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

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.

Multiwavelength surface contouring from phase-coded noisy diffraction patterns: wavelength-division optical setup

“…The notation and the image formation model presented in this section follow those in our paper. 26 We present these results here for completeness of the presentation and in order to make clearer relations of the problems considered in Ref. 26 and in this paper.…”

“…This paper is a further development of the WD setup 27 with more details concerning the approach and the algorithm as well as the simulation study performed for the complexvalued objects and parameters of the experiments different from those in Ref. 26. The main results of this paper can be summarized as an extension of the conference paper 27 with demonstration of the efficiency of the proposed algorithm, which is computationally simpler, much more accurate and faster than the algorithm for WM in Ref.…”

“…We are focused on the reconstruction of the absolute phase φ o from a set of single wavelength experiments produced in a successive manner, which are registered by a wide-band gray-scale CCD sensor, instead of using all wavelengths simultaneously with CFA and demosaicing processing as it is done in the WM algorithm derived in Ref. 26.…”

“…The main results of this paper can be summarized as an extension of the conference paper 27 with demonstration of the efficiency of the proposed algorithm, which is computationally simpler, much more accurate and faster than the algorithm for WM in Ref. 26. The experimental study of the algorithm is restricted to simulation tests.…”

“…24,25 An approach to multiwavelength phase retrieval has been proposed in our recent papers. 26,27 The phase retrieval in the wavelength multiplexing (WM) setup is studied in the first of these two papers. A broadband light source radiates all wavelengths (RGB in our tests) simultaneously and a CMOS sensor equipped with a color filter array (CFA) registers spectral measurements.…”