Noise-resistant phase imaging with intensity correlation

Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.