Zenith-Distance Dependence of Chromatic Shear Effect: A Limiting Factor for an Extreme Adaptive Optics System

Consider a perfect AO system with a very fine wavefront sampling interval and a very small actuator interval. If this AO system senses wavefront at a wavelength, lambda_{WFS}, and does science imaging at another wavelength, lambda_{SCI}, the light paths through the turbulent atmosphere at these two wavelengths are slightly different for a finite zenith distance, z. The error in wavefront reconstruction of the science channel associated with this non-common path effect, or so-called chromatic shear, is uncorrectable and sets an upper bound of the system performance. We evaluate the wavefront variance, sigma^2(lambda_{WFS},lambda_{SCI},z) for a typical seeing condition at Mauna Kea and find that this effect is not negligible at a large z. If we require that the Strehl ratio be greater than 99 or 95%, z must be less than about 50 or 60 deg respectively, for the combination of visible wavefront sensing and infrared science imaging.