This paper presents a novel optical system for the realization of the Radon transform in a single frame. The optical system is simple, fast and accurate and consists of a 4F system, where in the 2F plane a vortex like optical element is placed. This optical element performs the rotation of the object, which replaces the need for mechanically rotating it, as is done in other common optical realization techniques of the Radon transform. This optical element is realized using a spatial light modulator (SLM) and an amplitude slide. The obtained Radon transform is given in Cartesian coordinates, which can subsequently be transformed using a computer to a polar set. The proposed concept is supported mathematically, numerically and experimentally.