  X-ray phase-contrast tomography (XPCT) is widely used for high contrast 3D
imaging using either synchrotron or laboratory microfocus X-ray sources. XPCT
enables an order of magnitude improvement in image contrast of the
reconstructed material interfaces with low X-ray absorption contrast. The
dominant approaches to 3D reconstruction using XPCT relies on the use of
phase-retrieval algorithms that make one or more limiting approximations for
the experimental configuration and material properties. Since many experimental
scenarios violate such approximations, the resulting reconstructions contain
blur, artifacts, or other quantitative inaccuracies. Our solution to this
problem is to formulate new iterative non-linear phase-retrieval (NLPR)
algorithms that avoid such limiting approximations. Compared to the widely used
state-of-the-art approaches, we show that our proposed algorithms result in
sharp and quantitatively accurate reconstruction with reduced artifacts. Unlike
existing NLPR algorithms, our approaches avoid the laborious manual tuning of
regularization hyper-parameters while still achieving the stated goals. As an
alternative to regularization, we propose explicit constraints on the material
properties to constrain the solution space and solve the phase-retrieval
problem. These constraints are easily user-configurable since they follow
directly from the imaged object's dimensions and material properties.
