Inverse Boundary Problem for the Two Photon Absorption Transport Equation

TL;DR

This paper investigates the inverse boundary problem for the two photon absorption transport equation, demonstrating unique determination of coefficients from boundary measurements, with explicit reconstructions in the absence of scattering.

Contribution

It establishes uniqueness results for the inverse problem and provides explicit reconstruction formulas when scattering is not present.

Findings

Absorption and scattering coefficients can be uniquely identified from the albedo operator.

Explicit reconstruction formulas are derived for the case without scattering.

The results do not require smallness assumptions on the incoming source when scattering is absent.

Abstract

This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If scattering is absent, we do not require smallness of the incoming source and the reconstructions of the absorption coefficients are explicit.