Closed-form expressions for the centroid-tilt error due to scintillation

TL;DR

This paper derives closed-form formulas for the centroid-tilt error caused by scintillation in adaptive optics, validated by simulations, aiding in the design and analysis of wavefront sensors.

Contribution

It provides the first analytical expressions for C-tilt errors due to scintillation under Kolmogorov turbulence, filling a gap in adaptive optics error modeling.

Findings

Analytical C-tilt expressions match wave-optics simulations well.

The formulas are applicable over a wide range of turbulence conditions.

This work enhances the understanding of scintillation effects on centroid measurements.

Abstract

In adaptive optics, the tracker and wavefront sensor commonly measure irradiance centroids (in their respective focal planes) to estimate the turbulence-degraded wavefront in the pupil plane. Several factors affect the accuracy of these centroid measurements, including noise, speckle, and scintillation. The centroid-tilt or ``C-tilt'' errors due to these factors have been studied by numerous researchers; however, to our knowledge, closed-form expressions for the C-tilt error due to scintillation have not been found. In this paper, we derive such expressions, assuming spherical-wave illumination of the pupil, a path-invariant index of refraction structure constant $C_n^2$, and Kolmogorov turbulence. We compare the analytically predicted C-tilt values to those obtained by wave-optics simulations. The agreement, at large, is quite good over a wide range of conditions. As a result, researchers and engineers will find this analysis useful when quantifying the performance of centroid-based trackers and wavefront sensors, both of which are critical adaptive-optics components.