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Area of Science:

Physics
Optics
Imaging Science

Background:

Grating-based phase-contrast imaging combined with X-ray microscopy presents complex image formation challenges.
Transverse fringe shifts typically exhibit a nonlinear relationship with wavefront phase differences.

Purpose of the Study:

To introduce an iterative reconstruction scheme that accurately models the nonlinear dependency in X-ray grating interferometry.
To enhance the applicability of X-ray grating interferometry for wavefront sensing and imaging.

Main Methods:

An iterative reconstruction scheme was developed utilizing a regularized maximum likelihood cost function.
The scheme was validated through comprehensive numerical simulations.

Main Results:

The proposed method effectively accounts for the nonlinear dependence of fringe shifts on phase differences.
The reconstruction scheme demonstrates significant advantages in low photon count scenarios.
It performs well when standard deconvolution-based reconstruction assumptions are not met.

Conclusions:

The developed iterative reconstruction scheme broadens the utility of X-ray grating interferometry.
This advancement supports more robust wavefront sensing and imaging applications, especially under challenging conditions.