RAPID EVALUATION OF D(0) - THE EFFECTIVE DIAMETER OF A LASER-GUIDE-STAR ADAPTIVE-OPTICS SYSTEM

The Kolmogorov theory is used to illustrate that the mean-square wave-front error E(2), 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 E(2) = (D/d(0))(5/3) Th, quantity d(0) is a measure of the effective diameter of the compensated imaging system (i.e., a telescope with a diameter equal to d(0) will have 1 rad of rms wave-front error) and is expressed as an integral over the C-n(2) profile. The C-n(2)-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 d(0) can be evaluated quite quickly on a microcomputer or a scientific calculator. In this study the quantity d(0) is evaluated for six C-n(2) profiles of interest, illustrating the importance of including the altitude weighting in the theoretical formulation of d(0). 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.