  Compressive sensing (CS) combines data acquisition with compression coding to
reduce the number of measurements required to reconstruct a sparse signal. In
optics, this usually takes the form of projecting the field onto sequences of
random spatial patterns that are selected from an appropriate random ensemble.
We show here that CS can be exploited in `native' optics hardware without
introducing added components. Specifically, we show that random sub-Nyquist
sampling of an interferogram helps reconstruct the field modal structure. The
distribution of reduced sensing matrices corresponding to random measurements
is provably incoherent and isotropic, which helps us carry out CS successfully.
