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We have obtained the power spectral description of the density and opacityfluctuations of the cold HI gas in the Galaxy towards Cas A, and Cygnus A. Wehave employed a method of deconvolution, based on CLEAN, to estimate the truepower spectrum of optical depth of cold HI gas from the observed distribution,taking into account the finite extent of the background source and theincomplete sampling of optical depth over the extent of the source. Weinvestigate the nature of the underlying spectrum of density fluctuations inthe cold HI gas which would be consistent with that of the observed HI opticaldepth fluctuations. These power spectra for the Perseus arm towards Cas A, andfor the Outer arm towards Cygnus A have a slope of 2.75 +/- 0.25 (3sigmaerror). The slope in the case of the Local arm towards Cygnus A is 2.5, and issignificantly shallower in comparison. The linear scales probed here range from0.01 to 3 pc. We discuss the implications of our results, the non-Kolmogorovnature of the spectrum, and the observed HI opacity variations on smalltransverse scales.Comment: 19 pages, 7 figures, to appear in the Astrophysical Journal of  November 1, 200

Power Spectrum of the Density of Cold Atomic Gas in the Galaxy toward Cassiopeia A and Cygnus A