Abstract
We identify the necessary and sufficient conditions for controlling the presence of optical vortices. Next, we unveil the use of two different pairs of transparent masks, which are useful for governing the presence of optical vortices. The elements of the first pair have quadratic helical variations. The elements of the second pair have cosinusoidal helical variations. In both cases, one element of the pair has a complex amplitude transmittance that is equal to the complex conjugate of the other element. By introducing an in-plane rotation, between the elements of a pair, one can control the presence of an optical vortex. We apply the previous results for detecting angular misalignments.
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