Abstract

Random scattering of light, which takes place in paper, paint and biological tissue is an obstacle to imaging and focusing of light and thus hampers many applications. At the same time scattering is a phenomenon of basic physical interest and its relation to the information content of light is subtle and in many cases focusing. metrology and imaging are still possible. Here we show shaped light fields that are relevant to imaging and measurements in scattering environments. We present maximum information states, which are light states that carry a maximum amount of information about a given observable, enabling the most precise measurements that are possible given a coherent input beam. Conversely, scattering invariant modes are the least sensitive modes to the presence of a scattering sample and they retain the same output profile whether propagated through a scattering material or through air. We demonstrate these states experimentally and show numerically their relevance to imaging inside scattering media.