Aperture filtration refers to the effects of viewing optical wavefront distortions of infinite extent through a finite aperture. If the length-scale of the aberration is larger than this aperture, then the portion of the aberration visible in the aperture at any moment in time will not reach the full magnitude of the aberration seen in its entirety. The aperture acts as a spatial filter, mitigating the effects of large-scale wavefront distortions while having little effect on smaller-scale aberrations, with the dividing line between large-scale and small-scale being the size of the aperture itself. This dissertation presents and charts the development of a set of analytic formulas for judging and predicting the effectiveness of adaptive-optic corrective systems applied over finite apertures. This includes some simplified formulas and benchmarks as guides for the minimum requirements a system will need to meet to be effective, and the maximum degree of effectiveness such systems can reasonably achieve.