The general formulae are constructed for studing the geometric anisoplanatism of an adaptive optics by the transverse spectral filtering method. At some peculiar situations,these formulae can be expressed to classical explicit form,while in general only a numerical value can be obtained. As an example,these formulae are used to study a special laser guiding star adaptive optical system whose defocus mode are also be corrected by the natural stars,besides the tip-tilt modes as the general laser guiding star adaptive optical system.