In optical propagation through atmospheric turbulence, the performance of compensation with adaptive optics depends on a beacon’s spatial distribution. With distributed beacons, the inefficiency of the modal correction, which is defined as the ratio of the anisoplanatic error of the <i>j</i>th mode and the Zernike-coefficient variance, is derived by use of the wave-front expansion on the Zernike polynomials for non-Kolmogorov turbulence. Numerical results are presented for laser beam propagation through constant turbulence with an offset point beacon and an on-axis uniform circular beacon. The results show that compensation for an on-axis uniform circular beacon is much more effective than that for an offset point beacon. The low-order modes are much more correlated than the higher-order modes. The larger the power-law exponent of the refractive-index power spectrum β, the smaller the propagation path length <i>L</i> and the larger the diameter <i>D</i> of the telescope aperture, the more effective the compensation is. For a specific extended degree of beacon for which there are a maximum number of modes <i>N</i><sub>max</sub> to be corrected, only low-order-correction systems are useful.
© 2001 Optical Society of America
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(010.1330) Atmospheric and oceanic optics : Atmospheric turbulence
Changhui Rao, Wenhan Jiang, and Ning Ling, "Adaptive-Optics Compensation by Distributed Beacons for Non-Kolmogorov Turbulence," Appl. Opt. 40, 3441-3449 (2001)