  The measurement of the Transmission Matrix (TM) of a scattering medium is of
great interest for imaging. It can be acquired directly by interferometry using
an internal reference wavefront. Unfortunately, internal reference fields are
scattered by the medium which results in a speckle that makes the TM
measurement heterogeneous across the output field of view. We demonstrate how
to correct for this effect using the intrinsic properties of the TM. For thin
scattering media, we exploit the memory effect of the medium and the reference
speckle to create a corrected TM. For highly scattering media where the memory
effect is negligible, we use complementary reference speckles to compose a new
TM, not compromised by the speckled reference anymore. Using this correction,
we demonstrate large field of view second harmonic generation imaging through
thick biological media.
