Dead time correction of photon correlation functions

Abstract

The dynamic range of single photon counting measurements in quasi elastic light scattering is restricted by detector and counter dead time effects. While distortions of single interval statistics have been treated at great length, only lowest order corrections or very special cases of dead time effects on temporal correlation functions were computed in the past.

Dead times result in a direct distortion of correlograms on time scales comparable to the dead time. This effect exists even at low count-rates. It is independent of the count rate for paralyzable systems. Nonparalyzable systems show a count rate dependence with increasing correlation times at high count rates.

Furthermore, counting saturation produces additional distortions extending to all lag times. These distortions are computed for the rather general case of Γ-distributed intensities with arbitrary shape of the photon correlation function. Such signals are commonly found in multiparticle homodyne experiments with a finite size detector, i.e. arbitrary value of the intercept or contrast of the correlogram. Exact results are provided for the paralyzable system including the effect of fluctuating dead times. The latter case is then used to compute a useful approximation for nonparalyzable systems as well.