Intensity measured with the optimal incident field when the hidden target is absent (left) and present (right). Because of complex scattering processes, these distributions appear as speckle patterns. Despite this complexity, the optimal light field is strongly affected by the presence of the target, which allows us to detect it with a minimum rate of error.
In free space, it is easy to determine whether an object is present or not by measuring the light it scatters. However, whenever this object is surrounded by a complex scattering environment, this task becomes extremely challenging due to the absorption and multiple scattering processes that occur within the system.
In this work, we theoretically and experimentally demonstrate how to detect an object hidden inside a disordered complex system with an exceptionally low photon flux. This is achieved by identifying and generating probe fields that are specifically optimized for this purpose. Light is guided through the disorder in an optimal way, not only to strongly interact with the object, but also to be efficiently detected by the observer. These results allow one to perform minimally-destructive measurements even in complex scattering systems, with potential applications for the metrology of semi-conductor devices and for the characterization of biological tissues.
Because of quantum noise fluctuations, the rate of error achievable in decision problems involving several possible configurations of a scattering system is subject to a fundamental limit known as the Helstrom bound. Here, we present a general framework to calculate and minimize this bound using coherent probe fields with tailored spatial distributions. As an example, we experimentally study a target located in between two disordered scattering media. We first show that the optimal field distribution can be directly identified using a general approach based on scattering matrix measurements. We then demonstrate that this optimal light field successfully probes the presence of the target with a number of photons that is reduced by more than 2 orders of magnitude as compared to unoptimized fields.
