Hilbert Transform Relations in Frequency-Domain Optical-Coherence Tomographic Imaging

Abstract

Interferometric imaging techniques typically embed the object phase information in the magnitude during the measurement process. During reconstruction, the phase is recovered from the magnitude by certain approximations on the measured magnitude and underlying phase. In this paper, we review some of our recent contributions on exact recovery of phase from Fourier transform magnitude measurements. We show that, under certain conditions, which are easily ensured during acquisition, the phase can be reconstructed accurately from the magnitude. More specifi cally, we show that there exist Hilbert transform relations between the logarithm of the magnitude and the phase. The new set of results constitute a generalization of the minimum-phase property to a larger class of signals than previously known in the literature. The key results are generic and are applicable to one-dimensional as well as two-dimensional signals. We fi rst present the results in a generic fashion. The theoretical claims are validated using the specifi c example of frequency-domain optical-coherence tomographic imaging.