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Spectroscopy Letters

Experimental Study of Periodically Modulated Light Beams by Measuring the Moment Generating Function of the Number of photopulses

F. González, Jose Maria Saiz, Pedro J. Valle, Fernando G. Moreno

Published Jun 1, 1993• 0 citations
Publisher

Abstract

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.

DOI
10.1080/00387019308011566

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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.
The authors show, through the analysis of a periodically modulated light beam with a square profile, the improvement in the signal-to-noise ratio by measuring the moment generating function of the number of photopulses, Q n (s, T), with respect to the measurement of the second normalized factorial moment, n (2) (T). An experimental verification in the low light level range (1-10 photoelectrons per period) for different values of the modulation factor has been made. The results and some conclusions are presented.
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.
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.
A modified Michelson interferometer in which one of the mirrors is driven by a piezoelectric crystal connected to a Gaussian random-noise generator has been used to phase modulate a light beam from a Spectra Physics 119 model laser. The recombination of the modulated and the unmodulated beam reflected by a stationary prism generates a randomly varying interference pattern whose intensity distribution has been analyzed by means of a standard photon-counting technique. The experimental data agree with the theoretical semiclassical predictions in the range of linearity of the piezoelectric crystal. Deviations from the theory have been detected and correlated with the hysteresis of the crystal for large root-mean-square voltages applied to it.
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.