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

Spatial correlations and photon counting

H C Kelly

Published Jan 1, 1972• 14 citations
Publisher

Abstract

The effect of incomplete spatial coherence on photon correlation measurements is calculated in terms of the solutions to integral equations. The n time generating function is calculated with a new approach to the 'short counting time' approximation and the two-time generating function is calculated exactly for a Lorentz spectrum. The joint counting rates for a full digital correlator are obtained and approximate solutions to the 'clipped' correlator counting rate problem are indicated.

DOI
10.1088/0305-4470/5/1/015

Related papers

Analysis of Gaussian Light by Clipped Photocount Autocorrelation: The Effect of Finite Sampling Times and Incomplete Spatial Coherence

Dennis E. Koppel

The theoretical treatment of clipped photocount autocorrelation of Gaussian light, introduced by Jakeman and Pike, has been extended to include the effects of finite-duration sampling intervals and incomplete spatial coherence. A system of ``interval partitioning'' is used to derive theoretical expressions for 〈Nq(0)N(τ)〉 and 〈N0(0) N0(τ)〉, the single- and double-clipped photocount autocorrelation functions. Here N(t) is the number of photons detected in a sampling interval centered at t and Nq(t) is the clipped count at level q. Each original interval is systematically partitioned in space and time. Multidimensional generating functions are applied to the sets of subintervals with the object of expressing g(1) (t), the first-order field correlation function, in terms of measurable quantities. It is shown that under certain well-defined conditions, 〈Nq(0) N(τ)〉−〈Nq〉〈N〉=γq|g(1)(τ)|2 and 〈1−N0〉−2−[1−2〈N0〉+〈N0(0)N0(τ)〉]−1=φ|g(1)(τ)|2, where, for a given set of experimental parameters, γq and φ can be taken as simple multiplicative factors independent of the delay time τ. For comparative purposes, a similar analysis is performed for the unclipped correlation function 〈N(0)N(τ)〉. Finally, computer calculated values of various quantities of interest are presented for several representative cases.

Journal of Applied Physics•Jul 1, 1971•38 citations

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

H C Kelly

This paper will begin with a survey of the general problem of correlation spectroscopy. It will present a novel approach to the derivation of theN-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(1/T) (\Gamma/\sigma_{\Gamma})^{2}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\Gammais the half-width of a Lorentz line,\sigma_{\Gamma}is the uncertainty in\Gammaas computed from a least-squares fit to the data, andTis the length of the experiment.

IEEE Journal of Quantum Electronics•Dec 1, 1971•17 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

Clipped photon-counting covariance functions

Richard G. Barakat

The joint probability of finding m2 photons in detection interval 2 and m1 photons in detection interval 1 was previously determined by the author [ J. Mod. Opt.34, 91 ( 1987)] in terms of a series expansion of the time-integrated intensity correlation function with coefficients given by a class of orthogonal polynomials in the discrete variables m2 and m1. This expansion is now used to obtain an expression for the average of two general functions υ(m2) and u(m1), 〈υ(m2)u(m1)〉. These functions are specialized to cover two important situations: singly and doubly clipped covariances for essentially arbitrary counting times. In the doubly clipped case, different clipping levels are permitted in the two channels in order to study the influence of clipping mismatch. Numerical calculations, in the form of graphs, are used to illustrate typical behavior.

Journal of the Optical Society of America A•Aug 1, 1988•3 citations

Two-fold photoelectron counting statistics: the clipped correlation function

J. Blake, Richard G. Barakat

Two-fold photoelectron counting statistics are studied for quasimonochromatic light of arbitrary spectral profile. A numerical scheme is developed for the evaluation of the double generating function from which the joint probabilities, the photoelectron correlation function, and the clipped photoelectron correlation function can be evaluated. The time need not be short compared to the coherence time as in previous studies. Numerical results are presented for the photoelectron correlation function and for the clipped correlation function for the spectrum which would be observed in a Brillouin scattering experiment.

Journal of Physics A Mathematical Nuclear and General•Aug 1, 1973•9 citations

Clipped correlation of integrated intensity fluctuations of gaussian light

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

Experimental confirmation is presented of recent theoretical results of Jakeman on the time ever aging of photon-counting fluctuations when utilizing clipping techniques for autocorrelation. The effects of finite electronic resolving time (dead-time correction) and finite receiving apertures (spatial-coherence correction) are included.

Journal of physics. A, Proceedings of the Physical Society. General•Nov 1, 1971•33 citations
The effect of incomplete spatial coherence on photon correlation measurements is calculated in terms of the solutions to integral equations. The n time generating function is calculated with a new approach to the 'short counting time' approximation and the two-time generating function is calculated exactly for a Lorentz spectrum. The joint counting rates for a full digital correlator are obtained and approximate solutions to the 'clipped' correlator counting rate problem are indicated.
The theoretical treatment of clipped photocount autocorrelation of Gaussian light, introduced by Jakeman and Pike, has been extended to include the effects of finite-duration sampling intervals and incomplete spatial coherence. A system of ``interval partitioning'' is used to derive theoretical expressions for 〈Nq(0)N(τ)〉 and 〈N0(0) N0(τ)〉, the single- and double-clipped photocount autocorrelation functions. Here N(t) is the number of photons detected in a sampling interval centered at t and Nq(t) is the clipped count at level q. Each original interval is systematically partitioned in space and time. Multidimensional generating functions are applied to the sets of subintervals with the object of expressing g(1) (t), the first-order field correlation function, in terms of measurable quantities. It is shown that under certain well-defined conditions, 〈Nq(0) N(τ)〉−〈Nq〉〈N〉=γq|g(1)(τ)|2 and 〈1−N0〉−2−[1−2〈N0〉+〈N0(0)N0(τ)〉]−1=φ|g(1)(τ)|2, where, for a given set of experimental parameters, γq and φ can be taken as simple multiplicative factors independent of the delay time τ. For comparative purposes, a similar analysis is performed for the unclipped correlation function 〈N(0)N(τ)〉. Finally, computer calculated values of various quantities of interest are presented for several representative cases.
This paper will begin with a survey of the general problem of correlation spectroscopy. It will present a novel approach to the derivation of theN-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(1/T) (\Gamma/\sigma_{\Gamma})^{2}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\Gammais the half-width of a Lorentz line,\sigma_{\Gamma}is the uncertainty in\Gammaas computed from a least-squares fit to the data, andTis the length of the experiment.
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.
The joint probability of finding m2 photons in detection interval 2 and m1 photons in detection interval 1 was previously determined by the author [ J. Mod. Opt.34, 91 ( 1987)] in terms of a series expansion of the time-integrated intensity correlation function with coefficients given by a class of orthogonal polynomials in the discrete variables m2 and m1. This expansion is now used to obtain an expression for the average of two general functions υ(m2) and u(m1), 〈υ(m2)u(m1)〉. These functions are specialized to cover two important situations: singly and doubly clipped covariances for essentially arbitrary counting times. In the doubly clipped case, different clipping levels are permitted in the two channels in order to study the influence of clipping mismatch. Numerical calculations, in the form of graphs, are used to illustrate typical behavior.
Two-fold photoelectron counting statistics are studied for quasimonochromatic light of arbitrary spectral profile. A numerical scheme is developed for the evaluation of the double generating function from which the joint probabilities, the photoelectron correlation function, and the clipped photoelectron correlation function can be evaluated. The time need not be short compared to the coherence time as in previous studies. Numerical results are presented for the photoelectron correlation function and for the clipped correlation function for the spectrum which would be observed in a Brillouin scattering experiment.