Hannover 2016 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 10: Quantum Optics II
Q 10.7: Vortrag
Montag, 29. Februar 2016, 16:00–16:15, f442
The 3D inverse optoacoustic source problem on the beam axis — •O. Melchert, J. Stritzel, M. Wollweber, M. Rahlves, and B. Roth — Hannover Centre for Optical Technologies, Leibniz Universität Hannover, Hannover, Germany
Today, optoacoustics is widely used in the life sciences, e.g. for imaging of biological tissue. A yet unsolved problem is to determine optical properties from the experimental signals. While the direct problem of absorption of light in biological media consists of solving the optoacoustic wave equation for an initial pressure distribution p0(r), the mathematically challenging inverse problem requires the reconstruction of p0(r) from a proper set of observed signals.
For the particular case of a Gaussian transverse beam profile, the signal p(z,τ,r⊥=0) at a point z along the beam axis (i.e. r⊥=0), at the (retarded) time τ, is given by an integral equation, linear in the initial pressure profile p0(τ) on the boundary of the absorbing medium. This integral equation can be interpreted as a Volterra equation of the second kind with known kernel, where p(z,τ,r⊥) is given and p0(τ) is an unknown function to be solved for. For this integral equation, technically feasible inversion schemes exist. We study the inversion of synthetic signals that correspond to different initial pressure distributions, compare the inversion in the far-field to an approximate method based on the solution of a simple differential equation and consider the effect of noise on the quality of the reconstructed profile.