The critical points of generic paraxial ellipse fields consist of singular points of circular polarization, called C-points, and azimuthal stationary points, i.e., maxima, minima, and saddle points. We define these stationary points here and review their properties. The sign rule for ellipse fields requires that the sign of the singularity indices I_(C)=±1/2 of the C-points on non-self-intersecting lines of constant azimuthal ellipse orientation (modulo π/2), i.e., a-lines, alternate along the line. We verify this rule experimentally, using a newly developed interferometric technique to measure C-points and a-lines in an elliptically polarized random optical field.
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