Dark Hollow Gaussian Laser Beams In Aberrated Optical Systems : The Intensity Distribution of Focused Dark Hollow Gaussian Laser Beams in Aberrated Optical Systems

We derived the radial intensity distribution of the HGB analytical based on Collins integral for aberration-free lens by two methods one of them is new "in the best of our knowledge." A numerical solution of a two dimensional generalized Collins diffraction integral equation for a HGB propagating through an apertured paraxial ABCD optical system is derived and investigated. The properties of the radial intensity distribution, dark spot size DSS and width-radius ratio WRR parameters of the HGB throughout the geometrical focal plane are studied and an optimum value for each is calculated. And we developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in lens exhibits relatively large of both positive spherical aberration PSA and negative spherical aberration NSA are calculated.