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Journal of Physics A Mathematical Nuclear and General

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

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

Published Apr 1, 1973• 8 citations

Abstract

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.

DOI: 10.1088/0305-4470/6/4/002

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Journal of Physics A Mathematical Nuclear and General•Jun 1, 1973•6 citations

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.

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.