Integrating cavities: temporal response
2006
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¯ 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
d¯ for arbitrary cavity shapes is then derived,
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
d¯=2D/3, exactly the same as
d¯ for the inscribed sphere.
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