Hierarchically optical double-image correlation using 3D phase retrieval algorithm in fractional Fourier transform domain

In this paper, hierarchically optical double-image correlation is proposed by using 3D phase retrieval algorithm with a series of random function orders in fractional Fourier transform domain. At each hierarchical level, two grayscale input images are divided into particle-like points placed in 3D space, which are encoded into phase-only patterns using an iterative phase retrieval algorithm with a series of random function orders in fractional Fourier transform. The results illustrate that when the extracted phase-only patterns are compressed, optical double-grayscale-image correlation can be effectively conducted without the visualization of input information at each hierarchical level in 3D space. The proposed method provides a novel strategy for 3D optical security, and can effectively enhance the flexibility for the optically secured correlation in 3D space.