# Research on Multipath Correlated Imaging with the Grayscale Target in Endoscopic Applications
## 3 Numerical and Experimental Results
To illustrate the change of grayscale distribution more clearly, we give the dependence of the normalized intensity for each slit on \(\eta\) in Figure 3. When \(\eta<0.3\), the grayscale values of the second and the third slits increase. After \(\eta\) reaches 0.3, the grayscale value of the third slit exceeds that of the fourth slit, so the image is significantly distorted. When \(\eta<0.3\), the grayscale distribution has slightly fluctuation, thus the disturbance of multipath effect can be ignored. It clearly emerges that when the mismatch ratio increases, a defocused image with the decreasing size is generated, which results in a decrease of the superposition area between the defocused image and the real image. At this point, the conclusion is drawn that the variation area of grayscale values for the reconstructed image is mainly determined by the mismatch ratio. It should be emphasized that, the deviation of the defocused image relative to the real image is 0 in Figure 3. For the case with the existence of the deviation, the maximum grayscale value may appear in other locations. To verify the correctness of the PSF in Figure 2, the dependence of \(\eta\) on imaging resolution is given in Figure 3. It is shown that the resolution presents a downward trend with an increase of \(\eta\). Then, we focus on another parameter, the reflection ratio, which determines the intensity change of the reflected light. Shown in Figure 5 and are the reconstructed images for different reflection ratios when \(\eta\) is 0.8. Because of energy attenuation in the process of the reflection, the power of reflected light is generally much lower than that of direct light, so the range of reflection ratio is chosen as \(0\leq\rho\leq 0.5\). The increase of \(\rho\) aggravates the interference caused by the defocused image, so the edges of the reconstructed image in Figure 5 and appear somewhat blurred. The dependence of the normalized intensity of four slits on \(\rho\) is given in Figure 5e. When \(\rho<0.2\), the fluctuation of grayscale distribution is quite small. The grayscale value of the third slit gradually reaches the maximum. As shown in Figure 5a-e, the increase of \(\rho\) lead to significant distortion of the image, and it is obvious that the variation amplitude of grayscale values for the reconstructed image increases with the increase of the reflection ratio. From the above discussion, the disturbance caused by multipath effect can be ignored when \(\rho<0.2\). By comparing Figure 3 with Figure 5, we can draw the conclusion that the influence of \(\eta\) on the grayscale distribution is bigger than that of \(\rho\). The influence of \(\rho\) on imaging resolution is also analyzed, and the results are plotted in Figure 5f. Obviously, imaging resolution dramatically decreases with the increasing \(\rho\), while the degree of decline is smaller than that in Figure 3i, which indicates that the effect from \(\eta\) is bigger than that from \(\rho\). For the sake of verifying the changes on the grayscale distribution and the resolution in numerical simulation, we implement CI with multipath effect experimentally. The corresponding results obtained over 5000 CCD frames are shown in Figure 6. The experimental results are in agreement with the above theoretical results, i.e., the conclusion about the variation of grayscale distribution of the reconstructed image is in accordance with the theoretical results, and \(\eta\) has a stronger influence on CI with multipath effect when compared with \(\rho\). Figure 5: Reconstructed images for (**a**) \(\rho=0.15\); (**b**) \(\rho=0.25\); (**c**) \(\rho=0.35\); (**d**) \(\rho=0.45\). The mismatch ratio \(\eta=0.8\), and other parameters are the same as those in Figure 3. The relationship between the normalized intensity of four slits (**e**) and the resolution (**f**) on reflection ratio.