# Neutron Transmission Strain Tomography for Non-Constant Stress-Free Lattice Spacing

## TL;DR

This paper introduces a new neutron transmission strain tomography method that jointly reconstructs strain and stress-free lattice spacing fields, overcoming previous limitations of assuming a constant $d_0$, and demonstrates its effectiveness on simulated data.

## Contribution

It presents a novel non-linear reconstruction algorithm for simultaneous strain and $d_0$ field estimation, incorporating equilibrium and boundary conditions.

## Key findings

- Successful joint reconstruction of strain and $d_0$ fields on simulated data.
- Method handles realistic noise levels effectively.
- Ensures reconstructed strain fields satisfy physical equilibrium constraints.

## Abstract

Recently, several algorithms for strain tomography from energy-resolved neutron transmission measurements have been proposed. These methods assume that the stress-free lattice spacing $d_0$ is a known constant limiting their application to the study of stresses generated by manufacturing and loading methods that do not alter this parameter. In this paper, we consider the more general problem of jointly reconstructing the strain and $d_0$ fields. A method for solving this inherently non-linear problem is presented that ensures the estimated strain field satisfies equilibrium and can include knowledge of boundary conditions. This method is tested on a simulated data set with realistic noise levels, demonstrating that it is possible to jointly reconstruct $d_0$ and the strain field.