The effect of windowing in Fourier transform profilometry applied to noisy images

Abstract

This paper analyses the effectiveness of windowing to reduce errors in Fourier transform profilometry (FTP). Various levels of random noise have been added to simulated digital images of a spherical dome illuminated by fringes projected from an offset angle. The noisy images have been analysed using FTP with various window functions applied to the data before the forward Fourier transform. The theoretical dome was subtracted from the reconstructed domes to give error maps. The maximum and root mean square errors were calculated and plotted against the added noise level. At very low levels of added noise applying a pre-transform window produced considerably lower errors, nearly 50% lower for the Blackman window with no added noise. However, above around 10% added noise the reductions in the errors were reduced to only a few per cent. Whether pre-transform windowing is worthwhile therefore depends strongly on the noise content of the images.