# Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy

## TL;DR

This paper introduces a symmetry-guided registration method to correct symmetry distortions in multidimensional photoemission spectroscopy data, improving the accuracy of electronic band structure mapping.

## Contribution

The paper presents an iterative symmetry-guided registration technique that effectively restores symmetry in distorted photoemission images, outperforming non-iterative methods.

## Key findings

- Iterative approach yields higher symmetry restoration.
- Method preserves the average shape of patterns.
- Applicable to various symmetry distortions.

## Abstract

Image symmetrization is an effective strategy to correct symmetry distortion in experimental data for which symmetry is essential in the subsequent analysis. In the process, a coordinate transform, the symmetrization transform, is required to undo the distortion. The transform may be determined by image registration (i.e. alignment) with symmetry constraints imposed in the registration target and in the iterative parameter tuning, which we call symmetry-guided registration. An example use case of image symmetrization is found in electronic band structure mapping by multidimensional photoemission spectroscopy, which employs a 3D time-of-flight detector to measure electrons sorted into the momentum ($k_x$, $k_y$) and energy ($E$) coordinates. In reality, imperfect instrument design, sample geometry and experimental settings cause distortion of the photoelectron trajectories and, therefore, the symmetry in the measured band structure, which hinders the full understanding and use of the volumetric datasets. We demonstrate that symmetry-guided registration can correct the symmetry distortion in the momentum-resolved photoemission patterns. Using proposed symmetry metrics, we show quantitatively that the iterative approach to symmetrization outperforms its non-iterative counterpart in the restored symmetry of the outcome while preserving the average shape of the photoemission pattern. Our approach is generalizable to distortion corrections in different types of symmetries and should also find applications in other experimental methods that produce images with similar features.