We present measurements of the intensity as well as the phase distribution in the various diffraction orders of computer-generated holograms designed to generate a higher order Gauss–Laguerre beam. For the direct measurement of the phase distribution in the diffraction orders a high-resolution interferometer is used, which allows access to a lateral length scale for the localization of phase singularities below the wavelength. It is experimentally shown that in beams that carry multiple singularities, the dislocations do not degenerate. This effect cannot be seen by analyzing only the intensity distribution of the laser beam.