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 Λ, 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 〈I 2〉, then applied to the bichromatic intensity correlation 〈I1I2〉. Viewed as a function of the frequency‐independent parameter ΛΦ, 〈I2〉 rises from 1 to 2, passing through a maximum which scales as log k(the wavenumber) at some intermediate value of ΛΦ that depends only on the form of the screen statistics. By constrast, 〈I1I2〉 saturates at 1. Moreover, even when ΛΦ 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/ΛΦ 2)).