Effect of a finite outer scale on the Zernike decomposition of atmospheric optical turbulence

Phase distortions in optical systems induced by atmospheric turbulence are investigated with the use of Zernike polynomial decompositions. An analytic solution for the variances of the Zernike coefficients is found for the case of Kolmogorov turbulence with a finite outer-scale length. It is shown that the effect of finite outer scale is to attenuate low-order Zernike components, even when the outer-scale length is much larger than the optical aperture. Effects are investigated for constant outer-scale size and for height-dependent outer scales. It is found that seeing effects on large telescopes are dependent more on the magnitude of the outer scale than on the shape of the outer-scale vertical profile.