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 jth 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 beta, the smaller the propagation path length L and the larger the diameter D 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 N-max to be corrected, only low-order-correction systems are useful. (C) 2001 Optical Society of America.