= Integrating-sphere port-loss factor
{title2=$1-f$}
The \b[integrating-sphere port-loss factor] $1-f$ is the fraction of a well-mixed reflected field that next encounters the wall rather than an absorbing opening, where $f$ is total port area divided by the internal spherical area. It is a geometric retention factor, not wall reflectance. With uniform wall reflectance $\rho$, successive wall encounters retain fraction $q=\rho(1-f)$. The primary sphere derivation explicitly separates the port fraction from reflectance and generalizes to nonzero port reflectances.<Integrating Sphere Theory and Applications by Labsphere>[§1.2, printedp2, equations6–12; §1.2.2, Average Reflectance]{ref}
An original energy-accounting example starts with energy $U$ incident on the wall after the input beam's first impact. At each encounter fraction $1-\rho$ is absorbed; fraction $\rho f$ reflects and escapes; fraction $q$ reaches the wall again. Summing the <geometric series> gives
$$
\frac{U_{\rm absorbed}}U=\frac{1-\rho}{1-\rho(1-f)},\qquad
\frac{U_{\rm escaped}}U=\frac{\rho f}{1-\rho(1-f)}.
$$
The two fractions sum to one. For stipulated $\rho=0.96$ and $f=0.04$, about $0.5102U$ is ultimately absorbed and $0.4898U$ escapes. Thus a four-percent port fraction does not mean that only four percent ever exits: repeated reflections give repeated opportunities. This is the <integrating-sphere escape probability> in the stated ideal encounter model.
The input convention matters: these fractions start at a wall encounter and omit any input beam that escapes without striking that wall. Real ports can contain reflective samples or detectors, and baffles change direct paths. A sphere experiment can vary an aperture while monitoring a stable injected <radiant flux>, but its response must include those surfaces and the receiver field of view. The factor $1-f$ alone is not a detector calibration or a universal collection efficiency.
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