ABSTRACT
This chapter presents methods that are suitable for studying water waves in focal regions within the framework of linearised theory. In addition to the assumption of linearity, we restrict our attention to water of constant depth. The chapter begins by considering a linearised boundary-value problem, in which the velocity potential is assumed to be known in a vertical plane. To this problem we derive exact solutions in terms of angular-spectrum representations and impulse-response integrals. The adjective 'perfect' is used to characterise an incident wave that in the limit of an infinitely large aperture would produce a d function field distribution on the focal line if account were also taken of evanescent waves. In the latter two cases the wave that propagates towards the focal point is assumed to originate from a point source and to be transformed by a lens, which delays the phase of the incident wave in a perfect manner without influencing its amplitude.
