Optical Models and Symmetries from Finite to Continuous

This contribution to the Proceedings bears the same title as the chapter by this author published in Progress in Optics, and recovers the basic construction starting from the compact algebras so(3) or so(4) for 1- and 2-dimensional finite pixellated-screen optics and their contraction to the Euclidean algebras, in which the geometric and wave models find their realization determined by two symmetry subalgebras, but with questions that may prompt further research. Here we follow and question the path from pixellated-screen optics to three-dimensional geometric optics by contraction between Lie algebras and groups.