Turbulence-degraded beam quality: improvement obtained with a tilt-correcting aperture

In this paper, we have calculated the degradation in the focal-plane irradiance distribution due to atmospheric turbulence and the potential improvement realizable by employing a wavefront filt-correcting aperture. It has been shown that, when the aperture diameter is of the order of the outer scale of turbulence, virtually no improvement is realized relative to the uncompensated case. For the case when the long-term coherence length is small compared with the diameter, there is a several-decibel improvement over the longterm case; however, for a full phase-compensating aperture (e.g., COAT), peak intensity can be increased an additional several decibels. When the coherence length is not much smaller than the diameter, close to diffraction- limited performance can be expected. Comparisons are also made of the reduction of on-axis intensity with no compensation, tilt-correction, and a full phase-compensating aperture. It is shown that the effective coherence length of the compensated aperture due to the residual amplitude fluctuations is greater than the long-term coherence length by a factor proportional to the square root of the Fresnel number of the aperture. Approximate formulas are also presented for the tilt-corrected MTF for arbitrary aperture irradiance distributions.