Photoacoustic spectrum analysis for spherical target size and optical property determination: A feasibility study

The photoacoustic signal generated by an optically absorbing target is determined by the spatial profile of absorbed optical energy within the target. The analysis of the time profile and frequency content of the signal enables the recovery of the geometry of the object, as well as information about the optical properties. The photoacoustic response of spheres with a homogeneous absorbed optical energy profile is well described, and it is known that the width of the photoacoustic pulse is determined by the diameter of the sphere and its sound speed. In practice, the optical attenuation coefficients within the sphere will result in an inwardly decaying fluence profile leading to a similarly decaying absorbed optical energy profile. Further, the optical attenuation coefficients may be inhomogeneously distributed in the sphere. The implication for both cases is that the existing model for spheres does not fully apply. In this work, we developed analytical expressions for the photoacoustic time traces and amplitude spectra generated by a sphere with absorbed optical energy only in a spherical shell, and by a sphere with an inwardly decaying optical energy profile. Numerical simulations and experiments were conducted on these two imperfect sphere types. Fitting our model to the simulated or measured spectra allowed us to test our model's ability to extract the sphere size and optical properties. We found that the radii can be recovered with high accuracy, even when the frequency response of the detector recording the photoacoustic pulse is not precisely known. The model was found to be less sensitive in recovering the optical attenuation coefficient, but it is feasible when the detector's frequency response is well known.