Modal decomposition of the phase variance between the wave front that is sampled to make a correction and the desired wave front allows inappropriate piston and tilt terms to be excluded from statistical estimates. Mathematical techniques that were developed for calculating Zernike-mode covariances for multiaperture optical systems lead to statistical expressions for angular and focal anisoplanatism and combinations thereof. The 5/3-law dependence that characterizes the angular dependence and also appears in connection with the standard Greenwood frequency is shown to be an artifact of infinite outer scale that is entirely removable by exclusion of the piston. Large piston and/or tilt components significantly affect critical angle and frequency estimates under conditions of practical interest. A finite inner scale or the removal of high-frequency components also produces a characteristic deviation from the 5/3 power law, including a substantial quadratic region for small angles.
© 1994 Optical Society of AmericaPDF Article