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Journal of the Optical Society of America A

Determination of the period of a low-intensity square-wave-modulated light beam by measuring a square-wave transform of the time-interval probability

Rafael J. López, M. Á. Rebolledo, Fernando G. Moreno

Published Mar 1, 1986• 7 citations
Publisher

Abstract

A photon-statistics technique that is based on the time-interval probability, W(θ), is studied. This technique consists of measuring the transform QR(X)=∫0∞W(θ)R(X,θ)dθ, where R(X, θ) is a square-wave function of frequency X. This function oscillates between one and zero as θ varies. The measurement of QR(X) can be carried out in a simple way. We study the error with which the period of a low-intensity square-wave-modulated light beam can be obtained by fitting a Lorentzian curve to the experimental values of QR(X). It is found that this technique is more accurate than the intensity-correlation technique when the intensity is small. The advantage increases as the intensity of the light beam decreases. This technique can be applied for those experiments in which oscillating-intensity light beams are obtained, the period providing the required information. For instance, it can be used in laser Doppler velocimetry and in quantum-beat spectroscopy.

DOI
10.1364/josaa.3.000365

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A photon-statistics technique that is based on the time-interval probability, W(θ), is studied. This technique consists of measuring the transform QR(X)=∫0∞W(θ)R(X,θ)dθ, where R(X, θ) is a square-wave function of frequency X. This function oscillates between one and zero as θ varies. The measurement of QR(X) can be carried out in a simple way. We study the error with which the period of a low-intensity square-wave-modulated light beam can be obtained by fitting a Lorentzian curve to the experimental values of QR(X). It is found that this technique is more accurate than the intensity-correlation technique when the intensity is small. The advantage increases as the intensity of the light beam decreases. This technique can be applied for those experiments in which oscillating-intensity light beams are obtained, the period providing the required information. For instance, it can be used in laser Doppler velocimetry and in quantum-beat spectroscopy.
In this paper, we have characterized an intensity square wave modulated light beam of period P and visibility factor, V, by measuring the moment generating function of the number of photopulses, Qn(s,T), for only one value of the counting time, T. This has been done for different values of the parameter s. A least square fitting procedure has been used to obtain simultaneously the characterizing parameters, P and V. A set of experimental measurements has been carried out for different values of both, the mean intensity per period, m, and the visibility factor, V.
Theoretical expressions for the factorial moments of the triggered photon-counting distribution that corresponds to a light beam with a periodically modulated intensity are derived. Two triggering procedures are considered: the time-window triggering procedure (which has been experimentally checked for Gaussian light by other authors) and the first-photopulse triggering procedure (which is a faster procedure). The theoretical expressions that correspond to the latter procedure are experimentally checked in this paper by using a square-wave signal. The errors involved in the analysis of the information contained in the light beam, when this information is obtained from the measurement of the first-order factorial moment, are studied.
In this paper a laser Doppler velocimetry (LDV) experiment with a water flow is performed to show that the experimental results for the Fourier transform of the two-photon time-interval probability QF{Q}_{F}QF​(\ensuremath{\nu}) agree with the theoretical results derived in previous papers. The conclusions of these papers can therefore be applied to a real LDV experiment. It is concluded that by using this technique for small scattered intensities the velocities can be obtained with much more accuracy than by measuring the autocorrelation function g(2){g}^{(2)}g(2)(\ensuremath{\tau}). The values of the intensity and of the Doppler frequencies that can be used are discussed.