A semi analytic framework for simulating the effects of atmospheric seeing in Adaptive Optics systems on an 8-m telescope is developed with the intention of understanding the origin of the wind-butterfly, a characteristic twolobed halo in the PSF of AO imaging. Simulations show that errors in the compensated phase on the aperture due to servo-lag have preferential direction orthogonal to the direction of wind propagation which, when Fourier Transformed into the image plane, appear with their characteristic lemniscate shape along the wind direction. We develop a metric to quantify the effect of this aberration with the fractional standard deviation in an annulus centered around the PSF, and use telescope pointing to correlate this effect with data from an atmospheric models, the NOAA GFS. Our results show that the jet stream at altitudes of 100-200 hPa (equivalently 10-15 km above sea level) is highly correlated (13.2σ) with the strong butterfly, while the ground wind and other layers are more or less uncorrelated.

An explanation for the origin of asymmetry along the preferential axis of the PSF of an AO system is developed. When phase errors from high altitude turbulence scintillate due to Fresnel propagation, wavefront amplitude errors may be spatially offset from residual phase errors. These correlated errors appear as asymmetry in the image plane under the Fraunhofer condition. In an analytic model with an open-loop AO system, the strength of the asymmetry is calculated for a single mode of phase aberration, which generalizes to two dimensions under a Fourier decomposition of the complex illumination. Other parameters included are the spatial offset of the AO correction, which is the wind velocity in the frozen flow regime multiplied by the effective AO time delay, and propagation distance or altitude of the turbulent layer. In this model, the asymmetry is strongest when the wind is slow and nearest to the coronagraphic mask when the turbulent layer is far away, such as when the telescope is pointing low towards the horizon. A great emphasis is made about the fact that the brighter asymmetric lobe of the PSF points in the opposite direction as the wind, which is consistent analytically with the clarification that the image plane electric field distribution is actually the inverse Fourier transform of the aperture plane. Validation of this understanding is made with observations taken from the Gemini Planet Imager, as well as being reproducible in end-to-end AO simulations.

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