Effect of imposed boundary conditions on the accuracy of transport of intensity equation based solvers

The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition (NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.

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