Isotropic n-dimensional quadrature transform and its applications in fringe pattern processing

In fringe pattern processing, quadrature operators are useful to obtain the corresponding modulating phase. In the case that a carrier exists (spatial or temporal), there are good methods for phase demodulation as Fourier analysis and asynchronous methods, for example. However, if there is no carrier or is too low, robust demodulation from a single image is a difficult task. In this work we present some recent advances in the processing of single fringe patterns with closed fringes based in a isotropic n-dimensional quadrature transform. In particular we address several problems related with the application of this quadrature operator. One of these problems is the Fringe direction, its role in the demodulation process is discussed and a practical method for its computation is presented. Fringe pattern normalization is also an important subject in the demodulation process from a singe image, taking this into account we present a technique for isotropic fringe pattern normalization based in the n-dimensional quadrature transform. All these techniques together configure a robust method for automatic demodulation of single fringe patterns. The performance and limitations of the method are discussed and illustrated by experimental results.