Multiwavelength Absolute Phase Retrieval from Noisy Diffractive Patterns: Wavelength Multiplexing Algorithm

Vladimir Katkovnik,Nikolay Petrov,Igor Shevkunov,Karen Eguiazarian

doi:10.3390/app8050719

Vladimir Katkovnik, Nikolay Petrov + Show 2 more

Open Access

https://doi.org/10.3390/app8050719

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Abstract

We study the problem of multiwavelength absolute phase retrieval from noisy diffraction patterns. The system is lensless with multiwavelength coherent input light beams and random phase masks applied for wavefront modulation. The light beams are formed by light sources radiating all wavelengths simultaneously. A sensor equipped by a Color Filter Array (CFA) is used for spectral measurement registration. The developed algorithm targeted on optimal phase retrieval from noisy observations is based on maximum likelihood technique. The algorithm is specified for Poissonian and Gaussian noise distributions. One of the key elements of the algorithm is an original sparse modeling of the multiwavelength complex-valued wavefronts based on the complex-domain block-matching 3D filtering. Presented numerical experiments are restricted to noisy Poissonian observations. They demonstrate that the developed algorithm leads to effective solutions explicitly using the sparsity for noise suppression and enabling accurate reconstruction of absolute phase of high-dynamic range.

Highlights

Reconstruction of a wavefront phase is on demand in holography [1,2], interferometry [3], holographic tomography [4,5] and is of general interest due to important practical applications in such areas as biomedicine, 3D-imaging [8], micromachining [9], etc
The system is lensless with multiwavelength coherent input light beams and random phase masks applied for wavefront modulation
We demonstrate the performance of the WM-Absolute Phase Reconstruction (APR) algorithm for this quite difficult test-objects provided very noisy Poissonian observations

Summary

Introduction

Reconstruction of a wavefront phase is on demand in holography [1,2], interferometry [3], holographic tomography [4,5] and is of general interest due to important practical applications in such areas as biomedicine (for instance for studies of living cells [6,7]), 3D-imaging [8], micromachining [9], etc. The phase unwrapping with simultaneous processing of multiwavelength complex-exponent observations have been developed based on the maximum likelihood techniques [41,42] Another group of the multiwavelength absolute phase imaging techniques uses as measurements amplitudes or intensities of coherent diffraction patterns of an object without reference waves. We use the approach which can be treated as a development of the Sparse Phase and Amplitude Reconstruction (SPAR) algorithms [32,33] and the maximum likelihood absolute phase reconstruction for multiwavelength observations [42] This approach has been exploited in our paper [52] for absolute phase retrieval from multifrequency in the different setup with observations obtained for multiple single wavelength experiments. That in this paper the experiments are multiwavelength and phase information for each wavelength is retrieved by the developed wavelength multiplexing algorithm

Multiwavelength Object and Image Modeling

Noisy Observations

Algorithm Development

Setup of Experiments

Reconstruction Results

Conclusions