# Image Transmission through Scattering Media Using Ptychographic Iterative Engine
## 4 Discussion and Conclusions  
Next, we show how the aperture size affects the reconstruction performance using a simulation. The target object we used was the 'Cameraman' with the size of \(300\times 300\) pixels. We zero padded it to \(1000\times 1000\) pixels in our simulations. We scanned the object with a circular aperture, the diameter  
Figure 4: A comparison between the PIE and Fienup algorithm. (**a**) Target image and the reconstructed image (**b**) using our method, and (**c**) the traditional HIO phase retrieval algorithm. Scale bar: 1 mm. Figure 5: Experimental results with object scanned. (**a**) The target and (**b**) the reconstructed image using our method. Scale bar: 1 mm. of which varied from 28 to 140 pixels. The overlapping ratio between two neighboring apertures in the course of scanning was fixed to be 75%. The scattering layer was a ground glass with the same structure. For simplicity, we supposed that the size of the target is within the range of the memory effect of the ground glass. Then, the probed image in each scan can be expressed as the convolution of the part of the target within the probe aperture with the point spread function \(S(r)\) of the ground glass. The speckle patterns used in our simulation were obtained by numerically calculating Equation (3), the convolution between the target and a series of \(S(r)\), which were experimentally collected in the lab. After feeding all the speckle patterns into the proposed algorithm, we obtained some typical reconstructed images, as shown in Figure 6b-h. Note that we just used the center \(200\times 200\) pixels of the reconstructed images in order to reduce the edge effect. We calculated the correlation coefficient between the target and the reconstructed image in all these cases, and the result is plotted in Figure 6i. The result suggested that the reconstruction performance of the proposed method is affected by the size of the probe aperture. The smaller the aperture, the better the reconstructed image quality. In our opinion, this result is mainly induced by two factors. First, a smaller probe aperture leads to a more compact constraint to the algorithm, which increases the robustness of the reconstruction. Second, in the speckle pattern, the number of independent realizations of the speckles is proportional to the area of the probed object. Thus, the use of smaller apertures results in higher speckle contrast [12]. We then made a simulation to show how the overlap ratio can influence the image performance. In this simulation, the diameter of the probe aperture was 66 pixels, and the overlap ratio varied from 39% to 91%. We moved the probe apertures to 255 different positions to show how large the effective area can be scanned in a given time. Some typical reconstructed images are shown in Figure 7b-h. The correlation coefficients between the target and the recovered results with center \(200\times 200\) pixels are demonstrated in Figure 7i with a red line. From the figure, we find that if the overlap ratio is less than 80%, the higher overlap ratio will lead to a better imaging performance. Figure 6: Effect of the diameter of the probe beam to the reconstruction performance. (**a**) The target, (**b**) 28 pixels, (**c**) 32 pixels, (**d**) 36 pixels, (**e**) 46 pixels, (**f**) 76 pixels, (**g**) 108 pixels, and (**h**) 140 pixels. (**i**) The correlation coefficient against a different aperture size. However, when the overlap ratio reaches a very high value, the reconstructed image quality will degrade, as the effectively scanned area will be reduced. We also calculated the correlation coefficient between the target and the recovered results with center \(150\times 150\) pixels (indicated with green line in Figure 7i) and \(100\times 100\) pixels (indicated with blue line in Figure 7i). The results indicate that a better reconstruction of the central part will come out with a higher overlap ratio.