Radiative transport model for coherent acousto-optic tomography

Abstract

The paper [13] describes a physical regime in which the ultrasound perturbation of a scattering optical medium leads to a frequency shift in some of the scattered light. In this paper we consider the inverse problem of recovering the optical properties of this medium from measurements of the frequency-shifted light, using a radiative transport equation (RTE) model for light propagation. Given some assumptions on the regularity and isotropicity of the coefficients of the RTE, we show that the absorption coefficient can be reconstructed from the boundary measurements of a single well chosen illumination, and that the scattering coefficients can be reconstructed from boundary measurements of a one-parameter family of illuminations. arXiv:1910.04798v1 [math.AP] 10 Oct 2019Lemma 5.2. Let g = g θ 2 h be defined by (5.2), and let v solve the adjoint RTE (2.1) with boundary condition v| Γ + = g| Γ + . Then

Ultrasound modulated bioluminescence tomography with a single optical measurement

“…This, together with the known attenuation coefficient and scattering kernel, is employed to compute Au(x, θ) in (22). Finally, we solve the adjoint RTE ( 13), (14) to get v, and compute H v (x) in (21) with the trapezoidal rule.…”

“…In the context of optical tomography, in which one seeks to reconstruct coefficients instead of sources, see for example [2-4, 8, 15, 16]. Other related optical problems include fluorescent ultrasound modulated optical tomography ( [21,22]) and multifrequency acousto-optic tomography ( [13,14]). Ultrasound modulated hybrid problems are also part of a broader group of hybrid inverse problems in which the interactions of multiple imaging modalities create well-posed problems; for a survey of such ideas, see [6].…”

Ultrasound Modulated Bioluminescence Tomography With A Single Optical Measurement

“…This, together with the known attenuation coefficient and scattering kernel, is employed to compute Au(x, θ) in (22). Finally, we solve the adjoint RTE (13) (14) to get v, and compute H v (x) in (21) with the trapezoidal rule.…”

“…In the context of optical tomography, in which one seeks to reconstruct coefficients instead of sources, see for example [2,3,4,8,16,15]. Other related optical problems include fluorescent ultrasound modulated optical tomography ( [21,22]) and multifrequency acousto-optic tomography ( [13,14]). Ultrasound modulated hybrid problems are also part of a broader group of hybrid inverse problems in which the interactions of multiple imaging modalities create well-posed problems; for a survey of such ideas, see [6].…”