DETERMINATION OF THE PARAXIAL RAY-TRANSFER CHARACTERISTICS OF AN OPTICAL-SYSTEM FROM RAYS PASSING THROUGH IT

The problem addressed here is that of determining the first-order ray- transfer characteristics of an unknown optical system from the positio ns and directions of rays entering and leaving the system. Mathematica lly, the problem is a rather daunting one of solving a set of linear e quations subject to a set of nonlinear constraints for a total of 10 o r 14 unknowns. The nonlinearities are removed by rephrasing the proble m, expressed initially in terms of the ray-transfer matrix of the syst em, into one in terms of the point characteristic matrix. The problem is then solved by converting it to a linear equation in a vector of th e unknowns.