Assessment of multifractal analysis in dynamic laser speckle signals using a spatial light modulator

Abstract

We assess and discuss several technical aspects of the multifractal statistical analysis applied to time series of dynamic speckle intensity signals. Due to the complexity of this goal, we implemented an optical setup that mimics the light scattering effect from the illuminated object using a spatial light modulator. The multifractal spectrum of the obtained dynamic speckle intensity signals is quantified by utilizing a mathematical framework based on the decomposition of wavelet leaders’ functions. The propagated light that is scattered utilizing the spatial light modulator verifies the well-known first- and second-order statistics of the obtained speckle images and also a given temporal correlation function determined by a copula algorithm adding several classes of fractional Gaussian noises. To experimentally implement these issues, we load appropriate dynamic temporal phase screens in the spatial light modulator working on phase-only mode and guide the light propagation through an optical setup composed of a 4f correlator. Different types of statistical trends in the scaling properties as a function of frequency sampling, intensity signal discretization, mean size of speckle, temporal correlation length, and vanishing moments of the elected mother wavelet analysis are theoretically and experimentally tested and compared.