  Random scattering of light in disordered media is an intriguing phenomenon of
fundamental relevance to various applications. While techniques such as
wavefront shaping and transmission matrix measurements have enabled remarkable
progress for advanced imaging concepts, the most successful strategy to obtain
clear images through a disordered medium remains the filtering of ballistic
light. Ballistic photons with a scattering-free propagation are, however,
exponentially rare and no method so far can increase their proportion. To
address these limitations, we introduce and experimentally implement here a new
set of optical states that we term Scattering Invariant Modes (SIMs), whose
transmitted field pattern is the same, irrespective of whether they scatter
through a disordered sample or propagate ballistically through a homogeneous
medium. We observe SIMs that are only weakly attenuated in dense scattering
media, and show in simulations that their correlations with the ballistic light
can be used to improve imaging inside scattering materials.
