REVEALING INTEGRATED INTENSITY DISTRIBUTIONS (RIID)

John F. Lesoine

                The ability to measure the distribution of a light source’s intensity fluctuations is important to many scientific disciplines.  These measurements are difficult to make because these integrated intensity fluctuations are convolved with Shot noise due to the photometric detection process.  Deconvolving the photon counting Shot noise from photon counting histograms without bias requires an approach that can account for a discrete, noisy and incomplete data set without additional assumptions, approximations or otherwise arbitrary massaging of the data.  Other approaches consider inverting the photo detection probability distribution to reveal the underlying integrated intensity distribution.  The difficulty with direct inversion of the photon detection probability distribution stems from the fact that it is an ill-posed problem.  I address this problem by developing a forward approach using the maximum entropy method (MEM) to deconvolve the nonlinear Shot noise from photon counting histograms.  This novel deconvolution technique may be extended to address experimental issues related to both detector dead time and after-pulsing.  The approach is tested by its application to several simulated photon counting data sets, and this approach is compared graphically to other approaches from the literature.  This MEM approach is found to deconvolve the photon counting Shot noise from photon counting histograms while providing a c2 value that is consistent with the photon counting noise.  This nondestructive analysis should be applicable to most classical photon counting histograms.