Variational Phase Imaging Using the Transport-of-Intensity Equation

Abstract—We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies—depending on the defocus value of the measurements—in a regularized fashion. The minimization task is solved iteratively via the alternatingdirection method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy d...

• Type: Journal
• Year: 2016
• Where: TIP
• Authors: Emrah Bostan, Emmanuel Froustey, Masih Nilchian, Daniel Sage, Michael Unser
• Keywords: Education, TIP 2016