Light Collection within the Framework of Geometrical Optics*

The problem of light collection is examined from first principles within the framework of geometrical optics. From the outset, we distinguish between light collection and the usual theory of image formation. From phase-space considerations, we derive the sine inequality, a generalization of the Abbe sine law appropriate to nonimaging systems. We construct two- and three-dimensional nonimaging systems that reduce the f number to the least allowed by the sine inequality. Such systems give substantially improved light collection as compared with conventional systems.