**Appendix**

90km) correspond to the offset angle of NGS between 2'' and 3''. It is also easy to see that the variance is a monotonically increasing function of the NGS offset angle and a almost monot‐ onically decreasing function of the LGS altitude. Therefore, if the NGS offset angle is smaller or 0'' (such as directly imaging of a bright satellite) using NGS to correct the defocus compo‐ nent, the variance is smaller. Otherwise, when the NGS offset angle is larger (for example, when projecting laser beams to a LEO satellite, the advance angle about 10'' must be consid‐

Using transverse spectral filtering techniques we reconsider the anisoplanatism of general AO systems. A general but simple formula was given to find the anisoplanatic variance of the turbulence-induced phase and its arbitrary Zernike components under the general ge‐ ometry of AO systems. This general geometry can describe most kinds of anisoplanatism appearing in currently running AO systems, including angular anisoplanatism, focal aniso‐ planatism and that induced by distributed sources or separated apertures, and so on. Under some special geometry, close-form solutions can be obtained and are consistent with classic

ered) using sodium LGS to correct the defocus the variance is smaller.

**Figure 8.** The anisoplanatism of the defocus component

**6. Summary**

214 Adaptive Optics Progress

Here we give some expressions describing the integrations of the anisoplanatic filter func‐ tion *Fn*,*m*(*κ*, *z*) for the Zernike mode *Z(m,n)* with respect to the radial component of the wave vector, i.e.,

*In*(*z*)=*∫* 0 <sup>∞</sup>*d<sup>κ</sup> Fn*,*m*(*κ*, *<sup>z</sup>*)*<sup>κ</sup>* -8/3
