The Kolmogorov theory is used to illustrate that the mean-square wave-front error E2, which results when the wave-front distortion associated with an artificial guide-star reference is used to compensate a telescope aperture of diameter D, for imaging an object at infinity is given by E2 = (D/d0)5/3. The quantity d0 is a measure of the effective diameter of the compensated imaging system (i.e., a telescope with a diameter equal to d0 will have 1 rad of rms wave-front error) and is expressed as an integral over the Cn2 profile. The Cn2-weighting function is expressed in terms of hypergeometric functions whose series representation converges very rapidly. (Typically only a few terms are required). As a result d0 can be evaluated quite quickly on a microcomputer or a scientific calculator. In this study the quantity d0 is evaluated for six Cn2 profiles of interest, illustrating the importance of including the altitude weighting in the theoretical formulation of d0. In addition, this study illustrates the importance of removing the piston and the tilt from the wave-front distortion when assessing the performance of an imaging system.
© 1994 Optical Society of America
Original Manuscript: October 1, 1992
Manuscript Accepted: October 20, 1992
Published: January 1, 1994
Glenn A. Tyler, "Rapid evaluation of d0: the effective diameter of a laser-guide-star adaptive-optics system," J. Opt. Soc. Am. A 11, 325-338 (1994)