Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale

Aperture-to-aperture correlations of Zernike coefficients associated with atmospheric turbulence with a finite outer scale have been calculated. It is shown that the effect of finite outer scale is to reduce the correlation rapidly for low-order Zernike terms as the aperture separation becomes large. The results can be used to determine the outer scale. We use published data from the Keck telescope to illustrate our method. The results suggest that finite outer scale effects may be important for telescopes in the 8 –10-m class.