Autocorrelation phase at one period lag: A rigorous approach

The method used by Birdsall et al. [J. Acoust. Soc. Am. 96, 2353–2356 (1994)] is a particular application of the generalized cross-correlation function introduced by Knapp and Carter in 1976 and extended for differential phase and Doppler estimation by Wax in 1982. The rigorous derivation of the phase estimate at one period lag in ocean acoustic tomography is reformulated, using the equivalence with an array model.