Determination of height profile from a two-dimensional fringe signal using a two-dimensional continuous wavelet transform

Authors: ÖZLEM KOCAHAN YILMAZ

Abstract: The main objective of this study was 3-dimensional (3D) profile measurements with standard fringe projection, consisting of a CCD and a projector. For obtaining height information of objects pixel by pixel, phases have to be calculated from the images taken by the fringe projection technique. In this study, the 2-dimensional continuous wavelet transform (2D CWT) phase method was used for phase extraction. 1D and 2D CWT analyses of noisy images were compared in simulations performed for a 2-dimensional fringe signal by introducing the carrier frequencies in two spatial directions, $x $ and $y$. Profile measurement of an object was made experimentally by cross optical axis geometry. Images, using fringes with two carrier frequencies, taken from this setup were analyzed with 2D CWT and 3D profiles of objects were obtained. Numerical simulations and actual experiments were carried out to show the validity of this technique for finding phase distributions from noisy images.

Keywords: Continuous wavelet transform, wavelet transform profilometry, fringe projection techniques, phase calculation, fringe pattern

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