An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium

Abstract

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to recover the anisotropic radiative sources from boundary measurements. The approach is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps. As an application, we determine necessary and sufficient conditions for the data coming from two different sources to be mistaken for each other.

Keywords:

• Radiative transport
• anisotropic sources
• source reconstruction
• scattering
• A-analytic maps

2010 Mathematics Subject Classifications:

• Primary 35J56
• 30E20
• Secondary 35R30
• 45E05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of D. Omogbhe and K. Sadiq were supported by the Austrian Science Fund (FWF), Project P31053-N32 and by the FWF Project F6801–N36 within the Special Research Program SFB F68 ‘Tomography Across the Scales’.