Image analysis for the destabilization process of the petal pattern in a liquid crystal light valve with rotational optical feedback (Q1038458)

The destabilization process of the static petal pattern by measuring the spatial power spectrum and the autocorrelation functions in time is investigated. When a spatial rotation \(\frac\pi6\) is imposed on the feedback, the six-fold static petal pattern appears. By analyzing the time correlation for specific modes, one identified the most relevant modes able to trigger the bifurcation towards a chaotic behavior. The fluctuations of the petal pattern are analyzed by adopting the Karhunen-Loeve (KL) decomposition -- which is equivalent to the singular value decomposition and principal component analysis, expands a sequence of patterns into mutually uncorrelated sequences of patterns. In Section 2 is described the structure of the liquid crystal light value (LcLv) and the experimental setup. In Section 3 the power spectrum and the correlation functions are defined and then KL decomposition is introduced. In Section 4 experimental results are presented and the characteristic features of the fluctuations are discussed. The results of the paper are summarized in the last section.