Fractal analysis of lyotropic lamellar liquid crystal textures

We apply fractal analysis to study the birefringence textures of lyotropic lamellar liquid crystal system (water/cethylpyridinium chloride/decanol). Birefringence texture morphologies are important as they provide information on the molecular ordering as well as defect structures and therefore has been adopted as a standard method in characterizing different phases of liquid crystals. The system under consideration shows a gradual morphological transition from mosaic to oily streak structures and then to maltese cross texture when the water content is increased. Since these textures are the characteristic fingerprints for the lyotropic lamellar phases, it is necessary to have robust techniques to obtain image quantifiers that can characterize the morphological structure of the textures. For this purpose we employ three different approaches namely the Fourier power spectrum for monofractal analysis, the generalized box-counting method for multifractal analysis and multifractal segmentation technique for estimating the space-varying local Hurst exponents. The relationships between estimated image parameters such as the spectral exponent, the Hurst exponent and the fractal dimension with respect to patterns observed in the birefringence textures are discussed.