Multifocal three-dimensional bootlace lenses

It is well known that a two-dimensional (parallel plate configuration) bootlace lens can be designed to have more than one focal point. Wide angle scanning capabilities of these lenses in two dimensions is well established, being larger for higher number of focal points. However, no three-dimensional bootlace lens having more than one focal point has been reported. It is the purpose of this paper to report on three-dimensional bootlace lenses having two, three, and four perfect focal points. Equations for lens surfaces are obtained for all three cases. The results of the aperture phase error analysis show that a lens with a larger number of focal points can be scanned to much larger angles in one plane at the expense of the scanning capability in the orthogonal plane.