Turbulent effects are very complicated and still not entirely understood. Light waves from an astronomical object are distorted as they pass through the atmosphere. The refractive index fluctuations in the turbulent atmosphere induce an optical path difference (OPD) between different parts of the wavefront, distorted wavefronts produce low-quality images and degrade the image beyond the diffraction limit. In this paper the image degradation due to 2-D Gaussian atmospheric turbulence is considered in terms of the point spread function (PSF), and Strehl ratio as an image quality criteria for imaging systems with different apertures using the pupil function teqneque. A general expression for the degraded PSF in the case of circular and square apertures (with half diagonal = π2, and 1) diffraction limited and defocused optical system is considered. Based on the derived formula, the effect of the Gaussian atmospheric turbulence on circular and square pupils has been studied with details. Numerical results show that the performance of optical systems with square aperture is more efficient at high levels of atmospheric turbulence than the other apertures.

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