Riesz Transforms for the Isotropic Estimation of the Local Phase of Moiré Interferograms

Abstract

The estimation of the local phase and local amplitude of 1-D signals can be realized by the construction of the analytic signal. This includes the evaluation of the signal´s Hilbert transform, which performs a phase shift. In the past, different definitions of the analytic signal of multidimensional signals have been proposed, all of which are based on different combinations of partial and total Hilbert transforms. None of these approaches is isotropic. We propose the use of Riesz transforms which are known to mathematicians as appropriate generalizations of the Hilbert transform to n-D. This approach allows the isotropic estimation of the intrinsically 1-D local image phase. Applications to Moir(´e) interferograms are shown.