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Review of Scientific Instruments

Clipping level dependence of the photon count autocorrelation amplitude from Gaussian–Lorentzian light

Paul Nieuwenhuysen, Julius Clauwaert

Published Jun 1, 1977• 9 citations
Publisher

Abstract

Experimental results are presented for the clipping level dependence of the photon count autocorrelation amplitude from Gaussian–Lorentzian light. These show temporal and spatial integration effects, as predicted by theory, which hinder the application of the clipping gate test for digital clipped correlators by Chen et al. [Rev. Sci. Instrum. 46, 1356 (1975)].

DOI
10.1063/1.1135114

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Journal of physics. A, Proceedings of the Physical Society. General•Jan 1, 1972•14 citations
Experimental results are presented for the clipping level dependence of the photon count autocorrelation amplitude from Gaussian–Lorentzian light. These show temporal and spatial integration effects, as predicted by theory, which hinder the application of the clipping gate test for digital clipped correlators by Chen et al. [Rev. Sci. Instrum. 46, 1356 (1975)].
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.
The authors investigate the statistical errors which arise in digital autocorrelation of photon counting fluctuations due to the finite duration of experiments. An expression for the accuracy with which individual points of the autocorrelation function of intensities can be measured is derived analytically and evaluated for Gaussian- Lorentzian light. The appropriate weighting for a 'least-squares' fitting procedure is determined and the error in spectral linewidth, obtained by this procedure from experiment, is calculated.
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.