Abstract

The original analysis of focus anisoplanatism¹ included an effect due to the difference between turbulence-induced full-aperture wavefront tilt for the artificial guide star and for starlight. However, for short-exposure imagery tilt effects should be excluded. (For a long-exposure it should also be excluded; guide star position is so uncertain it provides no overall tilt information. That information must come from some other source, so the tilt difference should not be charged to focus anisoplanatism.) We have analyzed the focus anisoplanatism’s effect on short exposure resolution/antenna gain, generating extensive numerical results. We also analyzed the mean^*-squares tilt-free focus anisoplanatism-induced wavefront error, E², for aperture diameter D, and showed that E² is proportional to D^5/3. Writing the constant of proportionality as d₀^-5/3, so that E² = (D/d₀)^5/3, we have d₀ as a measure of the strength of focus anisoplanatism—a measure independent of aperture diameter. Dividing our short exposure focus anisoplanatism antenna gain results by the diffraction-limited antenna gain for an aperture diameter d₀, and expressing these normalized results as a function of the normalized aperture diameter D/d₀, all our results condense to a single curve, independent of wavelength, guide star altitude, zenith angle, or turbulence distribution.