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Review of Scientific Instruments

Measurement of optical autocorrelation functions using a signal averager

Peter P. Crooker, J. A. Hoover

Published May 1, 1976• 4 citations
Publisher

Abstract

We show that the autocorrelation function of an optical signal may be simply obtained using a signal averager and a weighted signal-averaging technique. The method applies to the measurement of either intensity fluctuations or photocount fluctuations, and we present expressions for the weighted signal average and its error for each case. Finally we test the results experimentally and compare the data with the corresponding theoretical expressions.

DOI
10.1063/1.1134683

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We show that the autocorrelation function of an optical signal may be simply obtained using a signal averager and a weighted signal-averaging technique. The method applies to the measurement of either intensity fluctuations or photocount fluctuations, and we present expressions for the weighted signal average and its error for each case. Finally we test the results experimentally and compare the data with the corresponding theoretical expressions.
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.
In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.
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.
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.