Quantitative phase imaging of weakly scattering objects using partially coherent illumination

In this paper, we extend our recent work on partially coherent quantitative phase imaging (pcQPI) from two-dimensional (2D) to three-dimensional (3D) imaging of weakly scattering samples. Due to the mathematical complexity, most theoretical modeling of quantitative phase image formation under partial coherence has focused on thin, well-focused samples. It is unclear how these abberations are affected by defocusing. Also, as 3D QPI techniques continue to develop, a better model needs to be developed to understand and quantify these aberrations when imaging thicker samples. Here, using the first order Born's approximation, we derived a mathematical framework that provides an intuitive model of image formation under varying degrees of coherence. Our description provides a clear connection between the halo effect and phase underestimation, defocusing and the 3D structure of the sample under investigation. Our results agree very well with the experiments and show that the microscope objective defines the sectioning ability of the imaging system while the condenser lens is responsible for the halo effect.