A comparison between Zernike and PCA representation of atmospheric turbulence

In ground-based astronomy seeing remains one of the biggest problem due to the presence of atmospheric turbulence affecting the radiation from the astronomical object of interest, along its travel path to the telescope device. The correction of the turbulence effects at the telescope pupil level, characterized statistically according to well-accepted models, is the focus of current generation of adaptive optics systems. Moreover, the representation of atmospheric turbulence, which is limited to the phase contribution since the amplitude degradation can be considered as negligible, is obtained through a modal decomposition. The choice of the modal representation is therefore a key issue in the turbulence study and the consequent design of control system to drive the deformation of the corrective mirrors. In the paper we discuss a possible solution to the problem, resorting to the principal component analysis of the atmospheric turbulence, and comparing this approach to the classically adopted Zernike's expansion.