Editing Ring-imaging Cherenkov detector (section)

=== Optical Precision and Response ===

This ability of a RICH system to successfully resolve different hypotheses for the particle type depends on two principal factors, which in turn depend upon the listed sub-factors;

* '''The effective angular resolution per photon''', <math> \sigma </math>
** ''Chromatic dispersion in the radiator'' (<math> n </math> varies with photon frequency)
** ''Aberrations in the optical system''
** ''Position resolution of the photon detector''
* '''The maximum number of detected photons in the ring-image''', <math>N_c</math>
** ''The length of radiator through which the particle travels''
** ''Photon transmission through the radiator material''
** ''Photon transmission through the optical system''
** ''Quantum efficiency of the photon detectors''
<math> \sigma </math> is a measure of the intrinsic optical precision of the RICH detector. <math>N_c</math> is a measure of the optical response of the RICH; it can be thought of as the limiting case of the number of actually detected photons produced by a particle whose velocity approaches that of light, averaged over all relevant particle trajectories in the RICH detector.   The average number of Cherenkov photons detected, for a slower particle, of charge <math>q</math> (normally ±1), emitting photons at angle <math> \theta_c </math> is then
:<math> N = \dfrac{N_c q^2 \sin^2(\theta_c)}{1 - \dfrac{1}{n^2}} </math>
and the precision with which the mean Cherenkov angle can be determined with these photons is approximately
:<math>\sigma_m = \frac{\sigma}{\sqrt{N}}</math> 
to which the angular precision of the emitting particle's measured direction must be added in quadrature, if it is not negligible compared to <math>\sigma_m</math>.