<title>Varieties Of Isoplanatism</title>

Isoplanatism is a somewhat exotic term used to indicate that the transfer function of an optical system is dependent on the field-angle, or to denote the region, called the isoplanatic patch, over which the transfer function is virtually independent of field-angle. For many years, the term has been used mostly as a sort of "charm" to "ward-off" the possibility that others might think we were unaware of mathematical subtleties we intended to ignore because they were physically inconsequential. However, isoplanatism assumes physical significance in imaging through turbulence. The need to take account of this has created some confusion since different types of imagery have different isoplanatic dependencies and so should be denoted by different terms. There are a variety of different effects each of which can be classi-fied as isoplanatism each distinct in its dependence on the propagation path. We have identified five distinct varieties of isoplanatism, which we call 1) predetection compensation isoplanatism, 2) post-detection short-exposure imagery compensation isoplanatism, 3) post-detection long-exposure compensa-tion isoplanatism, 4) angle-of-arrival isoplanatism, and 5) speckle interferometry isoplanatism. Formulas giverning each of these types of isoplanatism will be presented.