Abstract

The temporal response of an integrating cavity is examined and compared with the results of a Monte Carlo analysis. An important parameter in the temporal response is the average distance $\overline{d}$ between successive reflections at the cavity wall; $\overline{d}$ was calculated for several specific cavity designs—spherical shell, cube, right circular cylinder, irregular tetrahedron, and prism; however, only the calculation for the spherical shell and the right circular cylinder will be presented. A completely general formulation of $\overline{d}$ for arbitrary cavity shapes is then derived, $\overline{d}=4V/S$ where V is the volume of the cavity, and S is the surface area of the cavity. Finally, we consider an arbitrary cavity shape for which each flat face is tangent to a single inscribed sphere of diameter D (a curved surface is considered to be an infinite number of flat surfaces). We will prove that for such a cavity $\overline{d}=2D/3$, exactly the same as $\overline{d}$ for the inscribed sphere.

© 2006 Optical Society of America

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