Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of physics. A, Proceedings of the Physical Society. General

Statistical accuracy in the digital autocorrelation of photon counting fluctuations

Eric Jakeman, Edward R. Pike, S. Swain

Published Nov 1, 1970• 40 citations
Publisher

Abstract

Optical measurements by intensity fluctuation spectroscopy are subject to errors arising from the statistical nature of light and of the photo-detection process. The authors report the results of a calculation of the expected errors, due to these causes, in linewidth measurements by digital autocorrelation of photon counting fluctuations.

DOI
10.1088/0305-4470/3/6/018

Related papers

Statistical accuracy in the digital autocorrelation of photon counting fluctuations

Eric Jakeman, Edward R. Pike, S. Swain

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.

Journal of physics. A, Proceedings of the Physical Society. General•Jul 1, 1971•108 citations

The effect of heterodyne detection on the statistical accuracy of optical linewidth measurements

Eric Jakeman

It is shown that an order of magnitude gain in the statistical accuracy of optical linewidths measured by digital autocorrelation of photon- counting fluctuations may be achieved by heterodyne detection in the weak signal limit.

Journal of physics. A, Proceedings of the Physical Society. General•Jun 1, 1972•15 citations

THE ACCURACY OF DIFFUSION-CONSTANT MEASUREMENTS BY DIGITAL AUTOCORRELATION OF PHOTON-COUNTING FLUCTUATIONS

Edward R. Pike

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.

Le Journal de Physique Colloques•Feb 1, 1972•3 citations

Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations

Eric Jakeman

Digital autocorrelation of optical signals is discussed with particular reference to the technique of clipping, reported briefly in an earlier publication. A detailed analysis of the relationship between the autocorrelation functions of clipped and unclipped photon-counting fluctuations is given. By evaluating the generating function for the joint distribution of intensity fluctuations, corrections to the earlier results are calculated which arise if the time over which the signal is sampled is not negligible compared with any coherence time of the light. The effect of clipping in heterodyne experiments is also analysed.

Journal of physics. A, Proceedings of the Physical Society. General•Mar 1, 1970•99 citations

Intensity-Correlation Spectroscopy

Vittorio Degiorgio, J. B. Lastovka

In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.

Physical Review A•Nov 1, 1971•103 citations

A measurement of optical linewidth by photon-counting statistics

Eric Jakeman, Christopher J. Oliver, Edward R. Pike

An optical linewidth of 20 Hz of laser light scattered by spherical particles undergoing Brownian motion has been measured experimentally by photon-counting statistics using the theory of the intensity-fluctuation distribution of Gaussian-Lorentzian light.

Journal of Physics A Mathematical and General•May 1, 1968•52 citations
Optical measurements by intensity fluctuation spectroscopy are subject to errors arising from the statistical nature of light and of the photo-detection process. The authors report the results of a calculation of the expected errors, due to these causes, in linewidth measurements by digital autocorrelation of photon counting fluctuations.
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.
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.
Digital autocorrelation of optical signals is discussed with particular reference to the technique of clipping, reported briefly in an earlier publication. A detailed analysis of the relationship between the autocorrelation functions of clipped and unclipped photon-counting fluctuations is given. By evaluating the generating function for the joint distribution of intensity fluctuations, corrections to the earlier results are calculated which arise if the time over which the signal is sampled is not negligible compared with any coherence time of the light. The effect of clipping in heterodyne experiments is also analysed.
In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.