Practical quantitative theory of photoacoustic pulse generation

Abstract

The problem of photoacoustic pulse generation is treated using generalized thermoelastic equations, specifically incorporating the hyperbolic heat conduction equation to avoid an infinite thermal propagation velocity. The assumption of equality of longitudinal and thermal velocities leads to a simplification of the solution in certain limiting cases, enabling insights into the character of the solution, without appreciably affecting the numerical results. The effect(s) of approximations made by previous authors may also be assessed. Numerical Hankel–Laplace transform inversion is shown to be practical for the general case, allowing such calculations to be duplicated by others.

A New Method for Calculation of Laser-Generated Ultrasound Pulses

“…The present formulation of pulsed photoacoustic generation [8] is both practical and quantitative. It should enable the study of applications of laser generated acoustic pulses by any interested investigator.…”

“…The next two terms in Uz (the first longitudinal, thf' s<econrl trAnsverse, both arising from mode conversion at the boundary) n•duce to those inverted analytically by Rose [14] (also see [8]). One other term must be considered.…”

“…The simple forms for u+ result from setting cy = c 1 , decoupling the elastic and thermal terms [8]; at a distance such that r2 > Dt (D the thermal diffusivity) the thermAl t<'>rms wi 11 be negligible (it should be noted that this assumption has negligible <'>ffect on all numerical results presented below).…”

“…Very recently a new formulation of pulsed photoacoustic generation (PPG) has been outlined [8]. This formulation utilizes numerical Hankel-Laplace transform inversion, and is based on generalized thermoelasticity (GTE) theory.…”

“…Doyle [6] and Schliechert et al [7] have described approaches which meet the first two criteria, but which are very computation-intensive. We will describe and illustrate a new formulation [8] which meets all three criteria. Numer i clll calculations will be presented to illustrate the efficacy of this approach, with emphasis on the effects of finite source dimensions and sample surface modification.…”