  We discuss in two companion papers (arXiv:1802.03737 and the present
manuscript) how Fourier-space measurements may be coupled to rheological tests
in order to elucidate the relationship between mechanical properties and
microscopic dynamics in soft matter. In this second companion paper, we focus
on Differential Dynamic Microscopy (DDM) under shear. We highlight the
analogies and the differences with Dynamic Light Scattering coupled to
rheology, providing a theoretical approach and practical guidelines to separate
the contributions to DDM arising from the affine and the non-affine part of the
microscopic displacement field. We show that in DDM under shear the coherence
of the illuminating source plays a key role, determining the effective sample
thickness that is probed. Our theoretical analysis is validated by experiments
on 2D samples and 3D gels.
