Photon statistics factor

In (98), Q is the Mandel factor [14], describing the deviation of the photon statistics from the Poisson distribution for the total intensity ... 

S Photon Statistics - The Bose Factor The equations above are normally used in the IR business, but be aware that they contain a small error Jones (1953, 1957) pointed out that the statistics for noise is not actually quite as stated here. Photons have a larger fluctuation rate than we have assumed. We can account for this by including the Bose Factor in any formulas that use the spectral photon irradiance Q(X) ... 

Fig. 7.7. Effects of Poisson photon noise on calculated SE and FRET values. (A) Statistical distribution of number of incoming photons for the mean fluorescence intensities of 5,10, 20, 50, and 100 photons/pixel, respectively. For n = 100 (rightmost curve), the SD is 10 thus the relative coefficient of variation (RCV this is SD/mean) is 10 %. In this case, 95% of observations are between 80 and 120. For example, n — 10 the RCY has increased to 33%. (B) To visualize the spread in s.e. caused by the Poisson distribution of pixel intensities that averaged 100 photons for each A, D, and S (right-most curve), s.e. was calculated repeatedly using a Monte Carlo simulation approach. Realistic correction factors were used (a = 0.0023,/ = 0.59, y = 0.15, <5 = 0.0015) that determine 25% FRET efficiency. Note that spread in s.e. based on a population of pixels with RCY = 10 % amounts to RCV = 60 % for these particular settings Other curves for photon counts decreasing as in (A), the uncertainty further grows and an increasing fraction of calculated s.e. values are actually below zero. (C) Spread in Ed values for photon counts as in (A). Note that whereas the value of the mean remains the same, the spread (RCV) increases to several hundred percent. (D) Spread depends not only on photon counts but also on values of the correction...

The interesting feature of Eq. (2.11) is that the induced and spontaneous emission combine into a factor as simple as Nv + 1. This is strongly suggestive of the factors N3- + 1, which we met in the probability of transition in the Einstein-Bose statistics, Eq. (4.2), of Chap. VI. As a matter of fact, the Einstein-Bose statistics, in a slightly modified form, applies to photons. Since it does not really contribute further to our understanding of radiation, however, we shall not carry through a discussion of this relation, but merely mention its existence. 

Fig. 5 illustrates the relative dependence of the fluorescence yield of the 337 nm line on different electron energies at a pressure of 400 hPa. The drawn curve corresponds to the Bethe-Bloch function [6] for ionization energy loss which was fitted to the data by a constant factor. The statistics in this plot is still very limited but the number of emitted fluorescence photons indeed seems to be proportional to the energy loss as it is suggested by Eq. (2). 

The enhanced spectral broadening observed in SL s is contained in the final three terms in Eq. (1). The first, ngp, is the spontaneous emission factor and gives the ratio of the rate of spontaneous emission into the laser mode to that of stimulated emission per photon in the mode. In many laser systems ngp is close to unity. However, this is not true of SL s due to the finite population of the lower level of the laser transition. In SL s, ngp approaches unity only at very low temperatures where the carriers are distributed according to Fermi-Dirac statistics. At room temperature ngp 2.5 for (GaAl)As lasers. 

Fluorescence decay in a population of excited-state molecules is a random process, so that the arrival time of the first photon is also random, although it is more likely to occur at the peak of the fluorescence decay than it is along the latter s tail. Because of this inherent statistical nature, over many excitation cycles one gradually builds us a statistical profile of the likelihood of emission versus time that corresponds to the decay profile. For a large enough number of counts, the uncertainty in the number of counts in a particular channel is equal to the count number s square root, which gives us the weighting factors to be used in the least-squares analysis of the data. 

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