# Depth dependent resolution in Electrical Impedance Tomography

## TL;DR

This paper analyzes how the resolution of electrical impedance tomography deteriorates with depth when the Dirichlet-to-Neumann map has measurement errors, providing explicit formulas for resolution limits in 2D Calderón's problem.

## Contribution

It introduces explicit formulas quantifying depth-dependent resolution limits in 2D electrical impedance tomography with measurement errors.

## Key findings

- Resolution decreases with depth from the boundary.
- Explicit formulas for resolution are derived.
- Results apply to localized perturbations near interior points.

## Abstract

We consider the two-dimensional version of Calder\`on's problem. When the D-N map is assumed to be known up to an error level $\varepsilon_0$, we investigate how the resolution in the determination of the unknown conductivity deteriorates the farther one goes from the boundary. We provide explicit formulas for the resolution, which apply to conductivities which are perturbations, concentrated near an interior point $q$, of the homogeneous conductivity.