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Optics Letters

Autocorrelation evaluation from clipped photon detection

Manuel P. Cagigal, Pedro M. Prieto, L. Vega

Published Apr 15, 1994• 1 citation
Publisher

Abstract

We present two new techniques for estimating the autocorrelation function, based on the measurement of the mean number of clipped photocounts and on the calculation of the second-order factorial moment of a series of clipped data. The first procedure has the advantage of simplicity, although it produces a poor signal-to-noise ratio. On the other hand, the second technique gives a very good signal-to-noise ratio, when compared with other known methods.

DOI
10.1364/ol.19.000584

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We present two new techniques for estimating the autocorrelation function, based on the measurement of the mean number of clipped photocounts and on the calculation of the second-order factorial moment of a series of clipped data. The first procedure has the advantage of simplicity, although it produces a poor signal-to-noise ratio. On the other hand, the second technique gives a very good signal-to-noise ratio, when compared with other known methods.
In this paper we develop a procedure to avoid the autocorrelation central hole that appears in clipped photon-counting detection. This method can be understood as a higher order approximation than the Hofmann procedure. It can be applied in combination with any of the alternative methods to evaluate the autocorrelation function in clipped conditions proposed up until the present. We especially analyse that based on the zero-count probability measurement. Fairly good autocorrelation estimates are obtained for low intensity signals.
This paper establishes a clear relation between the photocount distribution (PCD) of a low light level signal and its autocorrelation function (AC). The conclusion is that the evaluation of the AC from the measurement of the PCD is equivalent to that of the AC. Although the signal to noise ratio decreases when AC evaluation is obtained from PCD measurements, this technique allows AC values to be obtained more quickly and easily. Theoretical evaluation of the variances involved in these measurements and a simulation checking procedure are also described.
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.