A centroid calculation method for knife-edge MTF measurement

Abstract

The present invention discloses a centroid calculation method for knife-edge MTF measurement. The centroid calculation utilizes an iterative Gaussian weighting method, with a Gaussian function as the weighting function. The center position and width of the Gaussian function are adaptively changed. The knife-edge is a straight line, and when calculating the centroid position of a differential image row by row, the center position and width of the weighting function after the previous iteration serve as the initial values ​​for the subsequent iteration. The present invention utilizes an iterative weighting method to effectively improve the accuracy of knife-edge differential image centroid calculation, thereby improving MTF measurement accuracy. The parameters in this method can be adaptively corrected, making it applicable to MTF measurements of various optoelectronic systems under test.

Description

Technical Field

[0001] The invention belongs to the technical field of MTF calculation and relates to a centroid calculation method for knife-edge MTF measurement. Background Art

[0002] Modulation Transfer Function (MTF) is the transfer function of the modulation index. It is a quantitative description of the spatial frequency transfer characteristics of the imaging system and is an important development in image evaluation methods.

[0003] Among the current methods for measuring MTF, the line-pair card method can obtain high-precision MTF values. However, the line-pair card method can only provide MTF values ​​at a limited number of integer spatial frequency positions and cannot achieve a comprehensive evaluation of the system transfer function.

[0004] To obtain the MTF curve of an imaging system over its spatial frequency range, commonly used measurement methods include the slit method (SlitCamera) and the knife-edge method (EdgeMethod). Japan defines the slit method as the standard method for measuring MTF, and the knife-edge method has also been designated as the standard method for measuring system MTF by the International Electrotechnical Commission (IEC). Comparing the different MTF curves obtained for the same system using the slit and knife-edge methods reveals that the former has a higher signal-to-noise ratio at high frame rates, while the latter has a higher signal-to-noise ratio in the low-frequency domain. The system MTF obtained using the slit method is accurate, simple to operate, and a mature method. However, due to its high machining difficulty (slit width ≤ 10 microns, error within 1 micron), it is difficult to promote in practical applications. Because knife-edge measurement instruments are relatively easy to manufacture, they are widely used in scientific research experiments and routine testing.

[0005] The knife-edge method can be used to obtain the edge response function (ESF) of the knife edge, which reflects the degree of edge diffusion after passing through the imaging system. The derivative of ERF is the line spread function (LSF), and the system MTF can be obtained by Fourier transform. Currently, most of the research on MTF is based on the knife-edge method technology.

[0006] In order to obtain a high-resolution MTF curve, an improved MTF knife-edge measurement method is currently generally used, in which the knife-edge direction is set at a certain angle to the image sampling direction to obtain the oversampled edge response function (ERF), and then a high-resolution MTF curve is obtained through Fourier transform.

[0007] A crucial step in the ERF oversampling process is determining the knife-edge image tilt angle. This can be obtained by calculating the centroid of each row of the knife-edge image difference image and then performing a linear fit (ISO12233). Therefore, the accuracy of the knife-edge image difference image centroid calculation determines the accuracy of the MTF solution.

[0008] However, image noise from the optoelectronic system can affect the accuracy of the differential image centroid calculation for the knife-edge image. Image blur caused by relative motion during dynamic MTF measurement can also affect the accuracy of the differential image centroid calculation. While various methods (such as thresholding and weighting) can improve the accuracy of differential image centroid calculation, these methods typically require adjustment based on the knife-edge imaging parameters. Summary of the Invention

[0009] (1) Purpose of the invention

[0010] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a centroid calculation method for knife-edge MTF measurement - an iterative weighted method, in which the center position and width of the weighting function can be adaptively changed. Moreover, because the knife-edge is a straight line, when solving the centroid position of the differential image line by line, the center position and width of the weighting function after the previous iteration can be used as the initial value for the next iteration, which can greatly reduce the amount of calculation and improve the calculation speed.

[0011] (2) Technical solution

[0012] In order to solve the above technical problems, the present invention provides a centroid calculation method for knife-edge MTF measurement. The centroid calculation adopts an iterative Gaussian weighted method, and the weighting function adopts a Gaussian function. The center position and width of the Gaussian function are adaptively changed; the knife edge is a straight line. When solving the centroid position of the differential image row by row, the center position and width of the weighting function after the previous iteration are used as the initial value of the iteration of the next row, which greatly reduces the amount of calculation and improves the calculation speed.

[0013] The steps for solving the problem row by row are as follows:

[0014] S1: For the first row of difference images, use the traditional centroid method to find the centroid position of the difference image, which is used as the initial value of the center position of the weighting function. The centroid method calculation formula is as follows:

[0015]

[0016] Wherein, I(x) is a row of the differential image, that is, the grayscale value of the differential image at the coordinate position x.

[0017] S2: Set the initial value σ0 and minimum value σ of the weighting function width m ;

[0018] S3: Solve the weighting function according to the center position and width of the weighting function;

[0019] The weighting function w(x) can be expressed as c , a Gaussian function with width σ:

[0020]

[0021] S4: Based on the difference image and weighting function, solve the weighted 0th, 1st, and 2nd order moments of the difference image:

[0022]

[0023]

[0024]

[0025] Where I(x) is a row of differential image.

[0026] S5: Solve the center of mass position based on the 0th-order moment and the 1st-order moment, which is used as the center position of the weighted function for the next iteration:

[0027]

[0028] S6: Solve the weighting function width of the next iteration based on the 0th, 1st, and 2nd order moments;

[0029] The Gaussian width can be expressed as:

[0030]

[0031] When the calculated Gaussian width σ is less than the set minimum Gaussian width σ m , then the Gaussian width takes the minimum value, that is: σ=σ m ;

[0032] S7: Repeat S4-S7 until the stopping criterion is reached and the iteration stops; the stopping criterion is: the change of the center of mass position is less than a certain value;

[0033] S8: Start calculating the centroid of the next row of differential images, using the final centroid position of the previous row as the initial value of the center position of the weighting function of this row;

[0034] S9: Repeat steps S2-S7 to complete the centroid calculation of the differential image of this row;

[0035] S10: Repeat steps S8-S9 until all row difference image centroid calculations are completed.

[0036] (3) Beneficial effects

[0037] The centroid calculation method for knife-edge MTF measurement provided by the above technical solution adopts an iterative weighting method, which can effectively improve the accuracy of centroid calculation of knife-edge image differential images, thereby improving the accuracy of MTF measurement; the parameters in this method can be adaptively corrected and can be applied to MTF measurement of various optoelectronic systems to be tested. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the original knife edge image.

[0039] Figure 2 is the knife-edge image of the selected region of interest.

[0040] Figure 3 is the difference image.

[0041] Figure 4 is the curve of the centroid position and Gaussian weighting function changing with the number of iterations.

[0042] Figure 5 The centroid position of the difference image and its fitting line calculated by the iterative Gaussian weighting method.

[0043] Figure 6 The centroid position of the differential image and its fitting line calculated by the traditional centroid method. DETAILED DESCRIPTION

[0044] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0045] The centroid calculation method for knife-edge MTF measurement in this embodiment includes the following steps:

[0046] Step 1: Collect the original knife edge image, such as Figure 1 As shown, there are 256 rows and 320 columns in total;

[0047] Step 2: Select the knife edge image of the area of ​​interest and capture Figure 1 The center 64 rows and 32 columns of data, such as Figure 2 As shown;

[0048] Step 3: Calculate the difference of the selected knife edge image by column, and obtain the difference image as follows Figure 3 As shown;

[0049] Step 4: Set the initial value of the weighting function width to 10 pixels;

[0050] Step 5: Set the criteria for stopping iteration: ① The change in the centroid position is less than 0.001 pixel; ② The number of iterations exceeds 10; ③ The weighting function width is less than 1 pixel. If any of the three criteria is met, the iteration is stopped.

[0051] Step 6: Determine the centroid of the first row of the differential image; use the centroid method to determine the centroid position of the differential image as the initial value of the center position of the weighting function; the curve of the centroid position and the width of the Gaussian weighting function changing with the number of iterations is as follows: Figure 4 As shown;

[0052] Step 7: Calculate the centroid of the difference images of other rows one by one and perform a straight line fitting on them, such as Figure 5 As shown;

[0053] Figure 6 The centroid position and fitting line of the differential image calculated by the traditional centroid method are compared. Figure 5 and Figure 6 ,It can be seen that compared with the traditional centroid method, the iterative weighted method improves the accuracy of centroid position calculation by 4 orders of magnitude.

[0054] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A centroid calculation method for knife-edge MTF measurement, characterized in that: The centroid calculation adopts the iterative Gaussian weighting method, and the weighting function adopts the Gaussian function. The center position and width of the Gaussian function are adaptively changed. The knife edge is a straight line. When solving the centroid position of the differential image line by line, the center position and width of the weighting function after the previous iteration are used as the initial value of the iteration of the next line. The steps for solving the problem row by row are as follows: S1: For the first row of differential images, according to the traditional centroid method, the centroid position of the differential image is solved as the initial value of the center position of the weighting function S2: Set the initial value σ0 and minimum value σ of the weighting function width m ; S3: Solve the weighting function according to the center position and width of the weighting function; S4: According to the difference image and the weighting function, solve the weighted 0th, 1st, and 2nd order moments of the difference image; S5: Solve the centroid position based on the 0th-order moment and the 1st-order moment, which is used as the center position of the weighted function for the next iteration; S6: Solve the weighting function width of the next iteration based on the 0th, 1st, and 2nd order moments; S7: Repeat S4-S7 until the stopping criterion is reached and the iteration stops; the stopping criterion is: the change of the center of mass position is less than the set value; S8: Start calculating the centroid of the next row of differential images, using the final centroid position of the previous row as the initial value of the center position of the weighting function of this row; S9: Repeat steps S2-S7 to complete the centroid calculation of the differential image of this row; S10: Repeat steps S8-S9 until all row difference image centroid calculations are completed.

2. The centroid calculation method for knife-edge MTF measurement according to claim 1, wherein: In step S1, the centroid method calculation formula is as follows: Wherein, I(x) is a row of the differential image, that is, the grayscale value of the differential image at the coordinate position x.

3. The centroid calculation method for knife-edge MTF measurement according to claim 2, wherein: In step S3, the weighting function w(x) is expressed as c , a Gaussian function with width σ:

4. The centroid calculation method for knife-edge MTF measurement according to claim 3, wherein: In step S4, the weighted 0th, 1st, and 2nd order moments of the differential image are: Where I(x) is a row of differential image.

5. The centroid calculation method for knife-edge MTF measurement according to claim 4, wherein: In step S5, the centroid position is:

6. The centroid calculation method for knife-edge MTF measurement according to claim 5, wherein: In step S6, the Gaussian width of the next iteration is solved according to the 0th, 1st, and 2nd order moments: When the calculated Gaussian width σ is less than the set minimum Gaussian width σ m , then the Gaussian width takes the minimum value, that is: σ=σ m .

7. An application of the centroid calculation method for knife-edge MTF measurement according to any one of claims 1 to 6 in the field of MTF solution technology.

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