  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.
