Algebraic ray-trace equations for axially symmetric optical systems are expanded in terms of system parameters and paraxial variables. The transfer parameter used is optical path, and equations are given for second-, fourth-, sixth-, and eighth-order differences in optical path of a ray from the axial value. Selected rays are traced to a tilted reference sphere in the exit pupil, optical path differences of given order are equated to the wave aberration polynomial of corresponding order and with proper coordinates, and the resulting linear equations are solved for wave aberration coefficients.
© 1976 Optical Society of America
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