# Image Transmission through Scattering Media Using Ptychographic Iterative Engine
## 3 Experiment and Results  
To demonstrate our method, we employed a simplified setup as shown in Figure 2a. In this experimental setup, a narrowband LED emitting at \(633\pm 10\) nm was used as the incoherent illumination source. The expanded uniformed beam was then shone onto a digital micro-mirror device (DMD) from Texas Instruments (DLP 9500). In order to demonstrate the performance of the proposed technique for imaging beyond the memory effect range, we should use a target image with sufficient large lateral extension and diffract the incoming beam in large angles. The target image we selected then was a binary fringe pattern of \(200\times 200\) pixels in size, as shown in Figure 2b. As the pixel size of our DMD is 10.8 \(\upmu\)m, this corresponds to the physical area of the target about \(2.2\times 2.2\) mm\({}^{2}\), or, in equivalent, 0.0037 radian in terms of FOV. Displaying the target image on the DMD offers the advantage that we do not need to mechanically scan the target stepwise so as to release the mechanical instability. Instead, we can use an aperture displayed on the DMD as well and perform a virtual scanning by changing its position. The size of the aperture, \(d\), should be small enough to ensure it is within the range of the memory effect \(d\leq z\cdot\mathrm{FOV}\), where \(z\) is the distance between the target and the nearest surface of the scattering medium; \(z=60\) cm in our setup, and the FOV of the medium was 0.0015 radian as we measured. This allows us to use a probe aperture with the size of \(d=900\)\(\upmu\)m in our experiments. The beam reflected by the DMD is then passed through a thick ground glass, and captured by an sCMOS camera (PCO Edge 4.2), which was placed 12 cm away from the back surface of the scattering medium. The scanning interval of the aperture was about 120 \(\upmu\)m in our experiment, so that the camera captured 121 diffraction patterns after the aperture scanned across the whole target image. The collected speckles were divided into a series of sub-images with the size of \(200\times 200\) pixels. This size was chosen so that most information of the autocorrelation of probed object can be covered [20]. Owing to the ergodic property of the speckle [19], the spatial averaging of the autocorrelation functions calculated from the sub-images is in principle equivalent to the time averaging of the speckle images, which is equal to that of the target according to Equation (2). This also holds for the energy spectrum density. Therefore, for each part of the target selected by the aperture \(P(r-r_{j})\), (\(j=1,\ldots,121\)), the suppression of noise can be achieved by spatially averaging the autocorrelation of all the sub-images from the corresponding speckle image. The estimated 121 energy spectrum densities were then fed into our PIE algorithm. After 30 times of iteration, the improvement of the reconstructed image quality becomes negligible as the iteration continues. The correlation coefficient is 0.998 in our study. It took 12 s in total on a common personal computer (with the Intel Core i5 CPU and 8 GB memory, implemented in Matlab R2014a platform) without parallel processing. In this way, we reconstructed an image of \(200\times 200\) pixels in size with 121 numbers of the patterns projected on the object. A similar technique was proposed in References [7; 8]. However, in their methods, they need to project a plenty of fringe patterns on the object. Usually, thousands of fringe patterns are needed to reconstruct even a 64 \(\times\) 64 pixels image. Using the memory effect of scattering media, the fringe patterns projected on the scattering media are dramatically reduced in our method. The main experimental results are illustrated in Figure 3. In Figure 3a, we plotted the ground truth target image, which was loaded on the DMD. The reconstructed image is shown in Figure 3b. It is clearly seen that the target can be reconstructed using the proposed approach. In principle, the resolution in this case is limited by several factors.