Minimizing the bright/shadow focal spot size for differently polarized incident waves through the additional apodization of the\r\nfocusing system output pupil by use of an optical element with the vortex phase dependence on angle and the polynomial amplitude\r\ndependence on radius is studied. The coefficients of the radial polynomial were optimized with the aim of fulfilling certain\r\nconditions such as the energy efficiency preservation and keeping the side lobes under control. The coefficients were chosen so\r\nas to minimize the functional using Brent�s method.
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