Laser Vibrometry of Shear Waves in a Layer of a Gel-Like Medium

A laser scanning vibrometer was used to measure the amplitudes and phases of the vibrational velocity of shear waves excited by a one-dimensional source in the form of a narrow rectangular bar in a gel-like medium. The vibrations of 26 plates reflecting the laser beam and located inside an optically transparent phantom along a segment with a length of 84.5 mm at a distance of 20 mm from the source were measured. The angular distributions of the amplitude and phase of shear waves at discrete frequencies from 59 to 500 Hz were measured in continuous mode. In pulsed mode, the vibrator excited a pulse in the medium with a duration of 1.5 periods of the 300 Hz frequency. The amplitudes and phases of shear waves were calculated by fast Fourier transform of the time profile of the vibration velocity of the plates with a duration of 50 ms. The angular amplitude distributions measured in the pulsed and continuous modes are qualitatively the same. At all frequencies, the distributions are symmetrical with respect to the vertical axis. The maximum oscillation amplitude is observed at angles close to ±45°. The velocity of shear waves, calculated from the measured phase distributions, increases from 2 to 2.5 m/s with a change in frequency from 50 to 500 Hz. It is shown that this velocity behavior is well described by a relaxation model of the medium with one relaxation time equal to 0.3 ms. Shear wave attenuation depends on frequency and exceeds 1 cm^–1 for waves with frequencies above 250 Hz. The maximum attenuation per wavelength is observed near the relaxation frequency of the medium in the 300–400 Hz range. The results can be used to optimize devices for measuring the elasticity of soft tissues.