A wavelet and Zernike-polynomial-based shearing interferometry approach to analyse hydrodynamic instabilities at interfaces

We present a hybrid algorithm to analyse complex interferograms with significant fringe deformations without an a-priori given zero-phase image containing the optical aberration of the instrument. Situations of this type frequently appear in fluid physics experiments using lateral shearing interferometers. The algorithm proposed employs a wavelet transformation in parallel with an approximation of the phase field directly after the experimental container is filled applying Zernike polynomials. As a result the aberrations of the interferometer can be described by a few coefficients. The subtraction of these phase aberrations can be traced back to a complex multiplication in the wavelet space which strongly reduces the effort of the phase unwrapping using the Goldstein algorithm. We explain the performance of the algorithm, which is not restricted to a particular interferometer type, by applying it to interferograms captured during a recent microgravity experiment.