Abstract
Optical coherence tomography (OCT) and photoacoustic tomography are emerging non‐invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform photoacoustic tomography and OCT imaging at once. In this paper, we present a mathematical model describing the dual experiment. Because OCT is mathematically modelled by Maxwell's equations or some simplifications of it, whereas the light propagation in quantitative photoacoustics is modelled by (simplifications of) the radiative transfer equation, the first step in the derivation of a mathematical model of the dual experiment is to obtain a unified mathematical description, which in our case are Maxwell's equations. As a by‐product, we therefore derive a new mathematical model of photoacoustic tomography based on Maxwell's equations. It is well known by now that without additional assumptions on the medium, it is not possible to uniquely reconstruct all optical parameters from either one of these modalities alone. We show that in the combined approach, one has additional information, compared with a single modality, and the inverse problem of reconstruction of the optical parameters becomes feasible. © 2016 The Authors. Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd.
Highlights
Recently, there have been developed experimental setups that can perform photoacoustic and optical coherence tomography experiments in parallel; see [1] and further developments in [2, 3]
Photoacoustic tomography is a hybrid imaging technique, which measures the acoustic response of an object upon illumination with an electromagnetic wave
We have seen that the inverse problems of quantitative photoacoustic imaging and Optical coherence tomography (OCT) both lack data to obtain a unique reconstruction of the material parameters depending on the specific modelling
Summary
There have been developed experimental setups that can perform photoacoustic and optical coherence tomography experiments in parallel; see [1] and further developments in [2, 3]. We derive a mathematical model for quantitative imaging of the multi-modal experiment based on Maxwell’s equations. Even though the mathematical modelling of optical coherence tomography based on Maxwell’s equations is well established, most of the literature relies on simplified models of the Helmholtz equation [5,6,7,8,9], where, as a consequence, the frequency dependence of the susceptibility is neglected. To formulate the dual-modal setup, we consider Maxwell’s equations as the basic modelling equations because both imaging techniques rely on the same excitation. This provides a more general model for quantitative photoacoustics based on Maxwell’s equations, which is applicable in the case of high frequency radiation.
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