The National Bureau of Standards has been making optical calculations for well over a year, using both their new high-speed SEAC and the commercially available IBM Card Programmed Electronic Calculator.
Formulas especially suitable for machine computation are presented here. These enable a general ray to be traced through a rotationally symmetrical system of spherical or nonspherical surfaces. Formulas are also given for computing first- and third-order coefficients for any centered optical system.
The formulas are derived from well-known forms, but they are transformed so that none of the quantities used in the machine ever becomes indeterminate or infinite. The formulas for first- and third-order coefficients are simpler than those frequently given and are very convenient for hand calculation.
DONALD P. FEDER, "Optical Calculations with Automatic Computing Machinery," J. Opt. Soc. Am. 41, 630-634 (1951)