Differentiation method for phase recovery

Official URL: http://dx.doi.org/10.1117/12.2078106

Here we consider a derivative based method for phase recovery and demonstrate a numerical method that can be described as differentiate and cross multiply operation to obtain the phase gradient. This method uses quadrature phase data that is in sine and cosine form, which is a natural outcome many interferometric measurements including that of digital holographic reconstruction. Since the differentiation is performed on trigonometric functions which are discrete, it is shown that the method of differentiation and the sampling rate are important considerations especially for the noise corrupt signals. The method is initially developed for ID phase signals, and then later extended to 2D. Noise performance of the method is also investigated, and it is shown that for extremely noisy signals the method can be adapted to an iteration routine which recovers the phase successfully. We present simulations and the experimental results which show the validity of the approach.