Transport-of-intensity phase imaging using Savitzky-Golay differentiation filter--theory and applications

Several existing strategies for estimating the axial intensity derivative in the transport-of-intensity equation (TIE) from multiple intensity measurements have been unified by the Savitzky-Golay differentiation filter--an equivalent convolution solution for differentiation estimation by least-squares polynomial fitting. The different viewpoint from the digital filter in signal processing not only provides great insight into the behaviors, the shortcomings, and the performance of these existing intensity derivative estimation algorithms, but more important, it also suggests a new way of improving solution strategies by extending the applications of Savitzky-Golay differentiation filter in TIE. Two novel methods for phase retrieval based on TIE are presented--the first by introducing adaptive-degree strategy in spatial domain and the second by selecting optimal spatial frequencies in Fourier domain. Numerical simulations and experiments verify that the second method outperforms the existing methods significantly, showing reliable retrieved phase with both overall contrast and fine phase variations well preserved.