The application of the Ronchi ruling beam characterization method to axially symmetric optical beams is analyzed. Specific results are derived for the Airy and focused annulus diffraction patterns. Plots of the ratio of minimum to maximum transmitted optical power versus the first null radius of the beam functions show that for the Airy pattern and other focused annuli with obscuration ratios smaller than approximately 0.30, the method should be just as useful as with Gaussian beams.