Application of multidimensional FFT for the extraction of wave vectors and computer-aided visualization of LDV measurements

Background, Motivation and Objective: Scanning Laser Doppler Vibrometers (LDV) have proved to be the versatile and precise instruments for the study of elastic wave propagation features at the surface of solids. With increase of the volume of acquired data, through the extension of operating bandwidth and scanning area, the qualitative interpretation and quantitative analysis of resultant data demands flexible but robust processing and visualization tools. Generation of various types of waves, multiple reflections from voids, walls and transducer edges or experimental setup imperfections (such as harmonic generation, limited source aperture or partial coupling) could jeopardize the analysis of experimental data. In our work we present diverse visualization tools, based on the FFT and filtering in frequency- and time- domain, which aim to help the UT NDT community in interpretation of SLDV data. Statement of Contribution/Methods: Typical LDV scan data consists of the displacement U recorded over the surface coordinates (x,y) and the time t. They could be processed in a several ways. First, by 3D FFT U(x,y,t) -> U(k_x, k_y, f) one may extract the 'dominant' wave vectors and estimate the energy density distribution. By performing the spatial FFT U(x,y,t) -> U(k_x, k_y, t) the time of wave arrival to the obstacle could be retrieved automatically from the wavevector field variation. Moreover, by manual selection of peaks, certain components of the wave package could be 'highlighted' in the spatial domain, by using the generated mask and inverse FFT. Finally, applying the 2D phase unwrapping algorithms to the short-time Fourier transform U(x,y,t) -> U(x,y,f, t) slices, one may easily extract the wave vector directions and phase velocities in the operating frequency band. This could be very useful for the advanced visualization both in near- and far field zones of the ultrasonic transducers. In particular, wave vector extraction could be helpful for studying the nonlinear wave interaction phenomena. Results/Discussion: In this contribution the robustness of several 2D phase-unwrapping algorithms to the measurement noise are compared. In addition, few implementation details, such as selection of STFT parameters, IFFT mask and scan parameters are discussed briefly. Finally, an interactive MATLAB GUI tool with implementation of methods is presented.