Superposition of sphero-cylindrical lenses using contour graphs.

Background: The superposition of thin sphero-cylindrical lenses with arbitrary angles between cylindrical axes is sometimes required in a clinical setting. For example, it may be useful in some instances to perform an overrefraction which, added to the spectacle or toric contact lens in place on the eye, yields a final correcting lens.
Methods: Computer calculations have been used to create contour graphs allowing a graphical solution to the problem of combining sphero-cylindrical lenses. Although conceptually strightforward, the method has not been presented before.
Results: The use of contour graphs to superpose sphero-cylindrical lenses is shown by examples to be accurate and much simpler than calculational methods.
Conclusions: Lacking a pre-programmed computer, the method of contour graphs offers a practical method of combining sphero-cylindrical lenses.