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

Correlation of scaled photon-counting fluctuations

Eric Jakeman, Christopher J. Oliver, Edward R. Pike, P. N. Pusey

Published Oct 1, 1972• 40 citations
Publisher

Abstract

The use of scaling for one-bit correlation processing in optical spectroscopy of nongaussian signals is discussed. A theoretical proof of its equivalence with uniform random clipping, and hence full correlation, is provided in certain cases.
DOI
10.1088/0305-4470/5/10/002

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

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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.

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The estimates of photoemission rate correlations that are obtained by clipped, e.g., one-bit, correlation techniques are in general distorted by the clipping, unless scaling techniques are used. It is shown that the Pois-son statistics of photoemission processes are such that the processes are inherently self-scaling when the range of signal fluctuations is contained in the range of inherent noise fluctuations. Self-scaling occurs, for example, when the total mean emission rate is large compared with the time varying signal rate. It permits clipped correlation to be used without distortion.
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.
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.