Periodic capillary‐gravity waves on a fluid of finite depth are studied theoretically by using various perturbation schemes. The classical perturbation scheme is utilized to obtain the wave profile up to and including the fourth order of approximation. The classical perturbation scheme possesses singularities for certain wave numbers, and Wilton's analysis for this situation is generalized to include finite depth. In the vicinity of the singular wave numbers, the method of strained coordinates as initiated by Pierson and Fife for infinite depth is extended to finite depth. Finally, short‐crested waves are studied for the nonsingular case.
The aberrations of systems having (1) two axes of symmetry, (2) one axis of symmetry, (3) no axis of symmetry are investigated via Hamilton's mixed characteristic function W. The mixed characteristic W is also the aberration function in the Luneberg-Kirchhoff diffraction integral. The result is employed to obtain the (incoherent) transfer function for a circular aperture in the presence of these aberrations as well as the point spread function (distribution of illuminance). Typical numerical results are discussed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.