A comparative evaluation of 2-D Hilbert transforms and 2-D continuous wavelet transforms for robust phase extraction in complex fringe patterns

Interferometric techniques are widely used to obtain the real-time phenomena in a majority of applications considering its advantages of non-intrusively, mapping changes in path length as small as the wavelength of the light source used, etc. Interferometers often recorded the changes in the path length in the form of fringe orientation. Depending upon the complexity of the phenomena under observation, interferometric fringes are formed from simple fringe ordinations to complex fringe structures. Extracting phase map from these fringe patterns are highly crucial to evaluate the phase change and the corresponding property change. In order to use the interferometers in its full potential, it is necessary to develop robust and accurate algorithms for phase extraction. In this paper, we discuss 2-D Hilbert transforms (HT) and 2-D continuous wavelet transforms (CWT) techniques to analyze fringe patterns of different orientation and inter-fringe spacing. Simulated interferograms were used to generate implemented fringe patterns with different orientation and spacing. MATLAB software is used to generate these simulated image. In order to check the efficiency of the mentioned algorithm, a white Gaussian filter with different noise levels (0%, 5%, 10%) has been added to the simulated interferograms. Interferometric fringes with noise is a common phenomenon in many transient and turbulent processes. Moreover, the in-build noise in optical configuration and external noises in the testing environment also adds to the noise. Hence, it is necessary to test the accuracy of algorithm for enhanced noises. The results show that the HT algorithm was difficult to implement on complex patterns and was also difficult to implement for a high degree of noise interference. The two-dimensional CWT, on the other hand, has good performance on complex striped patterns and can handle noise disturbances with a good degree of accuracy. The continuous wavelet transform is insensitive to noise interference patterns and gives accurate results. The processing time is very short and it can handle both simple and complex fringe patterns within a very short period of time. It can also be concluded that the 2-D CWT algorithm is very effective and robust.