OPTI696a – Fall 2007
Advanced Optical Design
Guest Lecturer: John Koshel – Due: 23 October 2007
Étendue is one of the most important terms in the field of illumination, and
for that matter optical design and analysis. As shown it is poorly understood
by the community, and there is a dearth of literature on the subject. In
class we touched upon: the definition, analogous terms, conservation of it,
and so forth. To ensure your understanding, answer the following:
1. There are many analogous terms to étendue and its conservation;
however, most of these terms are used incorrectly when
substituted for étendue. Please define the following analogous
terms by using words, pictures, and so forth. Also, explain how
each term differs from étendue. Note: some of the older
literature was prior to the formal definition of étendue!
a. Lagrange Invariant
b. Radiance
c. Brightness
d. Extent
e. Throughput
f. Abbe Sine condition
2. In class we showed that there is Conservation of Etendue using a
generalized formulation that only uses geometrical aspects of
propagation through an optical system. There are many other
methods to do it, with the simplest being through the Conservation
of Radiance through both transfer and refraction. Prove such
finding both:
a. The transfer equation (conservation of radiance): ts LL =,
using the picture below to help.
dAsdAt
θ
θ
t
r
âsât
