Explicit Cartesian oval as a superconic surface for stigmatic imaging optical systems with real or virtual source or image

Cartesian ovals, also known as rigorously stigmatic surfaces, are the simplest optical systems capable of producing a perfect point image. Exist both implicit and explicit expressions to represent these surfaces, but they treat both refractive and reflective surfaces independently. Because of the complexity of explicit expressions, the ray-tracing techniques for these surfaces are implemented using third-party software. In this paper, we express Cartesian ovals as a degenerated superconic curve and get a new explicit formulation for Cartesian ovals capable of treating image formation using both object and image points, either real or virtual, and in this formulation can deal with both reflective and refractive rigorously stigmatic surfaces. Finally, using the resultant expressions and the vector Snell–Descartes Law, we propose a self-contained analytical ray-tracing technique for all these surfaces.

James Clerk Maxwell at Aberdeen - 1856-1860

EARLY in 1856 James Clerk Maxwell, then a Fellow of Trinity College Cambridge, applied for the Chair of Natural Philosophy at Marischal College, Aberdeen. He was at that time the author of eight papers, the earliest— on Cartesian Ovals—being written when he was still a schoolboy at Edinburgh Academy. In an 1855 paper he had invented the additive process of colour photography by which he was later (1861) to take the first colour photograph; and another 1855 paper had manifested his interest in Faraday’s Lines of Force, an interest that over the next ten years was to result in the Electromagnetic Theory. He was also the author of several delightful essays. That on analogies dated February 1856, pointed out that an analogy, in discovering one truth under two expressions, is the reciprocal of a pun, which hides two truths under one expression (1). And an essay of a month later asked whether autobiography was possible, remarking that ‘When a man once begins to make a theory of himself, he generally succeeds in making himself into a theory’. The liveliness of mind transfusing these essays and the physical insight shown in his serious papers made Maxwell’s candidature a strong one despite the fact that he was no more than 24 years of age.