Reliability-guided phase unwrapping in wavelet-transform profilometry

The phase unwrapping algorithm plays a very important role in many noncontact optical profilometries based on triangular measurement theory. Here we focus on discussing how to diminish the phase error caused by incorrect unwrapping path in wavelet transform profilometry. We employ the amplitude value map of wavelet transform coefficients at the wavelet-ridge position to identify the reliability of the phase data and the path of phase unwrapping. This means that the wrapped phase located at the pixel with the highest amplitude value will be selected as the starting point of the phase unwrapping, and that pixels with higher amplitude value will be unwrapped earlier. So the path of phase unwrapping is always in the direction of the pixel with highest amplitude value to the one with lowest amplitude value. Making full use of the amplitude information of wavelet coefficients at the wavelet-ridge position keeps the phase unwrapping error limited to local minimum areas even in the worst case. Computer simulations and experiments verify our theory.