Abstract
Imaging of an underwater object beneath a wind-ruffled random sea surface requires the determination of undersurface (random refraction) and above surface (random reflection and scattering) point spread function (PSF). A finite element analysis was employed assuming a point source taken below the surface, and a large but definite number of rays was propagated through the surface to give a cumulative distribution there. The direction that each ray continues after interacting with a random facet of the sea surface is itself a random function. The probability density of the spherical coordinate angles of the emerging rays that have been emitted from the source (underwater) at arbitrary angles was derived. Figure 1 shows the 1-D probability density for a ray propagating at an arbitrary angle from the vertical and through a random surface for different wave slope variances. For the large, but finite, number of rays that leave the point source, an incoherent sum of the many emergent probability densities about the surface will give a measure proportional to the expected field intensity. This incoherent sum thus yields the desired PSF.
© 1988 Optical Society of America
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