The Owens Valley Radio Observatory interferometer has been used to carry out a program of aperture synthesis in the interstellar neutral hydrogen absorption line. Maps having resolutions of 0.2 km s/sup -1/ and about 1.3 have been produced using a novel Fourier inversion method. This paper is devoted to discussions of the observing and analyzing procedures and of the results for the Perseus arm feature in the spectrum of Cassiopeia A. The lower velocity part of this absorption feature is interpreted as arising in regions immediately following a density-wave shock front, while the higher velocity part arises in the main body of the Perseus arm. Cloud diameters of about a parsec (the beamwidth) or less and cloud densities on the order of 50 cm/sup -3/ within the arm and 300 cm/sup -3/ within the post-shock region are suggested by the data. From the extensive small-scale structure found, it is clear that the difference in the observed widths of hydrogen emission and absorption profiles is due, at least partly, to the difference in spatial resolution in the two types of observation. One unusual feature is found which may be interpreted as a rotationally unstable cloud.