Abstract

Recently objective measures of the information densities in both the spatial and spectral domains have been developed in the context of satellite retrievals of temperature and moisture profiles of the atmosphere (Purser and Huang, 1993; Huang and Purser, 1993). Densities of two measures of "information" are formulated. The first measure, "degrees of freedom for signal" (DFS) corresponds approximately to the effective dimensionality of the constraints imposed upon each retrieval by the set of measurements (Wahba, 1985). The second measure is the decrease in "entropy" in the sense defined by Shannon (1984) in the theory of communication. The matrix algebra of optimal linear retrieval suggests very natural definitions of both of these quantities, not only as distributions in height but, with equal validity, as densities distributed in the infrared spectrum itself.

© 1993 Optical Society of America