The Telescope Point Spread Function

New observations are used to accurately define the stellar point spread function produced by atmospheric turbulence at the focus of large telescopes and to compare its profile to those computed from wavefronts characterized by various structure functions. Excellent agreement is found with the PSF expected from Kolmogorov statistics, except for the presence of an extended aureole of light which appears to results from a combination of instrumental and atmospheric light scattering. Simple yet accurate analytic fits are developed to represent the PSF profile over a range of 15 magnitudes in surface brightness. The relation between the Strehl ratio S of the PSF and the value of the parameter D/r0 is re-discussed, both for a natural wavefront and for a wavefront whose variance DeltaN is reduced by an adaptive optics systems. A simple expression for S(D/r0, DeltaN) is proposed and shown to yield essentially correct Strehl ratios for any value of the parameters.