Fringe projection techniques: Whither we are?

Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry

We present an analysis of a spatial carrier-fringe pattern in three-dimensional (3-D) shape measurement by using the wavelet transform, a tool excelling for its multiresolution in the time- and space-frequency domains. To overcome the limitation of the Fourier transform, we introduce the Gabor wavelet to analyze the phase distributions of the spatial carrier-fringe pattern. The theory of wavelet transform profilometry, an accuracy check by means of a simulation, and an example of 3-D shape measurement are shown.

Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry

A novel technique that uses a fan two-dimensional (2D) continuous wavelet transform (CWT) to phase demodulate fringe patterns is proposed. The fan 2D CWT algorithm is tested by using computer generated and real fringe patterns. The result of this investigation reveals that the 2D CWT technique is capable of successfully demodulating fringe patterns. The proposed algorithm demodulates fringe patterns without the requirement of removing their background illumination prior to the demodulation process. Also, the algorithm is exceptionally robust against speckle noise. The performance of the 2D CWT technique in fringe pattern demodulation is compared with that of the 1D CWT algorithms. This comparison indicates that the 2D CWT outperforms its 1D counterpart for this application.

Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform

Fringe analysis: Premise and perspectives

In order to overcome the limitations of conventional Fourier transform and Gabor transform analyzing nonstationary signals, dilating Gabor transform is applied to analyze the optical fringes of 3-D shape measurement. The dilating Gabor transformation is introduced by using a changeable window of Gaussian function in a conventional Gabor transform. This phase analysis method provides more accurate results than Fourier transform and Gabor transform. Simulation and experimental results are presented that demonstrate the validity of the principle.

Jiawen Weng

Papers

Dilating Gabor transform for the fringe analysis of 3-D shape measurement