Low frequency fringe pattern analysis via a Fourier transform method

The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that significant errors can arise when a low number of cycles of a sinusoid are present in the signal. In the following, we examine the case where the fringe pattern of interest only contains a few cycles of a sinusoid, looking at the adjustments that need to be made to the previous method in order to allow it to be used successfully, the causes of errors that arise, and the accuracy that can be expected to be obtained.