Theoretic analysis of expanded beacon’s anisoplanatic error

Using a special spectral filtering method, the anisoplanatism of expanded beacon in two typical scenes is modelled. And the formulae that describe the total expanded anisoplanatic error and different Zernike model components are obtained. Using two typical turbulent outlines, the characteristics of the expanded anisoplanatic error are studied, and the results indicate that: when the dimension of beacon equals to that of the receiver aperture, the expanded and focal coupling anisoplanatic error is minimal, while the high-order components that the piston, tilt and focus components are removed are not minimal. When the high-order components are minimal, the dimension of beacon should be less than that of the receiver aperture. When the beacon expanded angle equals to beacon departure angle, the expanded anisoplanatic error is about 2.2% of the angle anisoplanatic error. Relative to the angle or focal anisoplanatic error, the anisoplanatic error induced by the dimension of beacon is very little. And in many scenes, it can be ignored.