Shifting of wrapped phase maps in the frequency domain using a rational number

Abstract

The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed both by using an initial computer simulation and is subsequently validated experimentally on real fringe patterns. The technique may offer in some cases the prospects of removing the necessity for a phase unwrapping process altogether and/or speeding up the phase unwrapping process. This may be beneficial in terms of potential increases in signal recovery robustness and also for use in time-critical applications.