Phase compensation in non-Kolmogorov atmospheric turbulence

Zernike polynomial decompositions are used for investigating phase distortion induced by atmospheric turbulence in optical systems. Closed-form expression of the Zernike-coefficient variances is derived. The finite size of the receiver aperture is analyzed using the filter function which is also particularly effective in the theoretical analysis of lower-order aberrations like tilt terms and piston-removed phase variance. The outer scale of the non-Kolmogorov turbulence is considered. The result shows that the effect of finite outer scale attenuates low-order Zernike mode of optical distortion and longer outer scale can lead to more energy in the tilt terms. The generalized exponent can only enhance tilt terms and attenuate other Zernike modes of optical distortion. Further, for different outer scale and generalized exponent, the residual phase variance decreases with more modes of phase compensation.