Random encoding with a modified Gerchberg-Saxton algorithm for accurate ghost transmission through complex scattering media

High-fidelity information retrieval through complex scattering media has been a challenge. To address this issue, we present a modified Gerchberg-Saxton (GS) algorithm that generates random amplitude-only patterns to serve as information carriers. The modified GS algorithm imposes a support constraint to a random pattern in the image plane and scales the amplitude of its Fourier spectrum to control the sum of the pattern. Therefore, random patterns generated by the modified GS algorithm are encoded with pixel values of the transmitted data. The patterns are sequentially displayed by a spatial light modulator, and optical wave is recorded by a single-pixel detector. Optical experiments have been conducted to evaluate the method under various conditions, e.g., dynamic and turbid water and non-line-of-sight (NLOS). It is experimentally verified that the method can realize high-fidelity ghost transmission in complex scattering media.