  Radiance is widely regarded as the principal quantity in light transport
theory. Yet, the concept of radiance in use today has remained mostly unchanged
since Lambert's work in the 18th century. His formulation of the measurement of
light intensity is based on classical differentials, and is known to suffer
from several theoretical and practical limitations. After tracing the historic
development of radiance and its shortcomings, we provide a modern formulation
of light intensity measurements that models radiance as a differential form. We
demonstrate the utility of this use of exterior calculus for questions in light
transport theory by rigorously deriving the cosine term and the area
formulation, without the need for postulates or heuristic arguments. The
formulation of radiance as a differential form introduced in this paper hence
provides the first step towards a modern theory of light transport.
