# Image Transmission through Scattering Media Using Ptychographic Iterative Engine
## 3 Experiment and Results
For example, the size of the illumination spot on the scattering medium determines the size of the speckle grand, which should be large enough to be resolvable by the camera. When this is met, the resolution is mainly determined by the effective diameter, \(D_{p}\), of the variable iris placed between the scattering medium and the camera, which is given by \(\delta x=z\lambda/(\pi D_{p})\)[19]. In our setup, \(D_{p}=3\) mm, giving a theoretical resolution \(\delta x=40\) um. More effects of the variable iris on the image performance can be found in References [3; 12]. As the angular range of the total scanning area to the scattering medium is about 0.0037 radian, about two folds of the memory effect range, the conventional memory-effect-based method that directly uses the hybrid input-output algorithm (HIO) [11; 12] will fail to recover the target image. Indeed, we plotted a typical reconstructed image in Figure 3c. Nothing about the target can be recovered but noise. We calculated the correlation coefficient of the two reconstructed images with respect to the target. The associated values for Figure 3b,c are 0.74 and 0.42, respectively. Figure 3: Experimental results with scanning probe aperture. (**a**) The target image and the reconstructed image using (**b**) the proposed method and (**c**) the traditional hybrid input–output (HIO) phase retrieval algorithm. Scale bar: 1 mm. Figure 2: Experimental setup. (**a**) Experiment setup, (**b**) the target, and (**c**) an example of the probed beam as marked in red circle in (**b**). Within the range of memory effect, the captured speckle intensity is highly correlated with the target image [18; 19]. It is therefore expected that both the conventional phase-retrieval algorithm [11; 12] and the proposed PIE-based algorithm can reconstruct the target image. In comparison to the conventional algorithm, however, the proposed method uses strong support constraints (shape and position of the probe aperture) at the target plane and therefore should be more robust against noise and false solutions [26]. Indeed, when we used only one of the captured speckle patterns for reconstruction, we received the reconstructed images using these two algorithms, respectively, shown in Figure 4b,c. It is clearly seen that the shape and contrast of the reconstructed image using the PIE algorithm resembles that of the target, which is shown in Figure 4a. The correlation coefficients for Figure 4b,c with respect to Figure 4a are 0.79 and 0.69, respectively. On the other hand, if the object rather than the probe aperture can be scanned, as in the case that the object behind the scattering medium is self-illuminating and moving, the FOV can be further enlarged. To demonstrate this concept, we digitally translated the target with respect to fixed apertures, both of which were displayed on the DMD in a similar optical setup to that shown in Figure 2. The size of the aperture was 1.4 mm so that the FOV would be within the range of the memory effect. We translated a target of 8 mm \(\times\) 8 mm (shown in Figure 5a) along the \(x\) and the \(y\) directions stepwise across the aperture. Twenty-three steps with a step interval of 0.3 mm were translated in both directions, resulting in \(23\times 23=529\) sub-images that were taken by the camera. Using the proposed algorithm, we can reconstruct the image of the extended target within 1 min. The result is shown in Figure 5b, and the correlation coefficient is 0.93, suggesting that the image has been faithfully reconstructed.