We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or through an inclined spherical lens. We also obtain similar analytical expressions describing propagation of an optical vortex generated when a Gaussian beam illuminates an inclined spiral phase plate (SPP) or when an elliptic Gaussian beam illuminates a SPP (not inclined). All these optical vortices with a topological charge (TC) n are described by the n-th order Hermite polynomial with a complex argument. It is shown that the argument is real only on a straight line in the transverse plane of the laser beam. There are n intensity nulls on this line. The treated here astigmatic transforms are used to determine the integer TC of optical vortices. We conduct a comparative experimental study of different astigmatic transforms and we show that the transform with a cylindrical lens is the best for determining the TC. Unlike other similar works, in this study we achieve transformation of n-degenerate intensity null of an optical vortex with the TC n=100 into n isolated first-order intensity nulls.