Phaseless uniqueness for determining internal source in photo-thermal effect

TL;DR

This paper proves that the internal source in a photo-thermal system can be uniquely identified up to sign using only external temperature measurements, despite the nonlinear coupling and phase loss in electromagnetic data.

Contribution

It establishes the first theoretical uniqueness result for internal source reconstruction in photo-thermal effects with phaseless electromagnetic data.

Findings

Internal source can be uniquely determined up to sign.

The proof is based on potential theory and asymptotic analysis.

Provides a theoretical foundation for source inversion algorithms.

Abstract

The paper investigates an inverse problem of recovering the internal source from external temperature measurements in photo-thermal effect. The photo-thermal effect actually involves two physical processes: electromagnetic scattering and heat transfer, described by a nonlinear coupled system of Maxwell's equation and the heat transfer equation. The nonlinear coupling term in the system is represented by the square of the modulus of the electromagnetic (missing the phase information of the electromagnetic field), and the absence of this phase information poses a significant challenge to the reconstruction of the internal source. In addition, the interaction and mutual influence of multiple physical fields, including electric field, magnetic field and temperature field, add to the complexity involved in the inversion of the internal source. Based on the potential theory and asymptotic analysis, we prove that the internal source can be uniquely determined up to sign by the external temperature field. This provides a solid theoretical basis for designing the internal source inversion algorithm and further exploring the theoretical aspects of photo-thermal effect.