  Cm-wavelength radio continuum emission in excess of free-free, synchrotron
and Rayleigh-Jeans dust emission (excess microwave emission, EME), and often
called `anomalous microwave emission', is bright in molecular cloud regions
exposed to UV radiation, i.e. in photo-dissociation regions (PDRs). The EME
correlates with IR dust emission on degree angular scales. Resolved
observations of well-studied PDRs are needed to compare the spectral variations
of the cm-continuum with tracers of physical conditions and of the dust grain
population. The EME is particularly bright in the regions of the rho Ophiuchi
molecular cloud (rho Oph) that surround the earliest type star in the complex,
HD 147889, where the peak signal stems from the filament known as the rho Oph-W
PDR. Here we report on ATCA observations of rho Oph-W that resolve the width of
the filament. We recover extended emission using a variant of non-parametric
image synthesis performed in the sky plane. The multi-frequency 17 GHz to 39
GHz mosaics reveal spectral variations in the cm-wavelength continuum. At ~30
arcsec resolutions, the 17-20 GHz intensities follow tightly the mid-IR, Icm
propto I(8 um), despite the breakdown of this correlation on larger scales.
However, while the 33-39 GHz filament is parallel to IRAC 8 mum, it is offset
by 15-20 arcsec towards the UV source. Such morphological differences in
frequency reflect spectral variations, which we quantify spectroscopically as a
sharp and steepening high-frequency cutoff, interpreted in terms of the
spinning dust emission mechanism as a minimum grain size a_cutoff ~ 6 +- 1A
that increases deeper into the PDR.
