Modeling the Chromatic Correction Error in Adaptive Optics: Application to the Case of Mid-Infrared Observations in Dry to Wet Atmospheric Conditions

L. Jolissaint^a and S. Kendrew

¹ Leiden Observatory, University of Leiden

^a e-mail: jolissaint@strw.leidenuniv.nl

Abstract

In this paper we extend to the mid-IR previous work from other authors on the effect of the chromatic correction error in adaptive optics, including the contribution of atmospheric water vapor content. An analytic model of the closed-loop AO corrected residual phase spatial power spectrum is presented that includes the overall mixed effect of anisoplanatism, servo-lag and refractive index dispersion. Calculating the Strehl ratio loss as a function of the refractive index dispersion, we demonstrate that (1) the error variance grows with the optical turbulence phase variance, but thanks to the aberration-damping effect of the outer scale of optical turbulence for large apertures, chromatic correction error variance is much reduced in comparison with an infinite outer scale case and is not a significant issue for ELTs; (2) in the mid-IR wavelengths, where the fluctuations of the refractive index of air due to water absorption lines are particularly strong, chromatic correction error might become relatively significant in terms of wavefront error (in the range 10-100 nm), but is totally negligible when compared to the imaging wavelength, even in rather wet conditions (20 mm of total integrated column of water); (3) tight errors budget, with WFS in the VIS and correction in the NIR domain, is the only case where chromatic error might become an issue, as with extreme AO systems. The power spectrum model presented here can be used to evaluate the chromatic correction error and its contribution to the long exposure PSF, using the spatial frequency approach.