Time-frequency analysis to determine wave arrival and particle velocities in velocimetry data

Interferometric experimental setups such as photonic doppler velocimetry (PDV) [D. H. Dolan, Rev. Sci. Instrum. 81, 053905 (2010)] are used to determine particle velocities in material under extreme stresses due to high velocity shock wave propagation. The goal of shockwave experiments is the determination of material properties, when subjected to high velocity impacts, which requires high resolution shock wave arrival time and particle velocity measurements. Uncertainty principles [L. M. Barker, AIP Conf. Proc. 4291, 833–836 (1998)] provide a need to find a balance for achieving both velocity and time resolution. Time-frequency analysis is also used in underwater backscattering experiments to identify and characterize enhancements to the backscattering from elastic objects such as cylinders [S. F. Morse and P. L. Marston, J. Acoust. Soc. Am. 111111, 1289–1294 (2002), B. R. Hall and P. L. Marston, JASA Express Lett. 2, 114001 (2022)]. In the present research, time-frequency analysis algorithms were created to obtain a “best” balance for determining velocity/frequency-time profiles. We will show applications of standard techniques such as wavelet, Hilbert, and Gabor transforms with an improvement using a modified bispectrum, on shockwave and high-frequency acoustic data. [Work supported by Los Alamos National Laboratory.]