Analysis of fringe patterns with variable density using modified Variational Image Decomposition aided by the Hilbert Transform

Analysis of fringe patterns with greatly variable density is a huge challenge for the single-frame fringe pattern analysis algorithms. The broad range of spatial frequencies contained in the image widens the Fourier spectrum and makes the separation of the information difficult or even impossible. The background and information differentiation is also a challenging task in the case of fringe pattern preprocessing. On the other hand single-frame fringe pattern analysis algorithms need to be taken into the consideration and developed because of their ability to analyze transient events. One of the newest phase demodulation method is the Hilbert spiral transform (HST). At the output of the HST the fringe-signal which is in quadrature with the input fringe pattern is obtained. Both fringe-signals form the 2D analytic signal with phase and amplitude clearly defined by angle and modulus of this complex valued analytic fringe pattern. Nevertheless, HST input signal has to fulfill a few requirements: zero mean value (which can be obtained by successful background removal), low-pass amplitude modulation function (according to Bedrosian's theorem) and successful noise removal. In this work the new approach to the preprocessing of images containing wide range of spatial frequencies will be introduced using modified variational image decomposition. By modifications we mean acceleration and improved background and fringes differentiation. It will be also proven that quality of the preprocessing plays a key role in the phase demodulation process. Received results will be compared with the ones provided by already well-established and versatile 2D Hilbert-Huang Transform technique.