Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution

We have applied the technique of Fourier fringe analysis to microscopic interferograms of needle crystals that grow from a solution. We use a differential technique in which an empty field interferogram is compared with one that contains distortion and obscuration by the growing crystal, and we demonstrate both analytically and experimentally a phase shift sensitivity of 0.01 fringe with a spatial resolution of half of a fringe spacing (~1 µm). Following the analysis of the interferogram in two dimensions, we show that the three-dimensional refractive-index field around the crystal can be deduced, assuming that it is axially symmetric, by an iterative method.