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 \pm 0.25 ( 3 \sigma 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 .