  A novel phase retrieval algorithm for broadband hyperspectral phase imaging
from noisy intensity observations is proposed. It utilizes advantages of the
Fourier Transform spectroscopy in the self-referencing optical setup and
provides, additionally beyond spectral intensity distribution, reconstruction
of the investigated object's phase. The noise amplification Fellgett's
disadvantage is relaxed by the application of sparse wavefront noise filtering
embedded in the proposed algorithm. The algorithm reliability is proved by
simulation tests and results of physical experiments on transparent objects
which demonstrate precise phase imaging and object depth (profile)
reconstructions.
