Reconstruction of 2D Gaussian phase from an incomplete fringe pattern using Fourier transform profilometry

Abstract

We show by simulation that Fourier transform profilometry (FTP) is capable of reconstructing a 2D Gaussian phase from incomplete fringe pattern. This incomplete fringe pattern is generated by removing some pixel information on the fringe. Using normalized mean square error (NMSE), we quantitatively analyze how much of the reconstructed Gaussian phase is affected by the removal of information on the fringe pattern. Results shows that the NMSE’s are considerably small with values scaled at 10^-2, which means that the reconstructed Gaussian phases are still comparable with the actual Gaussian phase. This study is important in fringe projection profilometry to determine how dark spots on the captured image affects surface measurements.