Simultaneous Reconstruction of Optical and Acoustical Properties in Photoacoustic Imaging Using Plasmonics

We propose an approach for the simultaneous reconstruction of the electromagnetic and acoustic material parameters, in the given medium [Formula: see text] where we want to image, using the photoacoustic pressure, measured on a single point of the boundary of [Formula: see text], generated by plasmonic nanoparticles injected inside [Formula: see text]. As measurements, we use the generated pressure, that we denote by [Formula: see text], depending on only one fixed point [Formula: see text], where we measure, the time variable [Formula: see text], in a large enough interval, and the incidence frequency [Formula: see text], in a large enough band. These measurements are repeated while the location [Formula: see text] of the nanoparticle is moved inside [Formula: see text] to scan it. We show that these measurements (which are [Formula: see text] in terms of dimensionality) are enough to reconstruct both the sound speed, the mass density, and the permittivity inside [Formula: see text] (i.e., [Formula: see text] coefficients of [Formula: see text] each in terms of dimensionality). Indeed, from the behavior of the measured pressure in terms of time, we can estimate the travel time of the pressure, for arriving points inside [Formula: see text], then using the eikonal equation we reconstruct the acoustic speed of propagation, inside [Formula: see text]. In addition, we reconstruct the internal values of the acoustic Green’s function. From the singularity analysis of this Green’s function, we extract the integrals along the geodesics, for internal arriving points, of the logarithmic gradient of the mass density. Solving this (internal) integral geometric problem provides us with the values of the mass density function inside [Formula: see text]. Finally, from the behavior of [Formula: see text] with respect to the frequency [Formula: see text], we detect the generated plasmonic resonances from which we reconstruct the permittivity inside [Formula: see text]. (This article was changed because of a production error.)