In the astronomically natural transitional approximations for waves near caustics in gravitational lensing, the familiar wavelength scalings associated with short-wave asymptotics are accompanied by a variety of dependences on disparate astronomical lengths, such as the Schwarzschild radius, separation of binary stars, and distance to the lens. These dependences are calculated analytically for spacings of interference fringes and the corresponding intensity amplifications, for two much-studied models: lensing of a distant source by an isolated star and near the fold and cusp caustics from a binary star lens. If the aperture of a telescope looking in the direction of the source is modelled by Gaussian apodization, the image is a complexification of the wave in the observation plane.