Real time statistical analysis of random patterns withliquid crystals

Abstract

Several authors have recently applied incoherent-to-coherent conversion and optical information processing, to harmonic analysis of random spatial structures (speckle interferometry [1] analysis of shadow patterns associated with stellar scintillation [2]). Spatial power spectra are obtained by adding on a single photographic plate the intensity of the diffraction patterns produced by a large number of statistically independant images recorded on a photographic film. On the other hand, incoherent-to-coherent conversion has been performed using the dynamic scattering mode in nematic liquid crystals as an image storing device [6], [7], [8]. Such a device meets the needs for a real time statistical analysis of random structures. It is shown that temporal filtering (modulation) can be combined with spatial harmonic analysis in order to obtain three dimensional power spectra W(k, ω) of evolving random structures, as a function of the wave number k and of the temporal frequency ω. An experiment has been performed in which a random distribution of light dots in uniform motion is analysed. The diffraction pattern, recorded on a photographic plate with a 2s integration time, shows clearly interference fringes out of the noise(fig. 4). The separation of adjacent fringes is proportionnal to the modulation frequency and to the inverse of the speed of motion. Application such as the continuous monitoring of the velocity of a flow or the identification of atmospheric turbulent layers from the analysis of the motion of the shadow patterns associated with stellar scintillation, can be anticipated.