  We have obtained the power spectral description of the density and opacity
fluctuations of the cold HI gas in the Galaxy towards Cas A, and Cygnus A. We
have employed a method of deconvolution, based on CLEAN, to estimate the true
power spectrum of optical depth of cold HI gas from the observed distribution,
taking into account the finite extent of the background source and the
incomplete sampling of optical depth over the extent of the source. We
investigate the nature of the underlying spectrum of density fluctuations in
the cold HI gas which would be consistent with that of the observed HI optical
depth fluctuations. These power spectra for the Perseus arm towards Cas A, and
for the Outer arm towards Cygnus A have a slope of 2.75 +/- 0.25 (3sigma
error). The slope in the case of the Local arm towards Cygnus A is 2.5, and is
significantly shallower in comparison. The linear scales probed here range from
0.01 to 3 pc. We discuss the implications of our results, the non-Kolmogorov
nature of the spectrum, and the observed HI opacity variations on small
transverse scales.
