ABSTRACT
Non-imaging optics are usually designed as two-dimentional profiles that are then extruded to form a trough-like optic, or rotated to generate a rotational optic, or crossed to form a square cross-section optic. This optics is usually not ideal in three-dimentional (3-D) geometry. The Minano design method using Poisson brackets utilizes an extra degree of freedom to design ideal 3-D optics. Three-dimensional optical systems are described by the canonical Hamiltonian equations in which H is the Hamiltonian. Two-dimensional optical systems have one less dimension and are described by the canonical Hamiltonian equations in which H is the Hamiltonian. The way light is transferred in phase space from the entrance to the exit apertures of an optical system defines its characteristic type of optics.
