# Well-posedness for Photoacoustic Tomography with Fabry-Perot Sensors

## TL;DR

This paper models photoacoustic tomography measurements using Fabry-Perot sensors, accounting for their directional response, and demonstrates the problem's well-posedness with numerical reconstructions via Landweber iterations.

## Contribution

It introduces a realistic mathematical model for Fabry-Perot sensors in photoacoustic imaging and analyzes the problem's well-posedness under this model.

## Key findings

- The photoacoustic problem is well-posed with Fabry-Perot sensors.
- Numerical reconstructions are successfully performed using Landweber iterations.
- The model incorporates the directional response of sensors, improving realism.

## Abstract

In the mathematical analysis of photoacoustic imaging, it is usually assumed that the acoustic pressure (Dirichlet data) is measured on a detection surface. However, actual ultrasound detectors gather data of a different type. In this paper, we propose a more realistic mathematical model of ultrasound measurements acquired by the Fabry--Perot sensor. This modeling incorporates directional response of such sensors. We study the solvability of the resulting photoacoustic tomography problem, concluding that the problem is well-posed under certain assumptions. Numerical reconstructions are implemented using the Landweber iterations, after discretization of the governing equations using the finite element method.