Computational Phase Imaging in Nonlinear and Quantum Systems

Abstract

The integration of optical hardware and computational software interweaves strengths and alleviates limitations of both sides in the design of imaging systems. For example, computational algorithms treat imaging as a signal sensing, suggesting smart sampling and incorporating a priori information of the desired signal. On the other side, add-on optics resolves ill-posed digital processing and intractable computation by utilizing physical components and modeling. This interdisciplinary approach, called computational imaging, integrates optics, image processing and computer science to optimize the design of imaging systems.

This dissertation starts with a classic example of computational imaging in phase measurement, which gives important information about object surface, internal structure, optical depth, and wave dynamics. However, the phase of light oscillates so fast that CCD / CMOS camera can only capture the average field (i.e. the intensity), resulting in the loss of the phase of optical signal. Nevertheless, phase accumulates during optical propagation, meaning that the complex components can still be retrieved through intensity-only measurements by cooperating well-designed algorithms. Popular computational algorithms include deterministic approaches such as the transport-of-intensity equation (TIE) and statistical methods such as the Gerchberg-Saxton algorithm (GS). The former solves a wave equation by a set of in-focus and defocused images. The latter iterates intensity observations at the near- and far-field to find the optimal phase. However, both of them employ assumptions of linear propagation of light in classical systems. In this dissertation, we relax these assumptions and generalize computational methods with higher-order optics, including light-field imaging, nonlinear photonics and quantum entanglement, leading to prominent computational phase imaging.