This article describes a characterization of the wavefront aberrations introduced by some typical misalignments and fabrication errors of laser resonators incorporating reflecting axicons. A set of orthonormalized functions were derived and coded into a subroutine of a general purpose interferogram reduction program called MCI. Because squares of coefficients of orthonormal functions may be added to yield the variance of the wavefront, such functions are especially useful in quantifying contributions to the wavefront variance caused by departures from the ideal construction parameters. A description of parabola-parabola reflaxicons in terms of their resonator and beam parameters is given. The resulting system of equations determines a single parameter family of parabolas satisfying the first-order requirements on the reflaxicon. Simple relations between the resonator's linear measurements and inputs to a lens design code are derived. This makes for ready analysis of the resonators using the lens design code linked with MCI. Optical path difference fans and simulated interferograms are presented.