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Spectroscopy Letters

Evaluation of the Autocorrelation Function from Measurement of the Photocount Distribution

Manuel P. Cagigal, Pedro M. Prieto

Published Aug 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1080/00387019208020699

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Proceedings of the Physical Society•Jan 1, 1967•75 citations
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 theoretical expression of the first-order factorial moment of a triggered delayed photocount distribution and a description of its SNR have been developed. We explain the adventages of this thecnique, in comparison with the second-order correlation function, when we measured a temporal signal under low light level. We derived the theoretical errors involved in determining a parameter by measuring both functions for a signal with a periodically modulated intensity, since this kind of signals usually appear in spectroscopy. We conclude that the first-order factorial moment of a triggered delayed photocount distribution is a useful tool for characterizing a signal at low; light level conditions.
The expression corresponding to the normalized first-order factorial moment (NFOFM) of a double triggered photocount distribution (DTPCD) has been developed. It is found that the NFOFM of a DTCPD has the spectral information of incident light corresponding to the third-order autocorrelation function. A theoretical error model was developed and checked by using a computer simulation method. We also compare the results obtained from the measurement of the NFOFM of a DTPCD with those obtained from the second- and third-order correlation functions.
The corrections to the photocount distributions, due to dead-time effects, are evaluated by use of the time-interval probability density of the counts. The normalized cumulative distribution function J k ( T , τ), associated with the detection of fluctuating light beams during a counting time interval T , with a counter having a constant dead-time τ, appear naturally as a convenient quantity to be used in comparing experimental results with theoretical predictions. The quantities J k ( T , τ) obey a simple recurrence relation and are readily derived from the photocount distribution p ( k, T , τ). A general expression is derived for J k ( T , τ) and p ( k, T , τ) associated with the detection of fluctuating light beams. Typical cumulative distribution functions, relating to the detection of thermal light, are evaluated as functions of the degree of polarization of the light, of the average number of photocounts < n 0 > in the absence of dead-time effects and of the ratio τ/ T . The distributions J k ( T , τ) and p ( k, T , τ) relating to detection of laser light are also calculated in a typical case.