Phase sensitivity evaluation and its application to phase shifting interferometry

In quantitative phase imaging, sensitivity is a key measure of system reproducibility. Despite continuous experimental breakthroughs in achieving highly sensitive detection, in-depth studies of theoretical constraints on sensitivity are inadequate and comparisons between different techniques are difficult. In this paper, we introduce the method to evaluate the sensitivity of phase shifting interferometry which is a major category of quantitative phase imaging techniques. The method discusses in detail several key concepts of sensitivity evaluation, including a general three-level evaluation framework, a complete interference signal model, Cramér-Rao bound and algorithm sensitivity, algorithm and system efficiencies, as well as energy efficiency of an algorithm. In discussions of specific phase shifting algorithms, we focus on the shot noise-limited model. This simplified model not only reflects the rapid developments in modern detectors that are often dominated by shot noise, but also permits the calculation of theoretical sensitivities based on measured data, which is important in evaluating experimental performance. As examples, we study several common phase shifting interferometric techniques. The results of different techniques are compared to provide insights into algorithm optimization and energy efficiency of sensitivity. A normalized algorithm sensitivity table is also provided for readers to conveniently estimate their system's algorithm sensitivity and compare against experiments.