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Journal of Physics A Mathematical and General

Theory of periodic sampling of photon-counting distributions

Eric Jakeman, Edward R. Pike

Published Nov 1, 1968• 17 citations
Publisher

Abstract

The statistical accuracy with which moments of the intensity-fluctuation distributions of optical fields can be determined, by photon-counting experiments of finite duration, is calculated.
DOI
10.1088/0305-4470/1/6/307

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Le Journal de Physique Colloques•Feb 1, 1972•3 citations
The authors investigate the statistical errors which arise in digital autocorrelation of photon counting fluctuations due to the finite duration of experiments. An expression for the accuracy with which individual points of the autocorrelation function of intensities can be measured is derived analytically and evaluated for Gaussian- Lorentzian light. The appropriate weighting for a 'least-squares' fitting procedure is determined and the error in spectral linewidth, obtained by this procedure from experiment, is calculated.
Constraints on the Origin of Universal 1/f21/f^21/f2 Photon-Count Spectra at Baseband
A series of 11.6-d-duration photon-counting experiments, employing a broad variety of light sources with different statistical properties and optical spectra, were carried out over a 1.5-yr period. All of the photon-count spectra at baseband followed a common 1/f21/f^21/f2 form over the frequency range 1×10−6⩽f⩽5×10−41 \times 10^{-6} \leqslant f \leqslant 5 \times 10^{-4}1×10−6⩽f⩽5×10−4 Hz, corresponding to a timescale range 333333 min $ \leqslant T_f \leqslant 11.6$ d, where Tf≡1/fT_f \equiv 1/fTf​≡1/f. The lower and upper timescale limits were established by the photodetector noise floor and the duration of the individual experiments, respectively. Unlike ordinary Brownian motion, all of the measured photon-count sample paths exhibited irregular long-timescale fluctuations, with durations ranging from hours to days. It has been established that the photon-count spectra cannot plausibly be ascribed to fluctuations of the current, voltage, or temperature of the source or the detector, nor to technical sources of noise associated with the optical system or local environment. Although the physical origin of the photon-count fluctuations remains unresolved, several heterodox hypotheses are set forth. From a statistical point-of-view, the photon counts appear to follow a doubly stochastic Poisson process with a slowly varying random intensity. Analogous experiments that rely on ionizing radiation and direct-conversion solid-state radiation detectors are proposed.
We discuss the accuracy of a measurement of a spectral linewidth using the method of digital correlation of single-clipped photon counting fluctuations with a given light flux and a given duration of experiment. Statistical effects due to the random nature of the light field and the photoelectric process limit this accuracy, so that the longer the duration of the experiment the more accurate the result, if all other factors are equal. Theoretical and experimental results are presented which show the accuracies obtainable as functions of the sample time, detector area and clipping level.