Optical resolution through a turbulent medium with adaptive phase compensations*

The theory of short-term average modulation transfer function developed by Fried is extended by considering the correlation between the turbulence-induced phase distortion and the residual phase aberrations after adaptive phase compensations. Calculation of the optical resolution shows that the original approximation is valid for the normalized lens diameter D/r0 less than 4.0; conversely, for D/r0 greater than 4.0 the optical resolution becomes arbitrarily large because the MTF is unrealistically overcorrected at high spatial frequencies. The extended formulation is then applied to the cases with higher-order phase compensations such as focus and astigmatism. The peak optical resolution occurs at larger values of D/r0 when the higher-order corrections are included.