Analytical solution for integrating sphere spectral efficiency inclusive of atmospheric attenuation
2008
An analytical solution to the attenuation of flux within an integrating sphere
due to spherical integrating source coating, exit port escape, and atmospheric
absorption is derived employing a geometric probability distribution of completed sphere
transits. This is used to determine the mean number of completed sphere transits and its
variance. Equations that provide the attenuation ratios for the three extinction
mechanisms are derived using the energy balance and summation of reflection methods. The
mean length of a transit of the sphere and its variance are presented and used to derive
expressions for the mean and variance of photon path lengths in the sphere.
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