Focus anisoplanatism effects on tip-tilt compensation for adaptive optics with use of a sodium laser beacon as a tracking reference

A Zernike decomposition of the pupil phase variance that is due to focus anisoplanatism for a sodium laser guide star is calculated, including the angular error variance associated with overall tilt. This quantity, or tilt focus anisoplanatism sigma(FA,tt)(2) is necessary in evaluating the usefulness of new techniques developed to measure the wave-front tilt from a sodium laser guide star. The analytical expression sigma(FA,tt)(2) in the case of refractive-index fluctuation with a Kolmogorov power spectral density is given together with numerical results for two different C-n(2),(z) profiles. Numerical calculations show that tilt focus anisoplanatism may be a limitation when a sodium laser guide star is used to sense the overall wave-front tilt at visible wavelengths, especially for 8-m-class telescopes. (C) 1996 Optical Society of America.