Fast Noncontinuous Path Phase-Unwrapping Algorithm Based on Gradients and Mask Carlos D´ ıaz and Leopoldo Altamirano Robles National Institute of Astrophysics, Optics and Electronics, Luis Enrique Erro # 1, Santa Maria Tonantzintla, Puebla, 72840, Mexico {cdiaz,robles}@inaoep.mx Abstract. Various algorithms based on unwrapping first the most-re- liable pixels have been proposed. These were restricted to continuous path and were subject to troubles on defining an initial pixel. The tech- nique proposed uses a reliability function that helps us to define starting points, it does not follow a continuous path to perform the unwrapping operation, and it uses a mask to pick out invalid pixels. The technique is explained with all the specifics and exemplify with some examples. 1 Introduction Optical techniques such as 3D profilometry, photoelasticity, and interferometry have the advantage of being noncontact, fast, and capable of providing whole- field information. They have already been developed for measuring a wide range of physical parameters such as stress, vibration, displacement, and surface profile. In all these techniques, the measured parameters are modulated in the form of a 2D fringe pattern. Demodulation by the use of fringe pattern processing is thus an essential and important procedure. First a wrapped phase map whose principal values range from -π to π is calculated from the fringe pattern. Phase unwrapping is then carried out to restore the unknown multiple of 2π to each pixel. When the recorded images satisfy the Nyquist criteria, the phase unwrapping process is straightforward. If the phase difference calculated for two adjacent points is equal to 2π, then 2π or multiples of 2π must be added to or subtracted from the calculated value of the second pixel. The entire phase map is obtained by working outward from the starting location. The diagram can explain the whole idea. Figure 1 shows the phase values calculated by arctangent at each pixel. Figure 2 shows the true phase values that are found by adding the correct number of 2π’s to each of these values. The above process only shows how to do 1D unwrapping. However, it is very easy to extend the 1D process to unwrap a 2D map. When phase wrap is getting by phase shifting interferometry there are addi- tional information as data modulation that can aid in phase unwrap process. The paper includes four sections: section 1 provides an overview of some existing phase-unwrapping algorithms, section 2 presents our proposal, section 3 gives experimental results of our algorithm, and finally, section 4 are conclusions. A. Sanfeliu et al. (Eds.): CIARP 2004, LNCS 3287, pp. 116–123, 2004. c  Springer-Verlag Berlin Heidelberg 2004