Partially coherent vortex beams focused by an aperture lens with coma

We investigate the influence of the coma of the lens on the focusing of partially coherent vortex beams. On the basis of the generalized Huygens-Fresnel diffraction integral, the formula for the intensity distribution in the focal plane is derived. The numerically calculated results are given to show that the coma of the lens leads to the asymmetry of focused intensity distribution. The influence of coherence length on the focused intensity distribution is also investigated. It is found that the effect of coma is not obvious when the coherence length is small. Intensity profiles for three different values of the azimuthal angle are plotted to illustrate the effect of coma and the influence of coherence length.