Patent ID: 8339716

Claim:
An illumination lens comprising: first surface and a second surface wherein at least a portion of the first surface has a shape described by a differential equation DE1 defined in a polar coordinate system: DE1 ∂ ∂ ϕ1 ⁢ r ⁢ ⁢ 1 ⁢ ( ϕ1 ) = - r ⁢ ⁢ 1 ⁢ n ⁢ ⁢ 2 ⁢ sin ⁡ ( ϕ2 - ϕ1 ) n ⁢ ⁢ 2 ⁢ cos ⁡ ( ϕ2 - ϕ1 ) - n ⁢ ⁢ 1 where: n2 is an index of refraction of the lens; n1 is an index of refraction of a medium surrounding the lens; r1 is a radial coordinate of the lens surface; phi1 is a polar angular coordinate of the first surface; phi2 is a polar angle of an ideal ray emitted at an origin of a coordinate system in which the differential equation DE1 is defined that was initially emitted at angle phi1 after the ideal ray passed through the second lens surface; with an initial condition r1_ini.