Maximum information states for coherent scattering measurements

“The use of coherent light for precision measurements has been a key driving force for numerous research directions, ranging from biomedical optics to semiconductor manufacturing. Recent work demonstrates that the precision of such measurements can be significantly improved by tailoring the spatial profile of light fields used for estimating an observable system parameter. These advances naturally raise the intriguing question of which states of light can provide the ultimate measurement precision and of how such states can be identified in an experiment. Here, we introduce a general approach to determine optimal coherent states of light for estimating any given parameter, regardless of the complexity of the system. Our analysis reveals that the light fields delivering the ultimate measurement precision are eigenstates of a Hermitian operator which quantifies the Fisher information based on the system’s scattering matrix. To illustrate this concept, we experimentally show that these maximum information states probe the phase of an object that is hidden by a disordered medium with a precision improved by an order of magnitude as compared to unoptimized states. Our results enable precision measurements in arbitrarily complex systems, with promising perspectives for metrology and imaging applications.”