Digital phase front retrieval from inline, Gabor-type holograms has to overcome the challenge of separating the object
wave from its conjugate by retrieving the phase of the optical field.
Recently, the so-called 'twin image problem' has received revived interest, mainly in conjunction with lens-less digital
holography applications in the XUV or X-ray bands. In this context, we propose to use a recently devised algorithm, the
iterative shadowgraphy method (ISM), to solve the twin-image problem and use the retrieved phase front for digital
The algorithm is based on the principle that the measurement of phase gradients, which drive the diffraction process,
enable the retrieval of the transverse phase profile of a field by observing its intensity distribution on different
We have proven rigorously that for small phase modulated object waves, the algorithm converges to the correct object
wavefront using just two snapshots of the propagated intensity field as input.
Because the algorithm is akin to a deconvolution algorithm, experimental noise can destabilize the iteration scheme. In
this work, we discuss the influence of noise in the ISM and apply a wavelet-based scheme to regularize the data. We
show that the phase retrieved from two experimental, defocused pictures of a weakly absorbing, scattering object can be
used to accurately reconstruct the object trough numerical back-propagation. Thus we prove that ISM is suitable for
digital holography applications.
We compare the ISM to various other schemes, such as direct backpropagation and the Gerchberg-Saxton algorithm and
find that the ISM scheme gives a much improved reconstruction of the phase front.