  Detection of scattered light can determine the susceptibility of dielectrics.
It is normally limited by Rayleigh's limit: details finer than the wavelength
of the incident light cannot be determined from the far-field domain. We show
that putting the dielectric in motion can be useful for determining its
susceptibility. This inverse quantum optics problem is studied in two different
versions: (i) A spatially and temporally modulated metamaterial, whose
dielectric permeability is similar to that of moving dielectrics. (ii) A
dielectric moving with a constant velocity, a problem we studied within
relativistic optics. Certain features of the susceptibility can be determined
without shining any incident field on the dielectric because the vacuum
contribution to the photodetection signal is non-zero due to the negative
frequencies. When the incident light is shined, the determination of dielectric
susceptibility is enhanced and and goes beyond the classical Rayleigh limit; it
pertains to evanescent waves for (ii), but reaches the far-field domain for
(i).
