2 - 1D First-Order Optical Systems: The Ray-Transfer Matrix

Abstract

This chapter analyzes the construction of the optical matrices, describing the propagation of light rays through linear stigmatic and simple astigmatic optical systems. The basic tools of the strategy are the optical Hamiltonian and the associated Hamilton's equations for the evolution of the light ray as propagating through the system along the optical axis. The Cartesian space spanned by the ray position and momentum coordinates is the geometrical optical phase space. The ray is represented by points in the 4D optical phase space and accordingly the ray path in real space corresponds to a trajectory of the ray representative point in phase space. It is found that within the ray picture of geometrical optics, a light beam may be described as a collection of rays. It covers a certain area on the reference screen and contains rays throughout a certain range of inclination angles. The invariance of the phase space density implies the invariance of the phase space volume of the region enclosing the ray-bundle representative points. The ray transfer operator and matrix are also elaborated.