By calculating the optimal wave pattern for the incident laser light, it becomes possible to accurately measure objects located behind disordered structures.

Laser beams can be used to precisely measure an object’s position or velocity. Normally, however, a clear, unobstructed view of this object is required – and this prerequisite is not always satisfied. In biomedicine, for example, structures are examined, which are embedded in an irregular, complicated environment. There, the laser beam is deflected, scattered and refracted, often making it impossible to obtain useful data from the measurement.

However, in collaboration with researchers at Utrecht University (the Netherlands) and TU Wien (Austria), we have been able to show that meaningful results can be obtained even in such complicated environments. Indeed, there is a way to specifically modify the laser beam so that it delivers exactly the desired information in the complex, disordered environment - and not just approximately, but in a physically optimal way: Nature does not allow for more precision with coherent laser light. The new technology can be used in very different fields of application, even with different types of waves.

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.