Modal Decomposition of the von-K\'arm\'an Covariance of Atmospheric Turbulence in the Circular Entrance Pupil

TL;DR

This paper explores a modal decomposition approach using the Karhunen-Loeve basis to analyze atmospheric turbulence, offering a potentially more precise method for estimating outer scales compared to traditional Zernike-based techniques.

Contribution

It introduces a novel methodology replacing Zernike basis with Karhunen-Loeve modes for turbulence analysis, including data acquisition and statistical hypothesis testing improvements.

Findings

Karhunen-Loeve basis provides statistically independent modes for turbulence analysis.

Sensing tip-tilt modes enhances data accuracy.

Variance ratio fitting enables hypothesis testing on outer scale models.

Abstract

Estimators of outer scales of atmospheric turbulence usually fit the phase screen snapshots derived from local wave front sensors to a Zernike basis, and then compare the spectrum of expansion coefficients in this basis with a narrowing associated with decreasing outer scales. This manuscript discusses aspects that arise if the Zernike basis is exchanged for a Karhunen-Loeve basis of statistically independent modes. Data acquisition turns out to be more demanding because sensing the tip-tilt mode is required. The data reduction methodology is replaced by fitting of variance ratios of an entire (long exposure) data set. Statistical testing of hypotheses on outer scale models can be applied to a set of modes - supposing other noise originating from detector readout and the optical train can be disentangled.