A method to identify the azimuthal index of vortices and the radial parameter of axicons, as well as their associated spatial frequencies, is presented. These constructive parameters are employed to design parallel superimposed computer-generated holograms (PSCGHs). The diffraction patterns are studied in correspondence with the constructive parameters of the PSCGH. Another diffractive structure serving as identification key is inserted in the entire beam emerging from the PSCGH. The method identifies the parameters set in the first and second diffraction orders. The robustness and sensitivity of the method were checked against parameter mismatches. This method can be exploited as an authentication tool for holographic stamps incorporating PSCGHs.