Goldstein began work in the mid 1980s on topographical mapping techniques using synthetic aperture radar. Initially using two antennas (and later a single antenna with a repeated track), he was able to use the phase interferometry to improve over stereoscopic optical mapping techniques. Goldstein then developed his revolutionary "crabgrass growing" algorithm for phase unwrapping, which resolves ambiguities in phase data and isolates local noise and errors that would otherwise cause global errors. This algorithm simplified the creation of accurate elevation maps, and made possible many new applications for radar interferometry, including satellite detection and quantification of small changes such as land subsidence, ice flow motion, ocean currents, and geological fault shifts. Subsequent work includes algorithms for mitigating thermal noise in the phase data, yielding dramatic improvements in the quality of measurement and phase data.