Phase Map Ridge Extraction Algorithm
The ridge of the 1D-CWT may be extracted from the modulus array using the maximum or the cost function ridge extraction algorithms. An alternative method is to extract the ridge from the phase array alone. We refer to this method as the phase map ridge extraction algorithm.
The phase map method is based on the following principle. When the daughter wavelet analysis frequency ω= ωs /s is either close to or is equal to the fringe pattern spatial frequency ωo, then the rate of variation of the phase of the wavelet transform, dφW(s,b) /db , is actually close to ωo. Where ωs is the frequency of the mother wavelet, and ωo = 2πfo.
The algorithm begins with an initial value of a scaling factor so . A new frequency ω1 is then determined as dφW(so,b)/db. The corresponding scale value s1= ωo /ω1 is then used to find ω2= dφW(s1,b)/db. The iteration stops when it gets to a value lower than a predetermined threshold. Once ωo(b) has been found, the algorithm continues at time b+1 with so= ωs /ωo(b). This algorithm produces higher accuracy than the modulus ridge extraction algorithms, but its performance deteriorates significantly with the presence of even low levels of noise in the fringe pattern.
For a detailed explanation of the phase map ridge extraction algorithm, please see AbdulBasit PhD thesis. A Matlab program that demonstrates the operation of this algorithm can be downloaded here.
