Fringe pattern demodulation using the fan two-dimensional continuous wavelet transform conjugate to Shannon entropy

Abstract

This paper proposes an algorithm for phase demodulating fringe patterns using a two-dimensional continuous wavelet transform (2D-CWT). This algorithm exploits the isotropy property of the fan mother wavelet conjugated to Shannon entropy to perform the ridge extraction process by using only 2D-CWT arguments. The proposed algorithm’s performance is shown through simulated fringe patterns corrupted by speckle noise. Also, to evaluate the accuracy of the ridge extracted from the modulus to that obtained from the arguments of 2D-CWT, the developed algorithm is compared to the maximum ridge extraction algorithm for 2D-CWT and cost function ridge extraction algorithm for 2D-CWT, which extract the ridge from the 2D-CWT modulus. Furthermore, we demonstrate the ability of the proposed algorithm to demodulate real fringe patterns derived from optical metrology for temperature measurement. The most important result of the proposed method is that it is provably optimal in estimating the 2D-CWT ridge of oriented fringes. The added strength of the algorithm is that it is simpler and has better resistance to speckle noise than previous methods because it employs scalograms of arguments, which are the origin of the definition of the ridge.