Minimal size of the focal spot when focusing a field in a waveguide using a vertical array

The paper considers the problem of using a vertical array to focus a monochromatic field in the vicinity of a given point of an underwater sound channel. The solution to the problem is discussed, which has been obtained with a limitation on the initial grazing angles of the emitted waves. The limitation is introduced to increase the stability of the solution to the influence of random perturbations of the sound velocity field. Then, the radiated field represents a wave beam propagating along a reference ray that connects the center of the array and the focusing point. In the geometric optics approximation, analytic estimates of the smallest possible dimensions of the focal spot are obtained. A simplified version of the formula is obtained for the vertical scale of the spot convenient for rough express estimates and comparison of the focusing properties of waveguides with different sound velocity profiles.