Noise phase singularities in noise contaminated images

As it is well known, the vortices or phase singularities are optimal encoders for position marking. The pseudo-phase singularities information can be obtained from the complex signal resulting from Laguerre-Gauss filtering of the intensity image. Each singularity has its unique anisotropic core structures with different ellipticity and azimuth angles from each other. Indeed, the Poincare sphere representation can be used to characterize the mentioned singularities. In optical vortex metrology the correct identification and the tracking of the complicated movement of pseudo-phase singularities is essential. In particular, it is relevant the singularity in the poles of the sphere. When the singularities are located at or near the equator of the sphere, the zero crossings of the real and imaginary planes cut in a straight line which makes their location difficult. These phase singularities near the equator tend to disappear when a transformation of the object, such as a deformation takes place. In this work, we analyze the number of vortices in analytical representation of a noise contaminated image. Different types of noise are analyzed (Gaussian, random, Poisson, etc.). We verified that the noise increases essentially the number of vortices at and near the equator of the Poincare sphere.