Refractive indices measurement of spherical particles by Fourier Interferometry Imaging

In this paper, the measurement of refractive indices of a set of spherical particles is presented. A set of particles is illuminated by a pulsed laser beam. The particles scatter the light toward a CCD camera. A complex interference fringe patterns are recorded by the CCD camera. These interferences fringes depend on these characteristics of the illuminated particles: 3D relative locations, sizes, and refractive indices. This is why it is possible to measure theses parameters from the analysis of interferences fringes. The interference pattern is a complicated 2D signal which may include Moiré effect patterns. In this work we present an analysis of the interference fringes using an approach based on Fourier Transforms, which provide a spectral representation of the fringes. The Fourier space representation of the fringes is a complex matrix characterized by a magnitude spectrum and a phase spectrum. In the Fourier magnitude spectrum, many spots are observed. The spot at the center of the spectrum corresponds to the fringes with low spatial frequency formed by interference between the reflected and refracted light signal scattered by each particle. The spots outside the center of Fourier magnitude spectrum correspond to the fringes with high spatial frequency, corresponding to interferences between light scattered by different particles. For the refractive index measurement of a pair of particles, an individual spot is selected and a rectangular filter centered on the spot is applied. Here, the magnitudes in Fourier space outside the filter are equal to zero. The next step is to take the inverse Fourier transform of the filtered Fourier space and trace the magnitude spectrum. The signal obtained is termed the “scattering composite function”. This function depends on refractive indices and sizes of the pair of particles. The inversion for the refractive index measurement is applied to this function.