Singular-value demodulation of phase-shifted holograms

Abstract

We report on phase-shifted holographic interferogram demodulation by singular value decomposition. Numerical processing of optically-acquired interferograms over several modulation periods was performed in two steps : 1-rendering of off-axis complex-valued holograms by Fresnel transformation of the interferograms; 2-eigenvalue spectrum assessment of the lag-covariance matrix of hologram pixels. Experimental results in low-light recording conditions were compared with demodulation by Fourier analysis, in the presence of random phase drifts.Recording optical holograms by time-modulated interferometry was proposed and demonstrated in early studies [1][2][3]. It pioneered the development of phaseshifting [4] holographic interferometry. Time-modulated phase-shifting interferometry involves recording of a sequence of interferograms over at least one modulation cycle of the intensity. Temporal demodulation consists in a linear combination of a sequence of recorded interferograms, whose coefficients are the ones of a discrete Fourier transform [5][6][7]. An important feature of holographic interferometry is to allow spatial signal modulation in off-axis recording conditions [8], which permits the discrimination of self-beating and crossbeating interferometric contributions of the object field and the reference field. In this configuration, spurious interferometric contributions can be filtered-off [9]. It was demonstrated that the combination of spatial and temporal signal modulation enables low-light imaging at shot noise levels [10,11]. Important features and applications include optical phase imaging [12][13][14][15] and detection tunability in the radiofrequency range for optical heterodyne detection [16], frequency-resolved narrowband sensing of scattered optical radiation [17][18][19]. Sensitivity is compatible with photon-counting recording conditions [20][21][22]. In standard phase-shifting interferometry, a sequence of interferograms with known phase shifts between probed and reference optical waves is recorded. When the modulation is not known, principal component analysis [23] can be used for nonparametric, non-iterative demodulation. It identifies uncorrelated variables in the structure of the data (the principal components) from the analysis of its correlations. Non-parametric approaches were also applied to image formation concepts [24], speckle reduction [25][26][27][28][29], and laser speckle contrast analysis of flows [30].In this letter, we demonstrate experimentally that the sensitivity of low-light optical signal retrieval in time-modulated holographic interferometry can be improved with respect to Fourier transform demodulation in practical conditions, when random signal fluctuations are present. For that purpose, a data-driven, nonparametric signal processing method is used. It consists of calculating the spectrum of eigenvalues in a singular value decomposition (SVD) of the lag-covariance matrix of recorded temporal fluctuations of the hologram's pixels, after spatial Fresnel transformation. The p...

Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography

“…Nevertheless, as both the reference field and the object field have a common optical path, it is impossible to act on one or the other independently. This issue can be tackled with an off-axis digital holography configuration [9], which, for instance, makes it possible to characterize both amplitude and phase objects [10,11] down to shot noise limits [12][13][14]. However, the complexity of the experimental set-up is not suitable for severe experimental environments.…”

Real-time digital holography of the retina by principal component analysis

“…It identifies uncorrelated variables in the structure of the data, the principal components, from the analysis of its correlations. It is the spatial average counterpart of the decomposition of local digital hologram variations with time demonstrated for low-light temporal demodulation in the presence of random phase drifts [5]. A window of opportunity for retinal imaging by inline digital holography in real-time is opened with such data-driven adaptive temporal signal demodulation on a graphics processing unit (GPU).…”