Characteristics of the Image System based on Photon Density Waves in Observing Underwater Objects through a Waved Surface

Abstract

The wavy surface effect on the resolution of optical imaging systems employing narrow modulated probing beams is studied. Relations are formulated connecting the complex amplitudes of the photon density waves (propagating through the wavy interface and the water layer) to the main parameters of the problem. These relations consider the finite waves height and the change in the photon trajectory length due to random refraction of rays upon entering the water. The optical transfer function of the wavy surface and the beam scattering function averaged over the ensemble of surface waving realizations are introduced. The dependences of these functions on the surface waves integral parameters, namely, the elevations and slopes dispersions, are examined. The contributions of surface waving and water layer to the generation of optical transfer functions and to the overall signal level from an underwater object when it is imaged using photon density waves are estimated. It is shown that in a certain range of depths, spatial frequencies, and illumination beam modulation frequencies, the systems employing photon density waves can demonstrate advantages over the systems with stationary illumination.