A Quadratic Conduction Gas Lens

A gas lens system to transmit a light beam through a tube should have a favorable refractive index, negligible aberrations, and a simple construction. The favorable refractive index must be such that all light rays parallel to the tube axis, but of varying distances from t h a t axis, converge at approximately the same point on the axis, the distance being called the focal length. Within the paraxial ray approximation it is easy to show that an r- variation of the refractive index has this property (see, for example, Refs. 1 and 2). Berreman obtained a refractive index (which varied approximately as the square of the radius) by flowing a gas through a cold cylinder enclosing a warm helix aligned on the axis.3 The interior of the helix has the desired refractive index. Marcuse and Miller simplified Berreman's lens by considering a cool gas flowing through a heated cylinder of uniform temperature (the Graetz problem). 1 - 2 2281 2290 T H E BELL SYSTEM T E C H N I C A L JOURNAL, SEPTEMBER