Abstract: The goal of this work is to introduce different techniques of phase modulation. Optical coordinate transformations are mathematically examined and used in an example. The main body is focused on manipulation of scalar Gaussian beams, as they represent the most basic solution to the paraxial equation and can behave as rays in geometrical optics. The results are then used on beams carrying the orbital angular momentum and the possibilites of performing arithmetic operations with the value of the OAM are presented.