The bichromatic intensity correlation of radiation reflected off a randomly irregular surface

When phase information is absent (incoherent detection), the basic statistical entity relevant to data processing is the bichromatic four-point coherence. Using the strength and size parameters Φ ²and A, an integral expression for this quantity is formulated and evaluated for a high-frequency signal scattered by a phase screen that represents the randomly reflecting ocean cover (or, alternatively, a randomly refracting thin layer). The evaluation is illustrated by a treatment of the monochromatic mean-square intensity (I²), then applied to the bichromatic intensity correlation (I₁I₂). Viewed as a function of the frequency-independent parameter ⋏Φ, (I²) rises from 1 to 2, passing through a maximum which scales as log k (the wavenumber) at some intermediate value of ⋏Φ that depends only on the form of the screen statistics. By constrast, (I₁I₂) saturates at 1. Moreover, even when ⋏Φ is large, the second and fourth coherence moments are found to be consistent with the assumption that the bichromatic signal possesses joint normal statistics only within a narrow range of frequency separations (~O(1/Φ)), which nonetheless encompasses the coherent bandwidth (~O(1/⋏Φ ²)).