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Canadian Journal of Physics

Comptage des Photoélectrons Provenant de Points Statistiquement Indépendants et d'une Surface Etendue de la Photocathode

Jacques Bures, Claude A. Delisle

Published May 15, 1971• 4 citations
Publisher

Abstract

The experimental photocount distribution from a photocathode illuminated by a pseudothermal source is compared with theory. The detection time is much smaller than the coherence time [Formula: see text]. The agreement is excellent for an illuminated area composed of holes small enough to be considered as points and far enough to guarantee incoherence among them. But, for an extended circular area, the agreement is good only in the limits when that area is very small or very large with respect to the coherence area. Finally, we consider on the one hand, the evaluation of an extended detection area as a function of the number of statistically independent points, L, and on the other hand, the relative size of a physical point.

DOI
10.1139/p71-150

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The experimental photocount distribution from a photocathode illuminated by a pseudothermal source is compared with theory. The detection time is much smaller than the coherence time [Formula: see text]. The agreement is excellent for an illuminated area composed of holes small enough to be considered as points and far enough to guarantee incoherence among them. But, for an extended circular area, the agreement is good only in the limits when that area is very small or very large with respect to the coherence area. Finally, we consider on the one hand, the evaluation of an extended detection area as a function of the number of statistically independent points, L, and on the other hand, the relative size of a physical point.
The statistical behavior of photoelectrons emitted at L points of a photocathode in partially coherent Gaussian light is considered. The exact formula for the cumulants and the factorial moment generating function is derived. An exact expression for the photocount distribution and for the factorial moments is obtained in the case when the detection time is much smaller than the coherence time. Two cases of interest which were treated earlier by the same authors are also considered. In particular, the case of two points of detection is of special interest because a physical meaning can be given to the difference of the normalized eigenvalues. Finally, both the exact and approximate theories are compared with the experimental photocount distribution for four different geometrical arrangements.
The analysis of the photocount distribution in incoherent Gaussian light detected in L space points of a photodetector is extended to the case of partially coherent light. The second moment of the derived distribution is exact. A function η is introduced which accounts for the spatial coherence aspect of light as does the function ξ, (Mandel) for the temporal coherence aspect. A more general function ζ, which for cross-spectrally pure light reduces to the product ζ = ηξ, depends on both spatial and temporal characteristics of coherence. It is shown both theoretically and experimentally that many different geometrical configurations yield the same normalized second moment. A pseudo-thermal source [Formula: see text] where T is the detection time and Tc the coherence time) is used for the experimental verification.
A simple semiclassical derivation is given of the statistics of the photoelectrons emitted from a photosurface illuminated by light with statistically time dependent intensity. Comparison is made with the quantum mechanical expressions. Experiments are described that yield the probability of emission ofnphotoelectrons within a fixed time interval from a photocathode illuminated by a laser below and above threshold. The experimental results are compared with the theory developed in this paper and expressions derived by Glauber.
The statistics of the sum of photocounts in partially coherent Gaussian light is investigated. Both the case of detection at LLL discrete points and the case of an extended surface of detection are considered. The combinatorial-analysis approach is applied to derive the moments and cumulants of the distribution. They all can be expressed in terms of the second-order correlation function. The results are generally valid independent of the ratio of the observation time to the coherence time of light. A comparison between the theoretical moments and the moments computed from experimental distributions as a function of the detector surface is carried out with the help of a pseudothermal source.
A simple semiclassical derivation is given of the statistics of the photoelectrons emitted from a photosurface illuminated by light with statistically time dependent intensity. Comparison is made with the quantum mechanical expressions. Experiments are described that yield the probability of emission of n photoelectrons within a fixed time interval from a photocathode illuminated by a laser below and above threshold. The experimental results are compared with the theory developed in this paper and expressions derived by Glauber.
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.