# The Experimental Study of the Validity of the Lagrange–Helmholtz Relationship in Geomagnetic Fields

## TL;DR

This study confirms that the Lagrange–Helmholtz relationship holds in streak cameras even under geomagnetic interference, improving image reconstruction stability.

## Contribution

The paper experimentally validates the Lagrange–Helmholtz relationship in streak tube systems under geomagnetic fields.

## Key findings

- The Lagrange–Helmholtz relationship remains valid in streak tube systems under geomagnetic interference.
- Imaging plane spatial resolution is consistent despite environmental disturbances.
- Specific image orientations are no longer required for reconstruction.

## Abstract

Streak cameras, known for their ultra-high spatiotemporal resolution, rely heavily on the spatial resolution capabilities of their core component, the streak tube, to ensure engineering stability. However, factors such as assembly inaccuracies and external magnetic fields, including geomagnetic interference, often cause deformation and shifts in the imaging plane. To enhance equipment stability and accelerate engineering advancements, a dual approach involving hardware improvements and computational imaging-based software corrections is essential. Future image reconstruction efforts in software require robust benchmarks; however, existing benchmarks are predominantly validated under idealized conditions, neglecting real-world interference factors. This study, grounded in electron optical imaging principles, experimentally confirms that the Lagrange–Helmholtz relationship remains valid within streak tube systems under geomagnetic field influences. These findings affirm that the imaging plane retains spatial resolution consistency despite such environmental disturbances. Consequently, the need for specific image orientations during reconstruction can be eliminated, enabling the development of more robust and efficient image reconstruction algorithms.