The Index of Refraction to Specific Volume Relation for Sea Water—a Linearized Equation of State

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Abstract
In response to re-emerging interest in optical oceanographic instruments, this Paper looks at the classical relation between specific volume and index of refraction. The specific volume is single-valued in the index of refraction only to 1 × 10−3 cm3 g−1; for accuracies greater than this the manner in which a specific volume change came about must be examined. This paper presents a linearized equation of state for sea water, relating the specific volume to the index of refraction, pressure, and temperature. The algorithm developed here provides specific volume to 5 × 10−5 cm3 g−1 for measurement accuracies of 1 × 10−5 in the index of refraction, 0.3°C in temperature, and 30 db in pressure. The linear approximation is good over the domain:which would be suitable for expendable oceanographic instruments, as well as many retrievable ones. For density-gradient measurements with steps less than 10‰, 20 dh, and 0.2°C, the linearized specific volume-index of refraction relation requires no correction and results in a specific volume accuracy of 4 × 10−5 cm3 g−1.

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