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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
where we want to image, using the photoacoustic pressure, measured on a single point of the boundary of
, generated by plasmonic nanoparticles injected inside
. As measurements, we use the generated pressure, that we denote by
, depending on only one fixed point
, where we measure, the time variable
, in a large enough interval, and the incidence frequency
, in a large enough band. These measurements are repeated while the location
of the nanoparticle is moved inside
to scan it. We show that these measurements (which are
in terms of dimensionality) are enough to reconstruct both the sound speed, the mass density, and the permittivity inside
(i.e.,
coefficients of
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
, then using the eikonal equation we reconstruct the acoustic speed of propagation, inside
. 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
. Finally, from the behavior of
with respect to the frequency
, we detect the generated plasmonic resonances from which we reconstruct the permittivity inside
. (This article was changed because of a production error.)
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