  Here, we present a concept based on the realization that a complex medium can
be used as a simple interferometer. Changes in the wavefront of an incident
coherent beam can be retrieved by analyzing changes in speckle patterns when
the beam passes through a light diffuser. We demonstrate that the spatial
intensity correlations of the speckle patterns are independent of the light
diffusers, and are solely determined by the phase changes of an incident beam.
With numerical simulations using the random matrix theory, and an experimental
pressure-driven wavefront-deforming setup using a microfluidic channel, we
theoretically and experimentally confirm the universal sensitivity of speckle
intensity correlations, which is attributed to the conservation of optical
field correlation despite multiple light scattering. This work demonstrates
that a complex media is a simple interferometer, and presents opportunities to
replace complicated reference-beam-assisted interferometers with a simple and
compact scattering layer in various applications in metrology, analytical
chemistry, and biomedicine.
