The ABCD matrices for reflection and refraction for any incident angle and surface

International audienceA method to derive the ABCD matrices for reflection and refraction for any diopter under arbitrary incident angle is developed. The result is benchmarked on a commercial software for an optical system compound of two cylindrical lenses. It is used to simulate the general astigmatism and calculate the resulting Orbital Angular Momentum of a laser beam that propagate through a pair of cylindrical lenses. It more generally useful to ease and simplify such kind of simulations in any optical system by avoiding use of complicated commercial softwares