|Quasi-Optical design of the Odin millimetre/submillimetre wave radiometer|
The equivalent of an off-axis ellipsoid mirror using a lens has the shape determined by a Cartesian Oval. A lens with a surface of revolution based on a Cartesian Oval will transform a beam of some phase radius into a beam of another, finite, phase radius.
The second surface of the lens is spherical and matches the phase radius of the beam at that distance. The second surface therefore makes no transformation on the beam, and all the beam shaping is done by the Cartesian Oval surface. This is called a "single-surface lens".
Knowing the quasioptical parameters of the beam, and the mechanical constraints, it is then a simple matter to generate a mechanical drawing for manufacture of the lens.