Studying the small scale ISM structure with supernovae
  AIMS. In this work we explore the possibility of using the fast expansion of
a Type Ia supernova photosphere to detect extra-galactic ISM column density
variations on spatial scales of ~100 AU on time scales of a few months.
  METHODS. We constructed a simple model which describes the expansion of the
photodisk and the effects of a patchy interstellar cloud on the observed
equivalent width of Na I D lines. Using this model we derived the behavior of
the equivalent width as a function of time, spatial scale and amplitude of the
column density fluctuations.
  RESULTS. The calculations show that isolated, small (<100 AU) clouds with Na
I column densities exceeding a few 10^11 cm^-2 would be easily detected. In
contrast, the effects of a more realistic, patchy ISM become measurable in a
fraction of cases, and for peak-to-peak variations larger than ~10^12 cm^-2 on
a scale of 1000 AU.
  CONCLUSIONS. The proposed technique provides a unique way to probe the
extra-galactic small scale structure, which is out of reach for any of the
methods used so far. The same tool can also be applied to study the sub-AU
Galactic ISM structure.
