Maximum information states for coherent scattering measurements

Abstract

The use of coherent light for precision measurements has been a key driving force for numerous research directions, ranging from biomedical optics1,2 to semiconductor manufacturing3. Recent work demonstrates that the precision of such measurements can be substantially improved by tailoring the spatial profile of light fields used for estimating an observable system parameter4–10. These advances naturally raise the intriguing question of which states of light can provide the ultimate measurement precision11. Here we introduce a general approach to determine the 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 that quantifies the Fisher information from the system’s scattering matrix12. To illustrate this concept, we experimentally show that these maximum information states can probe the phase or the position of an object that is hidden by a disordered medium with a precision improved by an order of magnitude compared with unoptimized states. Our results enable optimally precise measurements in arbitrarily complex systems, thus establishing a new benchmark for metrology and imaging applications3,13.