The general formularies to study the anisoplanatism of adaptive optical systems are constructed by the transverse spectral filtering method. At some peculiar situation, these formularies can be expressed to explicit form, and the classical scalar law and the relevant characteristic scale can be obtained and generalized. While in general, only numerical values can be obtained. As an example, the lunar laser ranging system with an adaptive optics (AO) to correct the uplink beam is used to explain the use of these formularies to study the anisoplanatism of AO systems.