Multipixel sub-shot noise phase measurement with classical light interferometry

We demonstrate accurate phase measurement from low photon level interference data using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods such as balanced homodyning or phase shifting that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase shifting method show that when the same photon resources are used, the optimization method provides phase recoveries with tighter error bars. In particular, RMS phase error performance of the optimization method for low photon number data (10 photons per pixel) shows $>$ 5X noise gain over the phase shifting method. In our experiments where a laser light source is used for illumination, the results imply phase measurement with accuracy better than the conventional single pixel based shot noise limit (SNL) that assumes independent phases at individual pixels. The constrained optimization approach presented here is independent of the nature of light source and may further enhance the accuracy of phase detection when a nonclassical light source is used.