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Spectroscopy Letters

Sine Transform of the Autocorrelation Function Applied to Single-Photon-Decay Spectroscopy.

Niceto Pérez Cagigal, J. Prieto, Manuel P. Cagigal, Pedro M. Prieto

Published Jun 1, 1994• 1 citation
Publisher

Abstract

In this paper we present the sine transform of the Autocorrelation Function of the time interval probability density, TIPD. It not only improves the Signal-to-Noise Ratio (SNR) obtained from a direct measurement of TIPD but even that obtained from the sine transform of TIPD. Expressions for variances and SNR are given. This technique is compared to the sine transform of TIPD when analyzing a Single-Photon-Decay Spectroscopy signal for low fluorescence intensity.

DOI
10.1080/00387019408000858

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In this paper we present the sine transform of the Autocorrelation Function of the time interval probability density, TIPD. It not only improves the Signal-to-Noise Ratio (SNR) obtained from a direct measurement of TIPD but even that obtained from the sine transform of TIPD. Expressions for variances and SNR are given. This technique is compared to the sine transform of TIPD when analyzing a Single-Photon-Decay Spectroscopy signal for low fluorescence intensity.
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In this paper we present a method for processing the time-interval data obtained in a single-photon-decay spectroscopy experiment. This method is based on the measurement of the Laplace transform of P ƒ ( t) [the probability distribution function of the time of arrival of the first photon (PDFP) after the excitation pulse] instead of the direct measurement of P ƒ ( t) by means of a multichannel analyzer. With the use of this method, a good estimation of the lifetime of the signal can be obtained with a shorter measurement time than that used in the conventional method, in which the recorded time intervals are used to construct P ƒ ( t). A theoretical model of the error involved in determining the lifetime is obtained for the Laplace method, and it is compared with that corresponding to the measurement of P ƒ ( t) by means of a multichannel analyzer. Finally, a computer simulation of the experiment is performed to corroborate the theoretical predictions.
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.
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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.