Medium and far infrared MTF measurement method based on inclined slit method

Abstract

The invention discloses a method for high-precision measurement of a modulation transfer function (MTF) of an optical system, and relates to the field of optical measurement. The method comprises the following steps of: acquiring a digital image of a slit target, and obtaining an accurate centroid position of a slit in each pixel row through a centroid positioning algorithm of an iterative adaptive window function for each pixel row intersected with the slit in the image. The method comprises the following steps: carrying out linear fitting on an accurate mass center position, calculating an accurate inclination angle of a slit relative to an image sensor pixel array, determining a super-sampling interval by using a geometrical relationship, constructing a super-sampling line spread function (SSLSF), and finally carrying out correction by using a joint correction model through Fourier transform to obtain an accurate MTF (Modulation Transform Function). According to the method, the problem of inaccurate MTF measurement caused by image noise and detector sampling frequency limitation in the prior art is solved, and the MTF measurement precision and the anti-noise capability are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of optical measurement and imaging system characterization technology, and in particular to a mid- and far-infrared MTF measurement method based on the tilted slit method. Background Technology

[0002] The modulation transfer function (MTF) is a recognized standard for objectively and quantitatively evaluating the performance of optical imaging systems. It integrates the two key concepts of resolution and contrast into a comprehensive metric that varies with spatial frequency, accurately describing the system's ability to transfer varying degrees of detail contrast from the object side to the image side. Therefore, accurate MTF measurement is crucial for the research and development of optical systems, quality control during production, and applications in key areas such as industrial automation inspection, high-end medical imaging, and aerospace remote sensing. Several existing MTF measurement methods exist, each with its inherent limitations.

[0003] Existing Method 1: Vertical Slit Method. This method measures MTF by imaging a slit placed strictly parallel to the row or column direction of the detector pixel array. The main drawback of this method is its extreme sensitivity to alignment accuracy. In practice, even a tiny angular deviation between the slit and the pixel grid will introduce significant measurement errors, and achieving perfect alignment is both difficult and time-consuming, greatly reducing the practicality and repeatability of the measurement.

[0004] Existing method 2: Tilted edge method (the method described in ISO 12233). This method overcomes the alignment problem of the vertical slit method by intentionally tilting a high-contrast sharp edge (blade) relative to the pixel array. This method obtains the edge spread function (ESF) from the edge image, then differentiates the ESF to obtain the line spread function (LSF), and finally obtains the MTF. However, mathematically, differentiation significantly amplifies high-frequency noise in the signal. In image processing, this means that any random noise present in the original image (such as shot noise or readout noise) will be amplified during the differentiation process to obtain the LSF, resulting in a severe deterioration of the calculated LSF signal-to-noise ratio. Ultimately, this makes the MTF measurement results in the high spatial frequency region inaccurate and unreliable.

[0005] Existing Method 3: Traditional Tilt Slit Method. This method uses a tilted slit target instead of a cutting edge. Its advantage is that the intensity distribution of the slit image is directly proportional to the LSF, thus eliminating the need for differentiation calculations and fundamentally avoiding the noise amplification problem of the cutting edge method. However, the traditional tilted slit method often uses a fixed oversampling factor without subpixel sampling based on the actual tilt angle of the slit. This may introduce systematic positional errors during the subsequent construction of the oversampled LSF, distorting the true shape of the LSF and ultimately reducing the measurement accuracy of the MTF, especially in the detail-sensitive high-frequency region.

[0006] Therefore, there is a need for an MTF measurement method that is computationally efficient, noise-resistant, and capable of determining the slit position and angle with extremely high accuracy. Summary of the Invention

[0007] The purpose of this invention is to solve the technical problem that the existing MTF measurement methods are limited by the camera sampling rate and affected by image noise, resulting in errors in the slit geometry parameters (position and angle), which in turn affects the final MTF measurement accuracy (especially at high spatial frequencies).

[0008] The technical solution to achieve the objective of this invention is as follows: a mid-to-far infrared MTF measurement method based on the inclined slit method, comprising the following steps:

[0009] Step 1: Obtain a digital image of the slit target using an MTF measurement system. The angle between the slit target and the pixel array of the image sensor is 1.5°~3°. Perform noise reduction and background subtraction processing on the digital image to obtain a preprocessed slit image.

[0010] Step 2: For multiple pixel rows intersecting with the slit in the ROI region of the preprocessed slit image, the centroid localization algorithm based on iterative adaptive window function is used to obtain the precise centroid position of the slit in each pixel row, as follows;

[0011] For each pixel row, the multi-feature fusion signal-to-noise ratio (MFFSNR) of that pixel row is calculated to obtain the corresponding SNR. An adaptive signal-to-noise ratio window function is then constructed using this SNR. The original intensity data of each pixel row in the ROI region of the preprocessed slit image from step 1 is multiplied point-by-point by the adaptive signal-to-noise ratio window function to obtain the intensity data of the windowed pixels. Based on the intensity data of the windowed pixels, the initial centroid position of the slit in that row is calculated. The adaptive signal-to-noise ratio window function is applied again, aligning its center with the initial centroid position of the slit in that pixel row obtained in the previous step, generating weighted intensity data. Based on the weighted intensity data, the optimized centroid position is calculated and used as the precise centroid position of the slit in that pixel row.

[0012] Step 3: Use least squares linear regression to fit a straight line to the precise centroid position of each pixel row, obtain the slope of the fitted line, and calculate the precise tilt angle θ of the slit relative to the image sensor pixel array based on the slope of the fitted line.

[0013] Step 4: Based on the precise tilt angle θ and the precise centroid position of the slits in each pixel row, first calculate the oversampling interval. ,by The pixel row is divided into multiple sub-pixel levels for the width, and the original intensity data of each pixel row is projected onto the corresponding sub-pixel level. Finally, they are merged into a sub-pixel coordinate system to construct the supersampling line spread function SSLSF.

[0014] Step 5: Perform a discrete Fourier transform on the SSLSF to obtain the uncorrected MTF; then, using the effective optical width, tilt angle, and oversampling interval of the slit target, use a slit width-tilt angle joint correction model to correct the uncorrected MTF to obtain the accurate MTF.

[0015] Compared with the prior art, the significant advantages of this invention are:

[0016] (1) Improved accuracy. This invention proposes for the first time a centroid localization algorithm based on an iterative adaptive window function, which actively suppresses noise interference at the root of centroid calculation, significantly reducing the determination error of centroid and angle. Combined with the slit width-tilt angle joint correction model proposed for the first time in this invention, the measurement error of the final MTF can be controlled within 1%;

[0017] (2) Excellent noise resistance. The iterative adaptive window function can actively and effectively suppress the influence of random noise on the calculation of key geometric parameters, making this method more robust to noise than traditional methods;

[0018] (3) High high-frequency fidelity. Because it ensures the integrity and accuracy of LSF, this method can provide reliable MTF values ​​at higher spatial frequencies, while existing methods often fail in these regions due to noise.

[0019] (4) Its insensitivity to noise ensures that repeated measurements under the same conditions produce highly consistent results, enhancing the reliability of the measurement method. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the MTF measurement system used in the method of the present invention.

[0021] Figure 2The images show a comparison of the LSF curves before and after image preprocessing. Figure (a) shows the LSF curve before preprocessing, and Figure (b) shows the LSF curve after preprocessing.

[0022] Figure 3 Figure (a) shows the preprocessed slit image (ROI region is selected), and Figure (b) shows the position of the centroid fitted line for each row of the ROI region.

[0023] Figure 4 This is a schematic diagram of the construction of an oversampled LSF based on the slit tilt angle and the centroid position of each row. In (a), the sampling interval is calculated, where dx is the oversampled interval and px is the pixel size of detector 1; and (b) the process of projecting each row of pixels onto a subpixel level to generate the SSLSF.

[0024] Figure 5 The figures show a comparison between the LSF curves obtained without oversampling and the LSF curves obtained with oversampling. Figure (a) shows the LSF curve obtained without oversampling, and Figure (b) shows the LSF curve obtained with oversampling.

[0025] Figure 6 This is a schematic diagram comparing the traditional slit method, the method of this invention, and the standard MTF curve.

[0026] Figure 7 This is a flowchart of the mid- and far-infrared MTF measurement method based on the inclined slit method described in this invention. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments and methods described herein are for illustrative and explanatory purposes only and are not intended to limit the scope of the present invention.

[0028] Combination Figure 7 A method for measuring mid- and far-infrared MTF based on the inclined slit method, comprising the following steps:

[0029] use Figure 1 The MTF measurement system shown includes a detector 1, a lens under test 2, a secondary mirror 3, a primary mirror 4, a light source 5, a target object 6, and a computer 7. Infrared light emitted by the light source (after passing through a filter) passes through the slit target object, then sequentially passes through the collimator composed of the secondary mirror 3 and the primary mirror 4, becoming parallel light that passes through the lens under test and is finally focused onto the detector 1 to form an image. The computer then performs image acquisition and subsequent MTF calculation steps.

[0030] Step 1: Obtain a digital image of the slit target using an MTF measurement system. The angle between the slit target and the pixel array of the image sensor is 1.5° to 3°. Perform noise reduction and background subtraction processing on the digital image to obtain a preprocessed slit image.

[0031] Combination Figure 2 A series of preprocessing methods were employed to improve the digital image quality of the slit target. Specifically, the following steps were included: adjusting parameters such as the integration time of detector 1 to ensure that the peak grayscale value of the slit image fully utilizes its dynamic range—that is, as high as possible while avoiding saturation—while ensuring that the signal strength in the background region is sufficient to overcome readout noise. Fifty digital images of the slit target were continuously acquired, then registered to correct for minor drifts, and finally, a pixel-by-pixel arithmetic average was performed to obtain an averaged image. This step significantly reduces time-related random noise (such as shot noise, thermal noise, etc.). On the averaged image, a histogram was first used to statistically analyze the grayscale distribution of the entire image. The grayscale value with the highest frequency was considered the background value, and then this value was subtracted from the grayscale values ​​of all pixels to obtain the preprocessed slit image. Figure 1 As can be seen, before preprocessing, the LSF tail exhibits significant fluctuations, which is equivalent to introducing additional high-frequency and low-frequency components into the spatial domain. During the Fourier transform process, these extra frequency components directly affect the shape of the MTF curve, leading to measurement errors. After preprocessing, the LSF tail noise is significantly reduced.

[0032] Step 2: For multiple pixel rows intersecting with the slit in the ROI region of the preprocessed slit image, the centroid localization algorithm based on iterative adaptive window function is used to obtain the precise centroid position of the slit in each pixel row, as follows;

[0033] For each pixel row, calculate the multi-feature fusion signal-to-noise ratio (MFFSNR) for that pixel row to obtain the corresponding SNR. Use the SNR to construct an adaptive signal-to-noise ratio window function. Multiply the original intensity data of each row of pixels in the ROI region of the preprocessed slit image in step 1 point by point with the adaptive signal-to-noise ratio window function to obtain the intensity data of the windowed pixels. Calculate the initial centroid position of the slit in that row based on the intensity data of the windowed pixels. Apply the adaptive signal-to-noise ratio window function again, aligning the center of the adaptive signal-to-noise ratio window function with the initial centroid position of the slit in that pixel row obtained in the previous step to generate weighted intensity data. Calculate the optimized centroid position based on the weighted intensity data and use it as the precise centroid position of the slit in that pixel row.

[0034] Combination Figure 3In the digital image of the slit target after background subtraction, a region of interest (ROI) is defined. The width of the ROI should be wide enough to capture the entire effective portion of the LSF, including its tails extending to both sides; its length (along the slit direction) should be long enough to provide a sufficient number of pixel rows for subsequent accurate angle determination and efficient oversampling synthesis. First, the multi-feature fusion signal-to-noise ratio (MFFSNR) for each pixel row within the ROI is calculated to obtain the corresponding SNR, and the calculation formula is as follows:

[0035] (1),

[0036] Where i is the row index of the current pixel. The mean gray value of the ROI region in the i-th row of the preprocessed slit image. Let be the standard deviation of the grayscale values ​​of the ROI region in the i-th row, and α and β be weighting parameters. This is the edge sharpness factor. Gradient weighting is applied to the SNR using the following formula:

[0037] (2),

[0038] in, This is the absolute value of the Laplacian response of the slit region in the ROI region. The Laplacian operator is very sensitive to abrupt changes in grayscale in the image. The larger this value is, the more obvious the edge features of the point are. This represents the maximum absolute value of the Laplacian response of all pixels in the ROI region of row i. The edge sharpness factor, obtained through normalization, is the ratio of the slit edge intensity to the strongest edge in that row, effectively distinguishing between genuine slit signals and pseudo-edges caused by noise. The closer the ratio is to 1, the sharper the slit edge. The contrast enhancement factor is calculated using the following formula:

[0039] (3),

[0040] in, is the average value of the background area in the i-th row. Contrast is incorporated as a weighting factor into the SNR calculation method to distinguish between high-contrast slits and low-contrast noise.

[0041] Based on the above The signal-to-noise ratio adaptive window function proposed in this invention is obtained. The details are as follows:

[0042] (4),

[0043] Where j is the column index of the current pixel; The base amplitude coefficient determines the baseline height and overall energy level of the window function; The modulation amplitude coefficient determines the main lobe width and side lobe attenuation characteristics of the window function; for The center position; N is the... Effective width; The adaptive gain coefficient determines the adjustment range of the window function as the signal-to-noise ratio changes; For bandwidth modulation parameters, by influencing the error function Adjust the rate of change Main lobe width; The signal-to-noise ratio of the current row; The error function has a shape that depends on the bandwidth modulation parameters. and signal-to-noise ratio Dynamic adaptive adjustments are made. When the signal-to-noise ratio (SNR) is low, the window function applies stronger suppression; when the SNR is high, more signal details are preserved. The raw intensity data of each pixel row within the ROI region of the slit image is used. The signal-to-noise ratio adaptive window function is multiplied point-by-point to suppress the most significant noise, especially that which is far from the possible location of the slit, to obtain the intensity data of the windowed pixels. :

[0044] (5),

[0045] based on The initial estimate of the centroid of each pixel row of the slit is calculated, that is, the initial centroid position of each pixel row of the slit. :

[0046] (6),

[0047] The first iteration uses a signal-to-noise ratio (SNR) adaptive window function with a period equal to the width of the ROI region in the slit image, covering the entire row of pixels. This ensures that the slit will fall within the coverage area of ​​the window function regardless of its actual location. The center point is half the width of the ROI region, meaning its center point is the geometric center of the ROI region along the row direction. The second iteration also uses an SNR adaptive window function with a period equal to the width of the ROI region, but its center is placed at the initial centroid position obtained in S2-1. This more precisely aligns the strongly weighted region of the SNR adaptive window function with the estimated slit position, generating weighted intensity data. Based on this weighted intensity data, the centroid calculation is further optimized to obtain the precise centroid position of the slit in each pixel row. :

[0048] (7),

[0049] in, This is the intensity data of each pixel after a second signal-to-noise ratio adaptive window function weighting, i.e., the weighted intensity data. Both weightings are based on the original data to avoid excessive attenuation or signal distortion.

[0050] Step 3: Use least squares linear regression to fit a straight line to the precise centroid position of each pixel row, obtain the slope of the fitted line, and calculate the precise tilt angle θ of the slit relative to the image sensor pixel array based on the slope of the fitted line.

[0051] The linear equation for least squares linear regression is: , where y is the pixel row number, x is the precise centroid position of that row, and k is the slope of the line equation. Figure 3 In (b), the precise centroid position is obtained by iteratively weighting all pixel rows within the ROI. Then, a least-squares linear regression is performed to fit a straight line, from which the tilt angle θ of the slit can be accurately calculated:

[0052] (8),

[0053] Step 4: Based on the precise tilt angle θ and the precise centroid position of the slits in each pixel row, first calculate the oversampling interval. ,by The pixel row is divided into multiple sub-pixel levels for the width, and the original intensity data of each pixel row is projected onto the corresponding sub-pixel level. Finally, they are merged into a sub-pixel coordinate system to construct the supersampling line spread function SSLSF.

[0054] Combination Figure 4 After the tilt angle θ and the precise centroid position of each pixel row are determined, the image sensor pixel size is used as the basis for further analysis. It can calculate the oversampling interval. Its formula is:

[0055] (9),

[0056] With the above oversampling interval Divide the image into rows for width, creating multiple sub-pixel levels. Then, iterate through each pixel row in the ROI again. For each pixel in that row, calculate its horizontal distance relative to the precise centroid position of the slit in step 2. Based on this distance, project the raw intensity data of each pixel and accumulate it into the corresponding sub-pixel level, while recording how many pixels have accumulated in each level. Figure 4In (b), the centroid of each row of the tilted slits can be projected onto a predetermined subpixel level, achieving oversampling. After all pixel rows within the ROI have been processed, the sum of the accumulated intensity data in each subpixel level is divided by the number of pixels accumulated in that level to obtain the average intensity data in each level. This series of average intensity values ​​representing each subpixel position constitutes the final smooth and refined SSLSF sequence.

[0057] Combination Figure 4 (b) SSLSF is constructed based on subpixel binning. The actual slit image has a tilt angle of 2.86° relative to the vertical direction, from which the oversampling interval can be obtained. A 0.05x pixel size achieves 20x oversampling. Iterate through each pixel in each row of the ROI, calculating the centroid of that pixel relative to the precisely determined centroid of that row. The horizontal distance is used to project and accumulate the intensity value of the pixel to the corresponding 0.05 times pixel size level based on this sub-pixel relative distance. The final generated SSLSF curve is then calculated at intervals of [missing information]. It is fitted from a series of points, which greatly improves the sampling density. Combined with Figure 5 The SSLSF obtained by this invention has a smoother curve and better performance compared to LSF without oversampling.

[0058] Step 5: Perform a discrete Fourier transform on the SSLSF to obtain the uncorrected MTF; then, using the effective optical width, tilt angle, and oversampling interval of the slit target, use a slit width-tilt angle joint correction model to correct the uncorrected MTF to obtain the accurate MTF.

[0059] Combination Figure 6 The final MTF curve is obtained through slit correction and interpolation. The constructed SSLSF is multiplied term-by-term by a Hamming window to reduce spectral leakage artifacts caused by the finite length of the data sequence during subsequent Fourier transform. A one-dimensional Fourier transform is performed on the windowed SSLSF to obtain the complex form of the optical transfer function (OTF). The modulus of the OTF is taken to obtain the MTF, which is then normalized to 1.0 at the zero spatial frequency to obtain the uncorrected original MTF.

[0060] Theoretically, the slit width should be as small as possible to simulate an ideal line light source. However, in actual measurements, if the slit width is too small, the light passing through the slit is very weak, resulting in a very low signal-to-noise ratio. Therefore, the actual slit has a certain width, and the measured LSF is actually a convolution of the true LSF with a rectangular function. This causes the original MTF obtained after the Fourier transform to be... Function modulation leads to high-frequency attenuation. Furthermore, during oversampling using a tilted slit, when discrete data from multiple pixel rows are projected and averaged to a sub-pixel interval, this grading and averaging process is itself equivalent to the true LSF being multiplied by a width of... The rectangular function convolution will also introduce a frequency domain. Functional attenuation. Furthermore, during SSLSF construction, the data is integrated along the slit direction (tilt direction), but ultimately projected onto a subpixel grid in the horizontal direction. This projection causes spatial frequency scaling; the equivalent frequency f in the horizontal direction in the tilt direction is... To eliminate the aforementioned effects, the obtained raw MTF data needs to be divided by a factor determined by the effective optical width of the slit target. Decision Function, slit tilt angle θ, and oversampling interval Decision The function eliminates the influence of the rectangular function through deconvolution:

[0061] (10),

[0062] Where f is the spatial frequency. This is the uncorrected MTF. The effective optical width of the slit target. To obtain the accurate MTF, the corrected accurate MTF is then subjected to cubic spline interpolation to obtain the final MTF curve, as shown below. Figure 6 As shown, the MTF accuracy measured by the method of the present invention reaches 1%, which is a significant improvement compared with the traditional slit method.

[0063] In summary, this invention provides a mid-to-far infrared MTF measurement method based on the tilted slit method. From obtaining a preliminarily denoised digital image of the slit target through multi-frame averaging, to utilizing a centroid localization algorithm based on an iterative adaptive window function, to constructing a high-fidelity SSLSF and employing a slit correction model, each step aims to minimize the introduction and propagation of errors, thereby significantly improving the accuracy and stability of MTF measurement.

[0064] The above description is merely a specific embodiment of the present invention and is not intended to limit it. Although, with reference to this embodiment, those skilled in the art should readily understand that they can still make equivalent substitutions for some of the technical features in the foregoing solution. These modifications and substitutions do not change the essence of the solution and should all be included within the protection scope of the present invention.

Claims

1. A method for measuring mid- and far-infrared MTF based on the inclined slit method, characterized in that, The steps are as follows: Step 1: Obtain a digital image of the slit target using an MTF measurement system. The angle between the slit target and the pixel array of the image sensor is 1.5°~3°. Perform noise reduction and background subtraction processing on the digital image to obtain a preprocessed slit image. Step 2: For multiple pixel rows intersecting with the slit in the ROI region of the preprocessed slit image, the centroid localization algorithm based on iterative adaptive window function is used to obtain the precise centroid position of the slit in each pixel row, as follows; For each pixel row, the multi-feature fusion signal-to-noise ratio (MFFSNR) of that pixel row is calculated to obtain the corresponding SNR. An adaptive signal-to-noise ratio window function is then constructed using this SNR. The original intensity data of each pixel row in the ROI region of the preprocessed slit image from step 1 is multiplied point-by-point by the adaptive signal-to-noise ratio window function to obtain the intensity data of the windowed pixels. Based on the intensity data of the windowed pixels, the initial centroid position of the slit in that row is calculated. The adaptive signal-to-noise ratio window function is applied again, aligning its center with the initial centroid position of the slit in that pixel row obtained in the previous step, generating weighted intensity data. Based on the weighted intensity data, the optimized centroid position is calculated and used as the precise centroid position of the slit in that pixel row. Step 3: Use least squares linear regression to fit a straight line to the precise centroid position of each pixel row, obtain the slope of the fitted line, and calculate the precise tilt angle θ of the slit relative to the image sensor pixel array based on the slope of the fitted line. Step 4: Based on the precise tilt angle θ and the precise centroid position of the slits in each pixel row, first calculate the oversampling interval. ,by The pixel row is divided into multiple sub-pixel levels for the width, and the original intensity data of each pixel row is projected onto the corresponding sub-pixel level. Finally, they are merged into a sub-pixel coordinate system to construct the supersampling line spread function SSLSF. Step 5: Perform a discrete Fourier transform on the SSLSF to obtain the uncorrected MTF; then, using the effective optical width, tilt angle, and oversampling interval of the slit target, use a slit width-tilt angle joint correction model to correct the uncorrected MTF to obtain the accurate MTF.

2. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 1, characterized in that: Step 1 involves noise reduction and background subtraction of the digital image, as detailed below: Noise reduction is achieved by continuously acquiring multiple digital images of the slit target, precisely aligning them at the pixel level, and averaging them point by point to reduce the impact of time-related random noise. Background subtraction is achieved by first statistically analyzing the grayscale distribution of the entire image after noise reduction using a histogram, taking the grayscale value with the highest frequency as the background value, and then subtracting this value from the grayscale values ​​of all pixels to suppress background noise.

3. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 2, characterized in that, In step 2, for each pixel row, the multi-feature fusion signal-to-noise ratio (MFFSNR) of that pixel row is calculated to obtain the corresponding SNR. The calculation formula is as follows: (1), Where i is the row index of the current pixel. The mean gray value of the ROI region in the i-th row of the preprocessed slit image. Let be the standard deviation of the grayscale values ​​of the ROI region in the i-th row, and α and β be weighting parameters. This is the edge sharpness factor; The gradient-weighted SNR is calculated using the following formula: (2), in, The absolute value of the Laplace response of the slit region within the ROI region; The ratio of the two values ​​is the maximum absolute value of the Laplacian response of all pixels in the ROI region of the i-th row; the closer the ratio is to 1, the sharper the slit edge. Contrast enhancement factor The formula is as follows: (3), in, is the average value of the background area in the i-th row.

4. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 3, characterized in that, In step 2, the signal-to-noise ratio adaptive window function is constructed using the aforementioned SNR. The details are as follows: (4), Where j is the column index of the current pixel. Based on the amplitude coefficient, The modulation amplitude coefficient, for The center position, N is The effective width, For adaptive gain coefficients, For bandwidth modulation parameters, The signal-to-noise ratio of the current row. It is an error function that can adaptively adjust according to the noise level of the current pixel row.

5. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 4, characterized in that, In step 2, the centroid localization algorithm for the iterative adaptive window function is as follows: S2-1. In the first iteration, the original intensity data of each pixel row in the ROI region of the slit image is multiplied point-by-point by the signal-to-noise ratio adaptive window function to obtain the intensity data of the windowed pixels. Based on the intensity data of the windowed pixels, the initial estimate of the centroid of each pixel row of the slit is calculated, that is, the initial centroid position of the slit in each pixel row. : (6), in, The intensity data of each pixel after the first signal-to-noise ratio adaptive window function weighting is the intensity data of the pixels after windowing. The signal-to-noise ratio adaptive window function used in the first iteration has a period of the width of the ROI region of the slit image and covers the entire row of pixels, ensuring that the slit will fall within the coverage of the window function no matter where it is actually located. The center is half the width of the ROI region of the slit image, that is, its center point is the geometric center of the ROI region in the row direction. S2-2, the second iteration also uses a signal-to-noise ratio (SNR) adaptive window function with a period equal to the width of the ROI region, but its center is placed at the initial centroid position obtained in S2-1. This more accurately aligns the strongly weighted region of the SNR adaptive window function with the estimated slit position, generating weighted intensity data. Based on this weighted intensity data, the centroid calculation is further optimized to obtain the precise centroid position of the slit in each pixel row. : (7), in, The intensity data of each pixel after the second signal-to-noise ratio adaptive window function weighting is called the weighted intensity data.

6. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 5, characterized in that, In step 3, the linear equation for the least squares linear regression is: Where y is the pixel row number, x is the precise centroid position of that row, and k is the slope of the line equation, the formula for calculating the precise tilt angle θ is: (8)。 7. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 6, characterized in that, In step 4, the SSLSF construction process is as follows: S4-1, Based on the precise tilt angle θ and the pixel size of the image sensor Calculate the oversampling interval for: (9), S4-2, with the above oversampling interval Divide the width into increments, creating multiple sub-pixel increments; S4-3. Traverse each pixel row, calculate the horizontal distance of each pixel relative to the precise centroid position of the slit in step 2, and project the original intensity data of each pixel into the corresponding sub-pixel level based on the horizontal distance, and finally merge them into a sub-pixel coordinate system. S4-4. After traversing all pixels, the sum of the intensity data accumulated in each sub-pixel level in S4-3 is divided by the total number of pixels falling into that level, and then averaged to obtain the SSLSF.

8. The mid- and far-infrared MTF measurement method based on the inclined slit method according to claim 7, characterized in that, In step 5, a discrete Fourier transform is performed on the SSLSF to obtain the uncorrected MTF. Then, a joint correction model of slit width and tilt angle is used to correct the influence of slit width and oversampling on the measurement results, as follows: Divide the above uncorrected MTF by the effective optical width determined by the slit target. Function, slit precise tilt angle θ, and oversampling interval Decision The function yields the accurate MTF: (10), Where f is the spatial frequency. This is the uncorrected MTF. The effective optical width of the slit target. For accurate MTF.

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