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Classical or quantum systems that stem from a basic symmetry are seen to be special in having several important properties. The harmonic oscillator and the Bohr system are such. Recent research into the Zernike system provides reasons to include it in this privileged class. Here we show that free motion on the 3-sphere can be projected down to produce classical orbits or complete and orthogonal bases for wavefronts in a circular pupil. This line of inquiry has been pursued in company with N.M. Atakishiyev, G.S. Pogosyan, C. Salto-Alegre, and A. Yakhno.

From Free Motion on a 3-Sphere to the Zernike System of Wavefronts Inside a Circular Pupil