Photons counting

The upper limit of the counting rate depends on the time resolution of the discriminator, which may be below 10 ns. This allows counting of randomly distributed pulse rates up to about 10 MHz without essential counting errors. 

The lower limit is set by the dark pulse rate [4.141]. With selected low-noise photomultipliers and cooled cathodes, the dark pulse rate may be below 1 per second. Assuming a quantum efficiency of r = 0.2 it should therefore be possible to achieve, within a measuring time of 1 s, a signal-to-noise ratio of unity already at a photon flux of 5 photons/s. At these low photon fluxes, the probability p(N) of N photoelectrons being detected within the time interval At follows a Poisson distribution 

A significant improvement of the signal-to-noise ratio in detection of low levels of radiation can be achieved with single photon counting techniques which enable spectroscopic investigations to be performed at incident radiation fluxed down to 10 W. This technique will be discussed in the next section. More details about photomultipliers and optimum conditions of performance can be found in the excellent introductions issued by EMI [4.66] or RCA [4.73]. An extensive review of photoemissive detectors has been given by ZWICKER [4.62]. 

Compared with the conventional analogue measurement of the anode current, the photon-counting technique has the following advantages  

1) Fluctuations of the photomultiplier gain G, which contribute to the noise in analogue measurements [see (4.135)], are not significant here, since each photoelectron induces the same normalized pulse from the discriminator as long as the anode pulse exceeds the discriminator threshold. 

2) Dark current generated by thermal electrons from the various dynodes can be suppressed by setting the discriminator threshold correctly. This discrimination is particularly effective in photomultipliers with a large conversion efficiency q at the first dynode, covered with a GaAsP layer. 

3) Leakage currents between the leads in the photomultiplier socket contribute to the noise in current measurements but are not counted by the discriminator if it is correctly biased. 

1 Baseline Subtraction and Normalizjation Because the scattering intensity /(f) fluctuates around its mean (/), it is convenient to separate its fluemating component A/(f) as 

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The other coimnon way of measuring nanosecond lifetimes is the time-correlated single-photon counting... 

One advantage of the photon counting teclmique over the phase-shift method is that any non-exponential decay is readily seen and studied. It is possible to detect non-exponential decay in the phase-shift method too by making measurements as a fiinction of tlie modulation frequency, but it is more cumbersome. 

O Conner D V and Phillips D 1984 Time-Correlated Single Photon Counting (London Academic)... 

Figure C1.5.12.(A) Fluorescence decay of a single molecule of cresyl violet on an indium tin oxide (ITO) surface measured by time-correlated single photon counting. The solid line is tire fitted decay, a single exponential of 480 5 ps convolved witli tire instmment response function of 160 ps fwiim. The decay, which is considerably faster tlian tire natural fluorescence lifetime of cresyl violet, is due to electron transfer from tire excited cresyl violet (D ) to tire conduction band or energetically accessible surface electronic states of ITO. (B) Distribution of lifetimes for 40 different single molecules showing a broad distribution of electron transfer rates. Reprinted witli pennission from Lu andXie [1381. Copyright 1997 American Chemical Society.

Birch D J S and Imhof R E 1977 A single-photon counting fluorescence decay-time spectrometer J. Phys. E Sol. Instrum. 10 1044-9... 

Figure 5 Schematic layout of a high-sensitivity PL system incorporating a laser and photon-counting electronics.

DC amplification and pulse counting (often inaccurately called photon counting ) are two types of signal amplifications often used. 

Abstract We compare homo-or heterod)me power and phase detection to the photon count-... 

Figure 4.6 shows an apparatus for the fluorescence depolarization measurement. The linearly polarized excitation pulse from a mode-locked Ti-Sapphire laser illuminated a polymer brush sample through a microscope objective. The fluorescence from a specimen was collected by the same objective and input to a polarizing beam splitter to detect 7 and I by photomultipliers (PMTs). The photon signal from the PMT was fed to a time-correlated single photon counting electronics to obtain the time profiles of 7 and I simultaneously. The experimental data of the fluorescence anisotropy was fitted to a double exponential function. 

As a side aspect, the HPLC-Raman correlation results allow us to calibrate the RRS instruments in terms of carotenoid concentration. According to the regression analysis, the cumulative skin carotenoid content c, measured in pg per g of skin tissue, is linked to the height of the C=C RRS skin carotenoid intensity, I, via c [pg/g]=4.3 x 10 5=/ [photon counts]. Integrating the RRS spectra with the instrument s data acquiring software therefore allows us to display skin carotenoid content directly in concentration units, i.e., in pg carotenoid content per g of tissue. 

Gompf B, Gunther R, Nick G, Pecha R, Eisenmenger W (1997) Resolving sonoluminescence pulse width with time-correlated single photon counting. Phys Rev Lett 79 1405-1408... 

Zimmerman HE, Goldman TD, Hirzel TK et al (1980) Rod-like organic molecules, energy-transfer studies using sinelo-photon counting. J Org Chem 45 3933-3951... 

Steady-state fluorescence spectra, fluorescence quantum yield (F) and lifetimes (tf) of DTT 15 and DTP 23a were estimated as shown in Table 8. F for DTT is higher than DTP. F for DTP is very small and it was difficult to estimate an accurate fluorescence lifetime by the photon counting method due to weak fluorescence. It is noted that the for DTP depends largely on the solvent and is 7.7 x 10-5 in acetonitrile. This low F value has been attributed to an addition reaction with the solvent. 

Advanced Time-Correlated Single Photon Counting Techniques... 

Say we do the experiment first with just one door open call this door f (which stands for fluorescence). We sit outside of the f-door, and after we start the experiment (at time T0 — 0), we record whether the monkey is still in the room at some time T, and record this. This is the same as a photon counting experiment. We divide up our observational/recording times into At equal increments. The probability that the monkey will still be in the room at time T() + At, if he had started there at time T(h is P(T0 + At) = (1 - k/At), where kf is the time-independent rate (probability per unit time) for finding the f-door. From now on we define Tq = 0. We repeat this experiment a large number of times, each time we record the time T + At when the monkey emerges through the f-door (so he was still in there at time T). For each experiment,... 

In time-gated photon counting, comparatively high photon count rates can be employed count rates as high as 10 MHz are often used. TG has the advantage of virtually no dead-time of the detection electronics ( 1 ns), whereas the dead-time of the TCSPC electronics is usually on the order of 125-350 ns. This causes loss of detected photons, and a reduced actual photon economy of TCSPC at high count rates. 

The lifetime resolution is the smallest variation in lifetime that can be detected. If external noise sources are ignored, the lifetime resolution depends essentially on the photon-economy of the system. For instance, if a 2 ns lifetime is measured with a 4 gate TG single-photon counting FLIM (F = 1.3) and 1000 photons, variations of about 80 ps can be resolved. However, for reasons discussed earlier, in biological samples these values could be higher. 

Lifetime heterogeneity itself can be the target of the measurement. In this case, high photon counts and alternative model functions like stretched exponentials and power-distribution-based models can be used [39, 43], These provide information on the degree of heterogeneity of the sample with the addition of only one fit parameter compared with single exponential fits. 

Generally, inaccuracies can also be expected at low photon counts (N < 100). Besides comparatively large statistical fluctuations, also a bias in lifetime is introduced by the data fitting procedure [37],... 

Furthermore, at very low photon counts in general low values of the reduced y2 ( 1) are obtained because of the high noise level in the data. Therefore, the reduced y2 and other goodness of parameters should be used with caution. 

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