Single-Shot Phase Retrieval by Interference Intensity: A Holography-Driven Problem for Periodic Signals

The phase-shifting digital holography (PSDH) is a typical problem in holography. It is traditionally conducted by the measurements from multiple shots. The four- and three-shot approaches to PSDH are commonly utilized for the imaging of static objects. Unlike this, the imaging of dynamic objects requires that PSDH should be conducted by single-shot measurements. Motivated by this, we are interested in the single-shot phase retrieval (PR) problem for periodic signals. The reference wave we use for such a PR model is the plane reference wave, and the measurements are the single-shot intensities. A single-shot PR algorithm is established. Additionally, it is observed that what is required for the four- and three-shot approaches are essentially the intensity differences. From the perspective of intensity difference, the stability of the algorithm is systematically investigated. In particular, it is found that the stability depends on the correlation between the wave vector and sampling set. Based on the wave vector, the choice scheme for sampling set is designed such that the recovery is well-conditioned in the noisy setting. The simulation of image recovery confirms the correctness of related results.