Lambertian surfaces with over- and under-filled field of view

Author(s): Nathaniel J. Field, Joseph A. Shaw

Abstract

Optical science and engineering education and practice make frequent use of the concepts of Lambertian surfaces, Lambertian reflectance, or Lambertian emission. These are all based on Lambert’s cosine law, which states that the radiant or luminous intensity [W/sr] reflected or emitted from a Lambertian surface varies as the cosine of the angle between the direction of incident (or emitted) radiation and the surface normal. However, a simpler definition is a Lambertian source produces radiance [W/(m2 sr)] that is constant with angle. This definition helps avoid common errors and confusion that arise when a Lambertian source is viewed in different geometries in which the field-of-view (FOV) solid angle is over- or under-filled by the source. In this paper we describe the theory of Lambertian reflection and emission for under- and over filled FOV situations and show measurements from a simple set of reflection experiments that help to prove these theories in practice by demonstrating that flux measured with an under-filled FOV varies as the cosine of the viewing angle, while flux measured with an over-filled FOV does not. We also show how to set up and conduct experiments to illustrate these different situations using a simple halogen lamp, lens, photodiode, and Lambertian panel.

Citation

Field, N. J., & Shaw, J. A. A. (2022). Lambertian surfaces with over- and under-filled field of view. In G. G. Gregory & A.-S. Poulin-Girard (Eds.), Optics Education and Outreach VII (p. 12). SPIE. https://doi.org/10.1117/12.2633738