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Applied Optics

Estimation of Optical Field Mean Intensities from Photocount Correlations

F. Davidson, Ramakrishna S. Iyer

Published Sep 1, 1974• 4 citations
Publisher

Abstract

An extremely simple procedure is given for estimating the mean intensity of each component of a twocomponent optical field from measurements of the number of photocounts recorded over counting intervals of T sec duration spaced tau sec apart. The only a priori knowledge required about each component is the functional form of the first- and second-order coherence functions and an order of magnitude estimate of their coherence times.

DOI
10.1364/ao.13.002171

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An extremely simple procedure is given for estimating the mean intensity of each component of a twocomponent optical field from measurements of the number of photocounts recorded over counting intervals of T sec duration spaced tau sec apart. The only a priori knowledge required about each component is the functional form of the first- and second-order coherence functions and an order of magnitude estimate of their coherence times.
Two techniques are described for obtaining information about the intensity correlation function of an optical field, from measurements of photoelectric counting distributions. The first method is based on double differentiation of the second factorial moment with respect to the counting time. It requires very accurate data, but is shown to be quite feasible, and yields the intensity-correlation function explicitly. The second procedure is less sensitive to inaccuracies and allows the correlation time and certain other parameters to be determined from the factorial moments. In addition, it yields some information about the general form of the correlation function, but no explicit function. The procedures are illustrated and compared by application to photoelectric counting measurements of a laser far below the threshold of oscillation.
In the history of optical science, we were satisfied with the measurement of mean intensity of light, namely the measurement of first-order coherence of light, for optical studies and observations, until the middle of 20th century when two astrophysicists Hanbury Brown and Twiss (HBT) introduced their “intensity interferometer”. “Correlation” emphasizes its statistical nature, while “coherence” emphasizes its interference nature. The chapter extends the concept of second-order coherence to Nth-order coherence (N > 2) and analyzes a few simple measurements on the third-order temporal and spatial coherence of thermal field. It also calculates the second-order temporal coherence function and the second-order spatial coherence function of thermal field by assuming idealized photodetectors and correlation measurement electronics.
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.
The asymmetry of photocount statistics in respect of the spatial and temporal coherence factors is demonstrated and explained. This asymmetry appears because of the of a counter receiving a non-Poisson photoelectron flux. A statistical model of an optical field, photoelectron flux, and counting flux is used in a computer study of the dependences of the distributions and moments of the number of counts in a given time interval on the ratio of the coherence factors. An explanation of the features of these dependences is provided. A determination is made of the range of conditions in which the asymmetry is significant. In particular, the asymmetry disappears in the case of a Poisson photoelectron flux and for a very short dead time.