  The Cold Dark Matter (CDM) model for galaxy formation predicts that a
significant fraction of mass in the dark matter haloes that surround L L*
galaxies is bound in substructures of mass 1E4-1E7Msun. The number of
observable baryonic substructures (such as dwarf galaxies and globular
clusters) falls short of these predictions by at least an order of magnitude.
We present a method for searching for substructure in the haloes of
gravitational lenses that produce multiple images of QSOs, such as 4-image
Einstein Cross lenses. Current methods based on broadband flux ratios cannot
cleanly distinguish between substructure, differential extinction, microlensing
and, most importantly, ambiguities in the host lens model. These difficulties
may be overcome by utilizing the prediction that when substructure is present,
the magnification will be a function of source size. QSO broad line and narrow
line emission regions are approximately ~1pc and >100pc in size, respectively.
When narrow line region (NLR) features are used as a normalisation, the
relative intensity and equivalent width of broad line region (BLR) features
will respectively reflect substructure-lensing and microlensing effects.
Spectroscopic observations of just a few image pairs would probably be able to
cleanly extract the desired substructure signature and distinguish it from
microlensing. In the rest-optical, the Hbeta/[OIII] region is ideal, since the
narrow wavelength range also largely eliminates differential reddening
problems. Simulations of Q2237+030 are done as an example to determine the
level of substructure that is detectable in this way, and possible systematic
difficulties are discussed. This is an ideal experiment to be carried out with
near-infrared integral field unit spectrographs on 8-m class telescopes.
