Wavefront reconstruction in digital off-axis holography via sparse coding of amplitude and absolute phase

Abstract

This work presents the new method for wavefront reconstruction from a digital hologram recorded in off-axis configuration. The main feature of the proposed algorithm is a good ability for noise filtration due to the original formulation of the problem taking into account the presence of noise in the recorded intensity distribution and the sparse phase and amplitude reconstruction approach with the data-adaptive block-matching 3D technique. Basically, the sparsity assumes that low dimensional models can be used for phase and amplitude approximations. This low dimensionality enables strong suppression of noisy components and accurate revealing of the main features of the signals of interest. The principal point is that dictionaries of these sparse models are not known in advance and reconstructed from given noisy observations in a multiobjective optimization procedure. We show experimental results demonstrating the effectiveness of our approach.

Noise minimised high resolution digital holographic microscopy applied to surface topography

“…Further development of that technique was produced in the recent paper [18]. The key idea of the new algorithm is the application of the sparse approximation technique [17] for modelling the object amplitude and phase as functions of the coordinates.…”

“…The details of this iterative algorithm referred as Sparse Phase and Amplitude Reconstruction (SPAR) can be seen in [18]. In this paper a number of modifications have been made in the algorithm in according with features of experiment and sample under investigation.…”

“…In this paper a number of modifications have been made in the algorithm in according with features of experiment and sample under investigation. First, a spherical reference wavefront as well as a plane one are incorporated in (7) contrary to the linear wavefront which is only exploited in [18]. Second, the operating window dimensions x m are 20-by-20 pixels, and Gaussian standard deviation is 5, which have been produced to improve the reconstruction results.…”

Experimental study of the effects of the spatial filtering on off-axis digital holography operating out and in of the diffraction limit

“…El orden cero de difracción con un nivel mayor de intensidad, esencialmente oculta la información de la imagen virtual (desenfocada) y de la imagen real (enfocada) que se alcanza a observar con muy bajo contraste. Se han reportado diferentes metodologías que permiten aislar la imagen de interés [19][20][21][22], bien sea la correspondiente al orden difractado +1 ó -1 . Sin embargo, el método que es de interés para el análisis realizado es el propuesto por Takeda y conocido con el nombre de filtrado espacial [18].…”

Fringe contrast enhancement of digital off-axis hologram via sparse representation

“…Efforts have been made to employ this tool in the digital holography field [11][12][13] . Katkovnik et al [14,15] utilized the sparse coding of the amplitude and absolute phase to reconstruct the wavefront in phase-shifting interferometry and digital off-axis holography. Memmolo et al proposed a refocusing criterion via sparsity measurements in digital holography [16] .…”