A Comparison of the Transient Propagation Properties of Gaussian and Bessel Waves

Abstract

Low-diffraction waves [1–5] have become of interest in ultrasound systems because of their longer depth of field for use in imaging and pulse- echo applications. Continuouswave (CW) Bessel waves of infinite extent suffer no diffraction spreading [6–9]. Continuous spatially truncated Bessel waves also have less spreading than CW spatially truncated Gaussian waves. Here we use a computer-based simulation to investigate the propagation properties of pulsed Gaussian and Bessel waves with circularly finite extent. If the width of the Gaussian or Bessel wave is a and the diameter of the circle that truncates the wave is d, the ratio of d/ a determines the propagation properties of the pulsed wave. Our propagation simulation uses fast Fourier spatial transforms to rapidly calculate the spatial impulse response wave, h(x, y, z, t), at a location z in front of the source. The complete temporal response can be found by convolving the impulse response h(x, y, z, t) with the time excitation waveform T(t). The predicted propagation patterns are presented to compare the behavior of the Gaussian and Bessel waves. For small ratios of d/ a, the Gaussian and Bessel excitations can be made quite similar and the resulting diffraction patterns are also nearly the same. For large values of d/ a, it is more difficult for the source functions to mimic each other and the wave patterns are quite different. In particular, in this regime of operation, the Bessel waves shows significant sidelobes, as the Bessel wave begins to have both positive and negative excitations. In the Gaussian wave, these sidelobes are absent, due to the smooth continuous nature of the Gaussian spatial excitation.