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

A method for the clipped intensity correlation measurement

S. H. Chen, P. Tartaglia, Nicole Ostrowsky

Published Nov 1, 1972• 6 citations
Publisher

Abstract

The authors propose an alternative scheme for the clipped light intensity correlation measurement which is complementary to the usual scheme as proposed by Jakeman and Pike (1969). The new scheme gives essentially the same statistical accuracy for the linewidth measurement and furthermore, it has some practical advantages when the mean number of counts per sampling time is sufficiently large.

DOI
10.1088/0305-4470/5/11/009

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Comment on the letter by Jakeman et al. 'Correlation of scaled photon-counting fluctuations'

P. Tartaglia, Theodore A. Postol, S. H. Chen

Jakeman et al. (see Abstr. A73542 of 1972) have presented a method for measuring the full photocount correlation function which might be called single channel scaling (SCS). The advantage of SCS is that it can be used in conjunction with a clipped correlator to measure directly the full photocount correlation rather than the clipped correlation function. The authors point out an equally simple way of performing the same measurement and finite sum by uniformly and sequentially clipping (USC) incoming photocounts. With this method one simply clips sequentially from some maximum clipping level k=l during each of l+1 sampling periods, then starts over again at k=l. In this way the uniformity of the sampling is automatically ensured and can therefore be used as a technique to test experimentally the clipping uniformity of SCS. They performed an extensive set of measurements using both SCS and USC over a wide range of scaling and sequential clipping levels and found both methods lead to exactly equivalent results.

Journal of Physics A Mathematical Nuclear and General•Apr 1, 1973•8 citations

Spectrum of clipped photon-counting fluctuations of Gaussian light

Eric Jakeman, Edward R. Pike

The analogue of a theorem of Van Vleck on the spectrum of clipped noise is formulated for use in optical spectroscopy.

Journal of physics. A, Proceedings of the Physical Society. General•May 1, 1969•112 citations

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
The authors propose an alternative scheme for the clipped light intensity correlation measurement which is complementary to the usual scheme as proposed by Jakeman and Pike (1969). The new scheme gives essentially the same statistical accuracy for the linewidth measurement and furthermore, it has some practical advantages when the mean number of counts per sampling time is sufficiently large.
This volume is the fourth in a series of monographs being published under the general title Quantum Electronics: Principles and Applications, and it is intended, the preface says, to call the attention of researchers engaged in light scattering experiments to the new techniques of photon counting and light beating spectroscopy. Researchers so engaged are already likely to be familiar with the excellent review articles of Jakeman and Pike on the former and Cummins and Swinney on the latter, and they will find little further enlightenment on these subjects here.
Jakeman et al. (see Abstr. A73542 of 1972) have presented a method for measuring the full photocount correlation function which might be called single channel scaling (SCS). The advantage of SCS is that it can be used in conjunction with a clipped correlator to measure directly the full photocount correlation rather than the clipped correlation function. The authors point out an equally simple way of performing the same measurement and finite sum by uniformly and sequentially clipping (USC) incoming photocounts. With this method one simply clips sequentially from some maximum clipping level k=l during each of l+1 sampling periods, then starts over again at k=l. In this way the uniformity of the sampling is automatically ensured and can therefore be used as a technique to test experimentally the clipping uniformity of SCS. They performed an extensive set of measurements using both SCS and USC over a wide range of scaling and sequential clipping levels and found both methods lead to exactly equivalent results.
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.