ABSTRACT

Here we derive the conservation of étendue from optical fi rst principles, utilizing a reference wave front from which we can calculate the optical path length to a given point P = (x1, x2, x3). It is then possible to defi ne a function S(P) = S(x1, x2, x3) that gives the optical path length between the reference wave front and any given point. The momentum or a light ray at point P is given by p = ∇S, where ∇ = (∂/∂x1, ∂/∂x2, ∂/∂x3). Accordingly, if we now consider another point P* = ( x 1*, x 2*, x 3*), we have p*= ∇*S, where ∇* = (∂/∂ x 1*, ∂/∂ x 2*, ∂/∂ x 3*).