A comparison of the information-gathering capacities of photon-correlation devices

Abstract

This paper will begin with a survey of the general problem of correlation spectroscopy. It will present a novel approach to the derivation of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -time generating functions and will use these generating functions to compute the expected signals in four kinds of photon-correlation devices and the noise associated with these signals. The four devices treated are 1) the full digital correlator, 2) the gated digital correlator, 3) the multichannel analyzer, 4) the pulse-separation analyzer. We compare the information-gathering abilities of the four systems by showing how the quantity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1/T) (\Gamma/\sigma_{\Gamma})^{2}</tex> varies as a function of the number of channels used, the number of observed correlation times, the average count rate, and the gating levels. Here <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma</tex> is the half-width of a Lorentz line, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sigma_{\Gamma}</tex> is the uncertainty in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Gamma</tex> as computed from a least-squares fit to the data, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> is the length of the experiment.