Wavefront reconstruction in phase-shifting interferometry via sparse coding of amplitude and absolute phase

Area of Science:

• Coherent optical metrology
• Computational imaging
• Signal processing

Background:

• Phase-shifting interferometry offers high accuracy and speed for applications like industrial quality inspection.
• Wavefront reconstruction is challenging due to Poissonian noise and 2π phase ambiguity.
• Conventional methods struggle with absolute phase reconstruction and simultaneous phase unwrapping.

Purpose of the Study:

• To develop a novel algorithm for accurate wavefront reconstruction in phase-shifting interferometry.
• To address limitations of conventional techniques in handling noise and phase periodicity.
• To enable simultaneous reconstruction of object amplitude and absolute phase.

Main Methods:

• Formulating wavefront reconstruction as a sparse inverse problem.
• Utilizing sparse linear representations for amplitude and absolute phase.
• Introducing the sparse phase and amplitude reconstruction (SPAR) algorithm.
• Employing data-adaptive block-matching 3D (BM3D) frames for sparse representation.
• Accounting for Poissonian (photon counting) measurements.

Main Results:

• The SPAR algorithm effectively reconstructs both amplitude and absolute phase.
• SPAR demonstrates improved accuracy in interferometric phase reconstruction.
• Simultaneous phase unwrapping is achieved by SPAR.
• Experimental comparisons validate SPAR's effectiveness against competing methods.

Conclusions:

• Sparse modeling provides a robust framework for wavefront reconstruction in phase-shifting interferometry.
• The SPAR algorithm offers a significant advancement in overcoming noise and phase ambiguity.
• SPAR enhances the reliability and applicability of interferometric techniques for quality inspection and other fields.