We describe here two non-interferometric methods for the estimation of the
phase of transmitted wavefronts through refracting objects. The phase of th
e wavefronts obtained is used to reconstruct either the refractive index di
stribution of the objects or their contours. Refraction corrected reconstru
ctions are obtained by the application of an iterative loop incorporating d
igital ray tracing for forward propagation and a modified filtered back pro
jection (FBP) for reconstruction. The FBP is modified to take into account
non-straight path propagation of light through the object. When the iterati
on stagnates, the difference between the projection data and an estimate of
it obtained by ray tracing through the final reconstruction is reconstruct
ed using a diffraction tomography algorithm. The reconstruction so obtained
, viewed as a correction term, is added to the estimate of the object from
the loop to obtain an improved final refractive index reconstruction.