# The decomposition of aberrated or turbulent wavefronts into a spatial mode spectrum using optical cavities

## TL;DR

This paper demonstrates that aberrated wavefronts excite specific higher order modes in optical cavities, and analyzing these modes reveals the type and magnitude of aberrations, aiding wavefront characterization.

## Contribution

It introduces a method to decompose aberrated wavefronts into spatial mode spectra using passive optical cavities, linking mode distribution to aberration characteristics.

## Key findings

- Higher order modes are excited by aberrations in the cavity.
- Spectral width correlates with aberration magnitude.
- Simulation confirms the relationship between phase delays and mode excitation.

## Abstract

It is shown that an aberrated wavefront incident upon a Fabry-Perot optical cavity excites higher order spatial modes in the cavity, and that the spectral width and distribution of these modes is indicative of the type and magnitude of the aberration. The cavities are purely passive and therefore frequency content is limited to that provided by the original light source, unless time-varying content is introduced. To illustrate this concept, spatial mode decomposition and transmission spectrum calculation are simulated on an example cavity; the effects of various phase delays, in the form of two basic Seidel aberrations and a composite of Zernike polynomial terms, are shown using both Laguerre-Gaussian and plane wave incident beams. The aggregate spectral width of the excited cavity modes is seen to widen as the magnitude of the phase delay increases.