Integrating cavities: temporal response

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 (d) over bar between successive reflections at the cavity wall; 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 a for arbitrary cavity shapes is then derived, (d) over bar = 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 (d) over bar = 2D/3, exactly the same as (d) over bar for the inscribed sphere.