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 mirror surfaces have errors at the same time are: ratio Ra = 0.36, then the tolerance limits of the three mirror surfaces 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 above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined 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 construction steps: Construct a general optical component processing error model; System imaging performance evaluation step: based on a given root mean square value of a machining surface error, determining the parameter boundary of the universal optical element machining error model, and randomly generating multiple sets of machining error parameters; Import the processing error parameters 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 error adjustment step: determining whether the minimum MTF value among the system MTF values ​​of each field of view obtained in the system imaging performance evaluation step is greater than a preset system index; if so, increasing the root mean square value of the processing surface error, and repeatedly performing the system imaging performance evaluation step until the minimum MTF value among the system MTF values ​​of each field of view obtained is less than the system index; Overall analysis step: performing the system imaging performance evaluation step and the processing surface error adjustment step on 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 performing the system imaging performance evaluation step and the processing surface 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; Where 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; Where 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 of the aperture D, 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 degraded image acquisition process includes: convolving the strip target image at the Nyquist frequency with the point spread function of each system field of view, and then adding it with 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 to the left of the bright target in the center of the restored image, and SDN3 is the average DN value of the dark stripe to the right 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 Where Err i is the processing error boundary of optical element i, Ra is the proportional 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 includes a system adjustment tolerance analysis step: setting system adjustment tolerances, which include 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-of-view comprehensive modulation transfer function or the full-field-of-view comprehensive diffuse spot radius as an evaluation indicator, the worst tolerance group of the system's assembly 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 based on the determined processing error boundaries of each optical element.

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