## 4 Practical Multidirectional MTF Measurement Method
### Multi-state MTF Measurement  
In order to reduce the fluctuation of MTF results caused by different ROI extraction, this paper will measure MTF several times by extracting different ROI-H and different positions in the same edge image and improve the accuracy of the edge method from the statistical point of view. The multi-ROI automatic extraction strategy proposed in this paper is shown in Algorithm 1. When the determined edge image size is large enough, the multi-ROI will be automatically extracted according to the condition that \(X_{max}\)-\(R_{min}\) > 10, and ten sub-ROIs with different sizes and positions will be extracted. \(R_{min}\) represents the least number of valid rows. \(X_{max}\)-\(R_{min}\) represents the maximal number of valid row areas. The specific calculation formula is shown in Algorithm 1. According to the analysis results in Section 3.3, when the ROI-H ratio is above 0.5, the robustness of MTF results is relatively high. Therefore, only six extracted sub-ROIs with an ROI-H ratio of 0.5\(\sim\)1: ROI5\(\sim\)ROI10 can be used in practical application.  
ISO-cos projection binning is adopted in the modified edge method. In order to further improve the accuracy, multi-phase binning is adopted as an auxiliary method (see Figure 1 for the schematic diagram of binning PS). For the specific application diagram of a multi-phase binning method, please refer to reference [15]. In this paper, the number of binning PS (_PS_Num_) is adaptively determined according to the edge angle as Equation (14). When the edge angle is \"too small,\" the projection data is the largest. It is not suitable for the ideal optimal OSR model, so the binning PS is set to the maximum (such as 8) to ensure the accuracy. When the edge angle is \"moderate,\" the stability and accuracy of the edge method are high, so the number of binning PS is set to a minimum (such as 4) to save the computational cost. When the edge angle is \"relatively small or large\", the accuracy of the edge method is average, so the number of binning PS is set moderately (such as 6).  
```
Input: \({}^{\text{\textregistered}}\)Edge image, \({}^{\text{\textregistered}}\)Edge angle(\(\theta\)), \({}^{\text{\textregistered}}\)Number of edge image row(\(R\)). Calculation: \({}^{\text{\textregistered}}\)Least number of valid rows (\(R_{min}\) = ceil(1/tan(\(\theta\)))), \({}^{\text{\textregistered}}\)Maximal number of valid row area (\(X_{max}\)-\(R_{min}\) = floor(\(R/R_{min}\))).  where ROI Height is \(k\)-Full or \(g\)-\(R_{min}\) (\(k\)\(\in\)(0,1], \(g\)\(\in\)\(Z\).);  where ROI Position should be determined from Top, Middle or Bottom. if\(X_{max}\)-\(R_{min}\)\(\in\)(0,3)  ROI-Num = 1\(\rightarrow\)ROI1(Full, Middle) elseif\(X_{max}\)-\(R_{min}\)\(\in\)(3,5)  ROI-Num = 4\(\rightarrow\)ROI1(3-\(R_{min}\), Top), ROI2(3-\(R_{min}\), Middle), ROI3(3-\(R_{min}\), Bottom), ROI4(Full, Middle). elseif\(X_{max}\)-\(R_{min}\)\(\in\)(5,10)  ROI-Num = 8\(\rightarrow\)ROI1(3-\(R_{min}\), Top), ROI2(3-\(R_{min}\), Bottom), ROI3(5-\(R_{min}\), Middle), ROI4(5-\(R_{min}\), Top), ROI5(5-\(R_{min}\), Bottom), ROI6(0.5-Full, Top),  ROI7(0.5-Full, Bottom), ROI8(Full, Middle). else\(X_{max}\)-\(R_{min}\)> 10  ROI-Num = 10\(\rightarrow\)ROI1(3-\(R_{min}\), Top), ROI2(5-\(R_{min}\), Bottom), ROI3(8-\(R_{min}\), Middle), ROI4(10-\(R_{min}\), Middle), ROI5(0.5-Full, Top), ROI6(0.6-Full, Middle),  ROI7(0.7-Full, Bottom), ROI8(0.8-Full, Top), ROI9(0.9-Full, Bottom),  ROI10(Full, Middle). end
```  
**Algorithm 1** Automatic determination strategy of multi-ROI for edge image  
\[PS_{Num}=\begin{cases}8&,\theta\in[0,3.18)\ or\Big{[}0,\arctan\Big{(}\frac{1}{18} \Big{)}\Big{)}\text{deg}\\ 6&,\theta\in[3.18,6.34)\ or\Big{[}\arctan\Big{(}\frac{1}{18}\Big{)},\arctan \Big{(}\frac{1}{8}\Big{)}\Big{)}\text{deg}\\ 4&,\theta\in[6.34,14.04]\ or\Big{[}\arctan\Big{(}\frac{1}{9}\Big{)},\arctan \Big{(}\frac{1}{4}\Big{)}\Big{]}\text{deg}\\ 6&,\theta\in(14.04,45]\ or\Big{(}\arctan\Big{(}\frac{1}{4}\Big{)},\arctan(1) \Big{)}\text{deg}\end{cases} \tag{14}\]