A theoretical study has been made of the intensity distribution and the encircled energy distribution in the far-field generated by diffraction, at circular apertures, of partially coherent light in the presence of spherical aberrations. The correlation function that has been used in this study is appropriate for representing the effect of atmospheric turbulence on the state of coherence of aperture illumination. The cases of both primary and secondary spherical aberrations have been considered separately. The aberration functions used are those provided by the Zernike-Nijboer theory of wave aberrations. Extensive numerical results concerning the intensity and the encircled energy distributions as well as the expected two-point resolution have been presented. Tolerance limits on the aberration coefficients corresponding to different states of coherence of the aperture illumination have also been given. © 1973 Taylor & Francis Group, LLC.