  We consider the differential equation that Zernike proposed to classify
aberrations of wavefronts in a circular pupil, as if it were a classical
Hamiltonian with a non-standard potential. The trajectories turn out to be
closed ellipses. We show that this is due to the existence of higher-order
invariants that close into a cubic Higgs algebra. The Zernike classical system
thus belongs to the class of superintegrable systems. Its Hamilton-Jacobi
action separates in three vertical projections of polar coordinates of a
sphere, polar and equidistant coordinates on half-hyperboloids, and also in
elliptic coordinates on the sphere.
