A quad-tree based phase unwrapping algorithm

One problem to be tackled when using interferometric phase shifting technology, is how the phase can be reconstructed.On account of the fact that an arc tan function appears in the formulation, the final data is not the phase, but the phase modulo 2π.In this paper the authors present a new phase unwrapping algorithm based on a two-step procedure.In the first step, the digital image to be analysed is divided into patches using a Quad-Tree like recursive procedure, in the second step the single patches are joined together to obtain larger, continuous ones.The basic idea of the procedure is to simplify the problem by factoring the complete image into "homogeneous areas" (i.e.areas where each pixel phase differs by less than π from its neighbours) so that only interfaces need to be dealt with.On account of the consistency of the data, the macro-areas assembled in this way are also homogeneous, so the procedure ends up with a fully unwrapped representation of the image.After a complete description of the algorithm, some examples of its use on synthesised digital images, with and without noise, are illustrated.Images derived from experimental data are also shown.Lastly the solution time has been examined.As the algorithm combines the local and global approach, it has proved to be fast and reliable. 1.