A method for calculating optical modulation transfer function based on knife-edge image

Abstract

The present invention provides a method for calculating an optical modulation transfer function based on a knife-edge image, comprising the following steps: using an optical modulation function measurement device to collect a knife-edge image and converting the knife-edge image into a grayscale image; calculating the knife-edge rising edge width of the grayscale image; performing a convolution operation on the grayscale image using a differential template matrix to obtain an LSF image; identifying the edge coordinates of the LSF image, and then rotating the LSF image using an affine transformation; and then performing a discrete Fourier transform to obtain an optical modulation transfer function curve. The optical modulation transfer function calculation method provided by the present invention calculates the average value of the rising edge pixel width of each row to obtain a corresponding adaptive differential convolution template, then convolves the knife-edge image to obtain a line spread function (LSF) image, and finally obtains an optical transfer function curve through a discrete Fourier transform. Because the differential method of this method relies on an adaptive differential template to perform convolution, it effectively removes noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical metrology, and in particular relates to a method for calculating an optical modulation transfer function based on a knife-edge image. Background Art

[0002] The optical modulation transfer function, also known as the spatial frequency response function (MTF), is an important indicator that quantitatively reflects the imaging quality of a system. In practical applications, it is measured as the number of rings or line pairs per unit length displayed in the image presented after the target passes through the optical system, generally expressed in line pairs per millimeter (lp / mm). Common methods for measuring MTF include the slit method, the knife-edge method, and the standard target method according to ISO 12233. The slit target used in the slit method is generally difficult to manufacture and expensive; the standard target relies on visual observation, which is less accurate and precludes precise quantitative analysis. The knife-edge method offers significant advantages in production and cost, as well as excellent accuracy and data analysis. Therefore, it is widely used to measure MTF in many applications.

[0003] Currently, traditional knife-edge MTF calculation algorithms primarily rely on directly fitting the edge spread function (EDF) or using the knife-edge image's histogram for calculation. However, due to the uncertainty of the mathematical model, the knife-edge edge pixel fitting method is prone to underfitting and overfitting, which increases the measurement error of the MTF calculation. Furthermore, the histogram-based calculation method is susceptible to the influence of image brightness and darkness, resulting in significant errors.

[0004] All of the traditional knife-edge image processing algorithms mentioned above require performing a differential operation on the image. This differential operation often increases the impact of noise, ultimately interfering with the MTF measurement results. Image noise is generally caused by the detector's dark current and background noise from ambient light. It is highly random and difficult to eliminate through filtering. Summary of the Invention

[0005] The purpose of the present invention is to solve the noise problem caused by the use of knife-edge images in imaging metrology in the prior art. It provides a method for calculating the optical modulation transfer function based on knife-edge images, and uses the method of constructing an adaptive image differential filter to achieve noise elimination and signal extraction.

[0006] To achieve the above objectives, the technical solutions provided by the present invention are:

[0007] A method for calculating an optical modulation transfer function based on a knife-edge image comprises the following steps:

[0008] Step 1: Use an optical modulation function measurement device to collect knife-edge images, and convert the collected multi-channel knife-edge images into a single-channel grayscale image;

[0009] Step 2: Traverse each pixel value in each row of the knife-edge image, count the number of pixels whose pixel values ​​are in the rising edge interval, and use the following formula to calculate the knife-edge rising edge width of the grayscale image:

[0010]

[0011] in, Represents the rising edge width of the grayscale image, The horizontal coordinate representing the pixel position, The vertical coordinate representing the pixel position, represent The ratio of the pixel value at to the maximum pixel value of the knife-edge image, Represents the number of pixels whose pixel values ​​are in the rising edge range, n represents the number of pixel columns in the knife-edge image, and the rising edge range refers to 10%-90% of the maximum pixel value of the knife-edge image;

[0012] Step 3: Based on the rising edge width of the knife edge, a differential template matrix is ​​constructed, and the differential template matrix is ​​used to perform a convolution operation on the grayscale image to obtain the LSF image;

[0013] Step 4: Identify the edge coordinates of the LSF image and then use affine transformation to rotate the LSF image to vertical;

[0014] Step 5: Perform discrete Fourier transform on the rotated LSF image to obtain the optical modulation transfer function curve.

[0015] Furthermore, in step 3, the length of the differential template matrix is ​​determined by the width of the rising edge of the knife edge.

[0016] Furthermore, in step 4, the edge coordinates of the LSF image are identified based on the ratio of the coordinate pixel value to the maximum pixel value of the knife-edge image, and the discrete point edge coordinates of the LSF image are obtained. The discrete point edge coordinates are fitted using the least squares method, and the slope and intercept of the fitting line are expressed as:

[0017]

[0018]

[0019] Among them, a represents the slope of the fitted line, b represents the intercept of the fitted line, and x i 、y i Represents the horizontal and vertical coordinates of discrete edge points, and M represents the number of calculated pixels; is the mean of the vertical coordinates of discrete edge points, is the mean of the horizontal coordinates of discrete edge points.

[0020] Furthermore, the slope and intercept of the fitting line can be used to obtain the tilt angle of the LSF image as -b / a, and the angle of rotation of the LSF image using affine transformation is the tilt angle.

[0021] Furthermore, the coordinates of each pixel point Perform affine transformation to obtain the corresponding pixel coordinates , expressed as:

[0022]

[0023] in, 、 The rotation matrix representing the affine transformation, , , 、 Represents the horizontal and vertical coordinates of the rotation center, represents the rotation angle, Represents the scale factor.

[0024] Furthermore, in step 5, the optical modulation transfer function curve obtained is:

[0025] X(k)=

[0026] in , Represents the horizontal coordinate of the corresponding pixel point, Represents the number of pixels in a row of the LSF image, Represents the horizontal coordinate sequence number of the original image pixel point, Represents the horizontal coordinate number of the new image after calculation, j represents an imaginary number;

[0027] The abscissa of the optical modulation transfer function satisfies:

[0028]

[0029] in, , the step size is 1, Represents the distance between two pixels.

[0030] The advantages of the present invention are:

[0031] The present invention provides a knife-edge image-based optical modulation transfer function calculation method. By calculating the average pixel width of each rising edge, a corresponding adaptive differential convolution template is obtained. This is then convolved with the knife-edge image to obtain a line spread function (LSF) image. Finally, the optical transfer function curve is obtained through a discrete Fourier transform. Because this method relies on an adaptive differential template for convolution, random noise fluctuations caused by adjacent points can be eliminated compared to traditional algorithms. Furthermore, it offers a high degree of automation, enabling automated and intelligent knife-edge image processing. Furthermore, it can fully extract and utilize the useful information contained in the knife-edge image to accurately calculate the modulation transfer function of the optical system. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The features and advantages of the present invention will become more readily understood through the following description with reference to the accompanying drawings, which are not drawn to scale and in which some features are exaggerated or minimized to show details of particular components.

[0033] Figure 1 1 is a schematic structural diagram of an optical modulation function measuring device according to an embodiment of the present invention;

[0034] Figure 2 is the knife edge image captured by the camera in the embodiment of the present invention;

[0035] Figure 3 is a flow chart of a method for calculating an optical modulation transfer function according to an embodiment of the present invention;

[0036] Figure 4 Schematic diagram of an algorithm for convolution of an adaptive differential template matrix and a grayscale image in an embodiment of the present invention;

[0037] Figure 5 is a graph of the edge spread function (ESF) of the knife edge in an embodiment of the present invention and the line spread function (LSF) of the two algorithms after differentiation;

[0038] Figure 6 The figure is a comparison of the optical transfer function calculated by the algorithm proposed in the present invention and the traditional algorithm in the embodiment of the present invention;

[0039] In the figure: 1-integrating sphere; 2-knife-edge target; 3-reflecting mirror; 4-camera. DETAILED DESCRIPTION

[0040] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is only for the purpose of illustration and is not intended to limit the present invention.

[0041] A method for calculating optical modulation transfer function based on knife-edge image, which is based on an optical modulation function measurement device. Figure 1 As shown, the optical modulation function measurement device includes: an integrating sphere light source 1, a knife-edge target 2, a reflector 3, a curved mirror 4 and a camera 5. The integrating sphere light source 1 emits white light, which is irradiated onto the knife-edge target 2 below it. The remaining light is reflected by one or more reflectors 3 below the knife-edge target 2 and is reflected onto the curved mirror 4 to form parallel light. Finally, the camera 5 collects the image as shown in FIG. Figure 2 The knife edge image is shown. The knife edge image is input into the computer for processing to obtain the optical modulation transfer function.

[0042] Optical modulation transfer function calculation method, such as Figure 3 As shown, the following steps are included:

[0043] Step 1: Use an optical modulation function measurement device to collect knife-edge images, and use a computer to convert the collected multi-channel knife-edge images into single-channel grayscale images using the following formula:

[0044]

[0045] Among them, R, G, and B represent the pixel values ​​under each channel, and GRAY represents the pixel value of the grayscale image.

[0046] Step 2: Calculate the width of the rising edge of the grayscale image.

[0047] Specifically, in the optical modulation function measurement device, the clarity of the knife-edge imaging is determined by the width of the boundary between the light and dark areas, that is, the rising edge width of the edge spread function of the knife-edge image. This width is usually defined as the width between 10% and 90% of the maximum pixel value. In the calculation of the knife-edge image, this is used as a benchmark to determine the size of the knife-edge rising edge width. Traverse each pixel value in each row to determine whether the pixel value is within the rising edge interval. If so, start counting, sum all the rows, and then calculate the average value. The knife-edge rising edge width of the grayscale image is calculated as shown in the following formula:

[0048]

[0049] Among them, width represents the width of the rising edge of the grayscale image, row represents the horizontal coordinate of the pixel position, height represents the vertical coordinate of the pixel position, and f(row,height) represents The ratio of the pixel value at to the maximum pixel value of the knife-edge image. number represents the number of pixels whose pixel values ​​are in the rising edge interval. n represents the number of pixel columns in the knife-edge image. The rising edge interval refers to 10%-90% of the maximum pixel value of the knife-edge image.

[0050] Step 3: Based on the width of the rising edge of the knife edge, a differential template matrix is ​​constructed, and the differential template matrix is ​​used to perform a convolution operation on the grayscale image to obtain the LSF image.

[0051] In optical theory: Due to the linear invariant optical system, the output light intensity distribution function (i.e. the grayscale image in this algorithm) is the input light intensity distribution function (i.e. knife-edge imaging illumination) and point spread function The convolution of the camera’s response efficiency to the knife-edge imaging illumination is expressed as:

[0052]

[0053] Among them, x and y represent the horizontal and vertical coordinate positions of the pixel point. Represents the convolution operation.

[0054] In the paraxial imaging region, the optical transfer function of the linear optical system is calculated by Fourier transforming the line spread function (LSF) image of the input light intensity distribution as a line pulse I(x). If the input light intensity is a line pulse I(x), then:

[0055]

[0056] The camera's response function to a line pulse is the line spread function (similar to a slit image in traditional algorithm processing), which is expressed as:

[0057]

[0058] Among them, it is manifested as the light intensity distribution in the horizontal axis direction after summing the vertical axis direction in the measured image.

[0059] The line spread function is the derivative of the edge spread function. It is expressed as:

[0060]

[0061] The specific operation in image processing is to perform pixel difference (i.e., derivative) on adjacent pixel points on the horizontal coordinate of the knife-edge image (i.e., edge spread function), and finally obtain the line spread function image.

[0062] In the present invention, the image pixels are convolved with the differential template to calculate, such as Figure 4As shown in the figure, the constructed differential template matrix is ​​a single row, and the length of the differential template matrix is ​​determined by the width of the rising edge of the knife edge obtained in step 3. The two end elements of the differential template matrix are 1, and the middle element is 0. After the differential template matrix is ​​constructed, the differential template matrix is ​​convolved with the grayscale image matrix. The specific operation is as follows: the differential template matrix is ​​placed at the top left position of the pixel matrix, the corresponding primary colors in the differential template matrix and the grayscale image matrix are multiplied and summed, and then the values ​​are replaced to the corresponding positions in the grayscale image matrix. Then, the differential template matrix is ​​differentially translated from left to right until the entire coverage calculation is completed, and the line spread function image is calculated, thereby achieving noise elimination.

[0063] Step 4: Identify the edge coordinates of the LSF image and then use affine transformation to rotate the LSF image to vertical.

[0064] The edge coordinates of the LSF image are identified based on the ratio of the coordinate pixel value to the maximum pixel value of the knife-edge image. The edge coordinates of the discrete points of the LSF image are obtained and fitted using the least squares method. The slope and intercept of the fitting line are expressed as:

[0065]

[0066]

[0067] Among them, a represents the slope of the fitted line, b represents the intercept of the fitted line, and x i 、y i Represents the horizontal and vertical coordinates of discrete edge points, and M represents the number of calculated pixels; is the mean of the vertical coordinates of discrete edge points, is the mean of the horizontal coordinates of discrete edge points.

[0068] The above formula can be used to obtain the tilt angle of the LSF image, and the LSF image can be rotated using affine transformation according to the tilt angle.

[0069] The coordinates of each pixel Perform affine transformation to obtain the corresponding pixel coordinates , expressed as:

[0070]

[0071] in, , The rotation matrix representing the affine transformation, , , 、 Represents the horizontal and vertical coordinates of the rotation center, represents the rotation angle, Represents the scale factor.

[0072] Step 5: Perform discrete Fourier transform on the rotated LSF image as shown below to obtain the optical modulation transfer function curve:

[0073] X(k)=

[0074] in , n represents the horizontal coordinate number of the LSF image pixel point, k represents the horizontal coordinate number of the new matrix calculated after discrete Fourier transform, Represents the horizontal coordinate of the pixel point, N represents the number of pixels in a row of the LSF image, and j represents the imaginary number i.

[0075] The abscissa of the optical modulation transfer function satisfies:

[0076]

[0077] in, , the step size is 1, Represents the distance between two pixels.

[0078] The algorithm of the present invention is compared with the traditional algorithm. The collected knife edge image is extracted as follows Figure 5 The ESF (edge ​​spread function) curve shown in the figure. After differential operation using two different algorithms, it is found that the width of the LSF curves calculated by the two algorithms are basically the same, indicating that the adaptive differential algorithm can basically guarantee the accuracy of MTF calculation. Figure 5 As can be seen, the line spread function curve calculated without the adaptive differential algorithm is asymmetrical, resulting in background noise within the abscissa of the ESF curve steps. This background noise is caused by the unevenness of the original knife-edge image. Therefore, using the adaptive differential algorithm of the present invention for image processing can eliminate this noise.

[0079] like Figure 6 As shown in the figure, the modulation transfer function curve calculated before the adaptive differential algorithm is used has obvious jitter and the low-frequency part changes rapidly, which shows that the experimental device has basic application value.

[0080] Finally, it should be noted that the features mentioned and / or illustrated in the above description of the exemplary embodiments of the present invention may be incorporated into one or more other embodiments in the same or similar manner, combined with features in other embodiments, or substituted for corresponding features in other implementations. The technical solutions obtained by such combination or substitution shall also be deemed to be included in the scope of protection of the present invention.

Claims

1. A method for calculating optical modulation transfer function based on knife-edge image, characterized in that: The following steps are involved: Step 1: Use an optical modulation function measurement device to collect knife-edge images, and convert the collected multi-channel knife-edge images into a single-channel grayscale image; Step 2: Traverse each pixel value in each row of the knife-edge image, count the number of pixels whose pixel values ​​are in the rising edge interval, and use the following formula to calculate the knife-edge rising edge width of the grayscale image: in, Represents the rising edge width of the grayscale image, The horizontal coordinate representing the pixel position, The vertical coordinate representing the pixel position, represent The ratio of the pixel value at to the maximum pixel value of the knife-edge image, Represents the number of pixels whose pixel values ​​are in the rising edge range, n represents the number of pixel columns in the knife-edge image, and the rising edge range refers to 10%-90% of the maximum pixel value of the knife-edge image; Step 3: Construct a differential template matrix. The length of the differential template matrix is ​​the width of the rising edge of the knife edge, and the elements at both ends are 1 and the middle element is 0. Use the differential template matrix to perform convolution operation on the grayscale image to obtain the LSF image. Step 4: Identify the edge coordinates of the LSF image and then use affine transformation to rotate the LSF image to vertical; Step 5: Perform discrete Fourier transform on the rotated LSF image to obtain the optical modulation transfer function curve.

2. The optical modulation transfer function calculation method according to claim 1, wherein: In step 3, the length of the differential template matrix is ​​determined by the width of the rising edge of the knife edge.

3. The optical modulation transfer function calculation method according to claim 1, wherein: In step 4, the edge coordinates of the LSF image are identified based on the ratio of the coordinate pixel value to the maximum pixel value of the knife-edge image, and the discrete point edge coordinates of the LSF image are obtained. The discrete point edge coordinates are fitted using the least squares method, and the slope and intercept of the fitting line are expressed as: Among them, a represents the slope of the fitted line, b represents the intercept of the fitted line, and x i 、y i Represents the horizontal and vertical coordinates of discrete edge points, and M represents the number of calculated pixels; is the mean of the vertical coordinates of discrete edge points, is the mean of the horizontal coordinates of discrete edge points.

4. The optical modulation transfer function calculation method according to claim 3, wherein: The slope and intercept of the fitting line can be used to obtain the tilt angle of the LSF image, which is -b / a. The LSF image is rotated by the rotation angle using affine transformation, where the rotation angle is equal to the tilt angle.

5. The optical modulation transfer function calculation method according to claim 4, characterized in that: The coordinates of each pixel Perform affine transformation to obtain the corresponding pixel coordinates , expressed as: in, 、 The rotation matrix representing the affine transformation, , , 、 Represents the horizontal and vertical coordinates of the rotation center, represents the rotation angle, Represents the scale factor.

6. The optical modulation transfer function calculation method according to claim 1, wherein: In step 5, the optical modulation transfer function curve obtained is: X(k)= in , Represents the horizontal coordinate of the corresponding pixel point, Represents the number of pixels in a row of the LSF image, Represents the horizontal coordinate sequence number of the original image pixel point, Represents the horizontal coordinate number of the new matrix after calculation, j represents the imaginary number; The abscissa of the optical modulation transfer function satisfies: in, , the step size is 1, Represents the distance between two pixels.

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