Phase-shifting interferometry is a coherent optical method that combines high
accuracy with high measurement speeds. This technique is therefore desirable in
many applications such as the efficient industrial quality inspection process.
However, despite its advantageous properties, the inference of the object
amplitude and the phase, herein termed wavefront reconstruction, is not a
trivial task owing to the Poissonian noise associated with the measurement
process and to the phase periodicity of the observation mechanism.
In this paper, we formulate the wavefront reconstruction as an inverse problem,
where the amplitude and the absolute phase are assumed to admit sparse linear
representations in suitable sparsifying transforms (dictionaries). Sparse
modeling is a form of regularization of inverse problems which, in the case of
the absolute phase, is not available to the conventional wavefront
reconstruction techniques, as only interferometric phase
modulo- is considered therein. The developed sparse
modeling of the absolute phase solves two different problems: accuracy of the
interferometric (wrapped) phase reconstruction and simultaneous phase
unwrapping. Based on this rationale, we introduce the sparse phase and amplitude
reconstruction (SPAR) algorithm. SPAR takes into full consideration the
Poissonian (photon counting) measurements and uses the data-adaptive
block-matching 3D (BM3D) frames as a sparse representation for the amplitude and
for the absolute phase. SPAR effectiveness is documented by comparing its
performance with that of competitors in a series of experiments.
© 2014 Optical Society of America
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