Analysis of the photoacoustic spectral dispersion in dielectric colloids

Abstract

The foremost advanced photoacoustic (PA) transport theory, dealing with image formation, relates to target volumes of shallow depths. It assumes the medium as homogeneous with negligible PA amplitude attenuation. Causal changes in the velocity distribution spectrum, as described in Debye’s theory, and related to propagation distance and sample's density, are also neglected. However, these are relevant for imaging targets at larger depths and improving image resolution of PA images of thick biological tissues. Here we introduce some concepts for extending the PA transport model. These are theoretical and experimental considerations for analysing PA attenuation and the significance of spectral dispersion; and in consequence, disclose those conditions at which they should be included as part of the PA transport theory. Departing from the PA Heaviside telegraph equation and causality conditions, we obtain analytic expressions for associated attenuation and dispersion coefficients. As part of the analysis, we propose expressions for the PA group and PA phase velocities, and for the group velocity dispersion parameter; those in analogy with optical fields. In this way we get a refined description for the spectral dispersion. As proof of consistency, the introduced expressions are tested with experimental data extracted from homogeneous colloid samples. The observed performance is compared against already known general acoustic dispersion theory.