Lens Design Fundamentals, 2nd Edition

Chapter 9

Coma and the Sine Condition

9.1 THE OPTICAL SINE THEOREM

The Lagrange theorem applies only to paraxial rays, while the optical sine theorem is the equivalent for marginal rays. The optical sine theorem provides an expression for the image height formed by a pair of sagittal rays passing through a single zone of a lens. It is valid for a zone of any size but only at very small obliquity. This obliquity limitation effectively removes all aberrations except coma, which is represented by a difference between the image height for the selected zone and the paraxial image height given by the theorem of Lagrange. Recall that coma can be considered a variation in magnification from one zone to another zone as discussed in Section 4.3.4.

To derive ...