  In germanium-based light detectors for scintillating bolometers, a SiO$_2$
anti-reflective coating is often applied on the side of the germanium wafer
exposed to light with the aim to improve its light collection efficiency. In
this paper, we report about a measurement, performed in the temperature range
25-35 mK, of the light-collection increase obtained thanks to this method,
which resulted to be of the order of 20%. The procedure followed has been
carefully selected in order to minimize systematic effects. The employed light
sources have the same spectral features (peaking at $\sim 630$ nm wavelength)
that will characterise future neutrinoless double beta decay experiments on the
isotope $^{82}$Se and based on ZnSe crystals, such as LUCIFER. The coupling
between source and light detector reproduces the configuration used in
scintillating bolometers. The present measurement clarifies the role of SiO$_2$
coating and describes a method and a set-up that can be extended to the study
of other types of coatings and luminescent materials.
