# Research on Multipath Correlated Imaging with the Grayscale Target in Endoscopic Applications
## 3 Numerical and Experimental Results  
In this section, we use the numerical simulations and experiments to further analyze the influence of multipath effect on CI with a grayscale target in endoscopic applications. The experimental setup is shown in Figure 1b. The light source, made by a 532 nm laser passing through rotating ground glass, is split into three parts by a combination of two 50%-50% nonpolarizing beam splitters. The transverse size of the source \(a=1\) mm. In the object arm, one way of light passes through the object directly, and the other way of light passes through the object after being reflected by the reflector. The object light is detected by a bucket detector (Thorlabs PDA100A2). In the reference arm, the light freely propagates to the charge-coupled device (CCD) detector (Thorlabs DDC3240C), exposure time of the CCD is 0.2 ms. As shown in Figure 3a, we choose a grayscale image with four slits whose grayscale changes from light to dark and the levels are clearly divided as the target object. It is not only convenient to investigate the grayscale reconstruction ability of multipath correlated imaging, but also convenient to calculate the resolution. The slit width \(w=0.3\) mm and the distance between two adjacent slits \(d=0.3\) mm. The resolution can be defined as:  
\[R_{i}=Y_{i}/X_{i}\;(i=1,2,3). \tag{8}\]  
where \(Y_{i}\) represents the maximum grayscale value of the slit, \(X_{i}\) represents the maximum grayscale value of the adjacent slit spacing. According to the model of the multipath CI system, the object light is divided into two paths, and the path length of reflected light is longer than that of the direct light. In the following, we will first discuss the effect from the path length of the reflected light, i.e., the mismatch ratio, on the grayscale values of the reconstructed image, and the corresponding results are given in Figure 3b-g. The solid curves in the lower are the normalized horizontal sections of the patterns in the upper and the dashed curves correspond to the original object. It is obvious that the grayscale values of the reconstructed image vary with the mismatch ratio, which is mainly due to the existence of the defocused image. Figure 2: The normalized PSF of the multipath CI system for different (**a**) \(\eta\) when \(\rho=0.5\) and (**b**) \(\rho\) values when \(\eta=0.5\). To explain the phenomenon in Figure 3, the defocused images under different mismatch ratios are depicted in Figure 4. The upper are the numerical simulation results obtained over 5000 CCD frames, and the lower are the corresponding normalized horizontal sections. For the sake of comparison, we give the numerical simulation about the real image in Figure 4a, i.e., the image when there is no multipath effect. It should be noticed that by comparing the curves in Figure 4a-f, the defocused image gradually becomes smaller and the part with higher grayscale value moves towards the left with an increase of \(\eta\). By comparing Figure 4a with Figure 4b-f, it is found that as \(\eta\) increases, the maximum grayscale value of the defocused image gradually moves from the fourth slit of the real image to the third slit, so the normalized intensity of the fourth slit in the reconstructed image decreases from 1.0 to 0.67 approximately, as shown in Figure 3b,d,g, and the normalized intensity of the third slit increases from 0.78 (see Figure 3b) to 1.0 (shown in Figure 3d), and then remains unchanged. Figure 3: Comparison of reconstructed images and their normalized horizontal sections for a four-slit grayscale image, \(z=z_{1}=500\) mm, \(z_{2}=5\) mm, and \(\rho=0.5\): (**a**) grayscale object; (**b**) no multi-path effect; (**c**) \(\eta=0.2\); (**d**) \(\eta=0.4\); (**e**) \(\eta=0.6\); (**f**) \(\eta=0.8\); (**g**) \(\eta=1.0\). (**h**,**i**) are the relationships between the normalized intensity of the four slits and the resolution on mismatch ratio, respectively.