A simple derivation is given of the phase autocorrelation function of a monochromatic signal during transmission through a medium with random fluctuations of refractive index. The resulting phase coherence function is then applied to the theory of the linear array antenna to yield a formula for the degraded directivity pattern.
The analysis developed here was conceived primarily with reference to acoustic signals and sonar ranging systems, although it may be applied, mutatis mutandis, to a wider variety of acoustic and even electromagnetic problems. For concreteness, however, we shall employ a vocabulary appropriate to the case of sonar signals and antennas.
The problem to be considered is the following: Given a source of monochromatic radiation situated far enough from the receiving antenna to be considered a point source, what will be the response, as a function of bearing angle, of a linear array antenna to the signal if the transmission medium has small random irregularities of its refractive index?