In this paper we present expressions derived for mathematical simulation of the process of image transfer in optoelectronic observational systems (OEOS). Such systems include, as their linear components, atmospheric and water channels and allow for the state of the air-water interface, the geometry of its illumination, and the parameters of the source of light and of the optical detector. We consider a scheme of observations, most interesting from the practical point of view, when a narrow beam receiver scans targets illuminated by a broad beam source. It is shown that an effect of enhanced backscattering may be observed in a transparent medium and large scale correlated waves. Computational results are compared to observational data. To estimate OEOS quality, we use detection and identification probabilities for a test target observed against an additive background. We analyze the dependences of these probabilities on the position of a layer of high turbidity between the target and the OEOS, when observations take place in the McClatchey-Fenn atmosphere. It is shown that when such a layer moves from target to observer, the detection probability monotonically decreases, while identification attempts may, depending on the angular size of the target, result in the tracing-paper effect, the t-effect, or a monotonic increase of identification probability.