Abstract
The problem addressed here is that of determining the first-order ray-transfer characteristics of an unknown optical system from the positions and directions of rays entering and leaving the system. Mathematically, the problem is a rather daunting one of solving a set of linear equations subject to a set of nonlinear constraints for a total of 10 or 14 unknowns. The nonlinearities are removed by rephrasing the problem, expressed initially in terms of the ray-transfer matrix of the system, 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 the unknowns.
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