Phase-compensated optical beam propagation through atmospheric turbulence.

The modulation transfer function and the irradiance profile of a phase-compensated laser beam propagating through atmospheric turbulence are calculated for various values of the normalized transmitter diameter, D/r(0). Both focused Gaussian beam and collimated beam with modal phase corrections of arbitrary orders are considered using Zernike polynomials as basic correcting modes. Examples are given for low-order corrections such as tilt, focus, and astigmatism as well as for higher order corrections. The beam quality criteria, defined in terms of Strehl ratio, spot radius, and energy in a bucket, are used to measure the beam performance with different compensating modes. The effects on the beam propagation of central obscuration of the transmitter are also examined, and numerical results are given.