Sub-Nyquist interferometry (SNI) provides a method for measuring wavefronts with large departures from a reference sphere, such as those encountered when testing steep aspheric surfaces. SNI allows wavefronts with several hundred waves of departure to be recorded and analyzed. The theory of SNI is reviewed, its experimental implementation described, and limitations in the hardware and potential improvements are discussed. The importance of calibrating the interferometer for non-null testing is demonstrated.