Photon detection statistics

The statistics of the detected photon bursts from a dilute sample of cliromophores can be used to count, and to some degree characterize, individual molecules passing tlirough the illumination and detection volume. This can be achieved either by flowing the sample rapidly through a narrow fluid stream that intersects the focused excitation beam or by allowing individual cliromophores to diffuse into and out of the beam. If the sample is sufficiently dilute that... 

Another possible solution that has been under development for three decades is to use a pulsed laser and time-resolved detection to allow the Raman photons to be discriminated from the broad luminescence background. The Raman interaction time is virtually instantaneous (less than 1 picosecond), whereas luminescence emission is statistically relatively slow, with minimum hundreds of picoseconds elapsing between electronic excitation and radiative decay. If we illuminate a sample with a very short (= 1 ps) laser pulse, all of the Raman... 

Fig. 1.13 An Interference pattern, e.g. from the Young s slits experiment in Fig. 1.4, observed so that individual photons can be detected. The vertical scale shows the number of photons counted by each of a bank of 50 detectors. When only a few photons have arrived (a) they appear to be randomly distributed. As more come (b) and (c) the interference pattern predated by the wave Iheory emerges, but only as a statistical effect.

Time-correlated single photon counting (TCSPC) [28] is one of the most sensitive methods for studying time-resolved emission. In this technique, single photon events are detected after excitation and a statistical distribution of photons representing the decay of the excited state is built up over time. 

Table 1. Basic Quantities in Analyses of CW Laser Scattering for Probability Density Function. In Eq. 1 within the table, F(J) is the photon count distribution obtained over a large number of consecutive short periods. For example, F(3) expresses the fraction of periods during which three photons are detected. The PDF, P(x), characterizes the statistical behavior of a fluctuating concentration. Eq. 1 describes the relationship between Fj and P(x) provided that the effects of dead time and detector imperfections such as multiple pulsing can be neglected. In order to simplify notation, the concentration is expressed in terms of the equivalent average number of counts per period, x. The normalized factorial moments and zero moments of the PDF can be shown to be equal by substitution of Eq.l into Eq.2. The relationship between central and zero moments is established by expansion of (x-a)m in Eq.(4). The trial PDF [Eq.(5)] is composed of a sum of k discrete concentration components of amplitude Ak at density xk. [The functions 5 (x-xk) are delta functions.]...

---