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In the last chapter expressions for phase and log-amplitude variances were derived. These expressions contained an aperture filter function. In this chapter explicit filter functions are derived for many cases of interest. First, those needed to calculate variances of any Zernike mode on an unobscured circular aperture are found. Next, expressions to find piston and tilt on an annular aperture are derived. Filter functions required to determine the effect of either a finite-size source or receiver on the scintillation are derived. The filter function to be used when both the receiver and source are finite in size is also given. Often in adaptive-optics systems the phase produced by a focused beam of finite size is used to correct an outgoing collimated beam. The source of the focused beam may not be coaxial with the outgoing beam. Filter functions that apply for each of these cases are derived.
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