Fourier transform ghost imaging with complexity-guided phase retrieval

The ghost imaging (GI) scheme uses the statistical correlation between the intensities of the reference light field illuminating the object and the intensity emerging after interaction with the object. However, phase information is lost in the intensity correlation function due to the inherent property of the fourth-order correlation. Here, we propose and experimentally demonstrate a new Fourier transform ghost imaging (FTGI) technique. To address the phase loss issue, we have successfully implemented a phase retrieval iterative algorithm that utilizes a complexity-guided relaxed averaged alternating reflections (CG-RAAR) algorithm. This technique is robust against noise in the intensity correlation function used for phase reconstruction, ensuring faithful reconstruction results in the FTGI. The experimental realization of the FTGI is carried out using single-exposure speckle patterns and measuring the spatial intensity correlation of two speckle patterns. The two speckle patterns are recorded with and without the object, and the intensity correlation is assisted by the CG-RAAR algorithm for phase recovery. The experimental recordings and reconstruction results are presented for four objects with uniform and varying phase features.