  When light propagates through a complex medium, such as a multimode optical
fibre (MMF), the spatial information it carries is scrambled. In this work we
experimentally demonstrate an all-optical strategy to unscramble this light
again. We first create a digital model capturing the way light has been
scattered, and then use this model to inverse-design and build a complementary
optical system - which we call an optical inverter - that reverses this
scattering process. Our implementation of this concept is based on multi-plane
light conversion, and can also be understood as a diffractive artificial neural
network or a physical matrix pre-conditioner. We present three design
strategies allowing different aspects of device performance to be prioritised.
We experimentally demonstrate a prototype optical inverter capable of
simultaneously unscrambling up to 30 spatial modes that have propagated through
a 1m long MMF, and show how this enables near instantaneous incoherent imaging,
without the need for any beam scanning or computational processing. We also
demonstrate the reconfigurable nature of this prototype, allowing it to adapt
and deliver a new optical transformation if the MMF it is matched to changes
configuration. Our work represents a first step towards a new way to see
through scattering media. Beyond imaging, this concept may also have
applications to the fields of optical communications, optical computing and
quantum photonics.
