The ability of space telescopes to see into nascent protostellar systems and even further into our universe is driven by the size of their deployable light collection area. While large monolithic mirrors typically weigh tons, inflatable membrane mirrors present a scalable, ultralightweight alternative. Leveraging decades of advances in adaptive optics technology, the possibility of a well-corrected 20 meter-class space observatory such as the Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is strikingly feasible. However, with great aperture size, comes great metrology requirements. Membrane reflectors are characteristically structured as one transparent and one metallized polymer membrane sealed around a steel tensioning ring. The inflated surface does not naturally conform to a known or prescribed conic but an approximate Hencky surface. Furthermore, multiple internal reflections and polarization interactions between the dielectric and metal layers disturb coherent light that probes it. A non-contact, full-aperture testing method is needed and further, one that can test highly varying membranes after thermoforming too. We present our method in obtaining the absolute shape of thermally formed, inflatable reflectors for space telescopes. Our work measures a 1-meter prototype of the OASIS primary inflatable mirror. Evolving from laser distance scanning to photogrammetry to deflectometry, our survey of metrology techniques for inflatable membrane optics is discussed.