Image formation with regard to object shadow for objects inside a scattering medium

The conventional theory of image transfer through a scattering medium treats objects located upon reflecting surfaces. It is shown that, when an object is located inside a scattering medium and shields a part of space, ignoring the shadowing leads to incorrect results, especially for modern time-gating systems. We develop a general theory of image formation including the shadowing effect when an object is located inside a scattering medium. The example of the observation of a submerged object through a windy ocean surface is chosen to illustrate this theory. A few unexpected effects in imaging of a submerged object are found and discussed, including contrast conversion for a sinking object and higher contrast in the shadow image than in the image of the object itself. The conclusion that using the shadow image for detection of a submerged object can be more efficient than using the image of the object itself is of practical significance.