Appendix A DERIVATION AND EXPLANATION OF THE ÉTENDUE INVARIANT, INCLUDING THE DYNAMICAL ANALOGY; DERIVATION OF THE SKEW INVARIANT
A.1 THE GENERALIZED ÉTENDUE
In Section 2.7 we introduced the invariant
The meaning of this was as follows: Let any ray be traced through an optical system, and let rectangular coordinate axes be set up in the entry and exit spaces in arbitrary orientations. Also, let the ray meet the x, y plane in the entry space in (x, y), and let its direction cosines be (L, M, N), and similarly for the exit space. Then for any nearby ray with coordinates (x + dx, y + dy, L + dL, M + dM) we have
We shall ...