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The Maxwell fish eye lens is a gradient index design from 1854 with a spherically symmetrical gradient. In one version the gradient index ball has an index of refraction of 3.0 at the center and 1.5 at its outer surface. It images perfectly any point on its surface to a point on the opposite side of the sphere. The ray paths are arcs of circles. A diagram like Fig.1 can be found everywhere in textbooks or on the internet. Fig 1. .Maxwell gradient index fish eye lens with spherical symmetry. In 1991 at the OSA annual meeting I pointed out that if a reflecting coating is placed on the outside of the ball then any ray from a point #1 on the surface will go to point #2, reflect and go back to point #1, reflect and continue around back and forth forever [1]. Then I showed by a very simple geometrical argument that such a system has a very unexpected property. Any point inside the volume of the ball is imaged perfectly, after just one reflection from the inside of the outer surface, to another point inside the ball with a magnification of -1.0 X. That means that the entire inner volume of the ball is perfectly imaged at -1.0X. After two reflections inside the ball every point is imaged perfectly back onto itself with a magnification of +1.0X. Since every point inside the gradient index ball is imaged perfectly after one inside reflection that means that any interior flat surface is also perfectly imaged to another interior flat surface. That type of perfect system had never existed before, of perfectly imaging a flat surface that is real to a flat image that is real. Table 1 shows how that new design from 1991 compared to the very few previously known perfect imaging systems. The perfect flat object and image are not in air, however, but are buried inside the gradient index ball. Point
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