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

Clipped correlation of integrated intensity fluctuations of gaussian light

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

Published Nov 1, 1971• 33 citations
Publisher

Abstract

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.
DOI
10.1088/0305-4470/4/6/008

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Journal of physics. A, Proceedings of the Physical Society. General•Nov 1, 1972•6 citations
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 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.
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.