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 c^{2}
value that is consistent with the photon counting noise. This nondestructive
analysis should be applicable to most classical photon counting histograms.