Photon count autocorrelation function

Dynamic scattering makes use of the (unnormahzed) photon count autocorrelation function q) computed fixim the... 

The normalized photon count autocorrelation function for a nematic m um see Eq. 85... 

The unnormalized photon count autocorrelation function, also G (x q) see Eq. 1... 

Up to now, we have given a general theoretical development of the self-beat technique. As a practical illustration of the experimental apparatus used to detect autocorrelation functions in scattering experiments, the equipment currently used in our laboratory will now be described. While our treatment of the autocorrelation function has been in terms of an analog signal, the computer that measures this function is actually a digital device. This is based on the fact that it is also valid to count the scattered photons in order to calculate Ci(r) as the optical intensity signal is essentially determined by the number of photons that strike the photocathode per unit time. We have then... 

Fourier transform -Autocorrelation function -Moments of photon count distribution... 

In fluorescence correlation spectroscopy (FCS) a small volume element or a small area) of a sample is illuminated by a laser beam and the autocorrelation function of fluctuations in the fluorescence is determined by photon counting. From this autocorrelation function the mean number densities of the fluorophores and their diffusion coefficients can be extracted. Measurement and analysis of higher order correlation functions of the fluorescence has been shown to yield information concerning aggregation states of fluorophores ). 

In this technique one counts the number of photomultiplier output pulses in a given time and computes the time-autocorrelation function of these photocounts. Since each pulse, in the ideal case, corresponds to one arriving scattered photon, one measures the time-autocorrelation function of the number of photons arriving at the detector. 

The time distribution of the fluorescence photons emitted by a single dye molecule reflects its intra- and intermolecular dynamics. One example are the quantum jumps just discussed which lead to stochastic fluctuations of the fluorescence emission caused by singlet-triplet quantum transitions. This effect, however, can only be observed directly in a simple fluorescence counting experiment when a system with suitable photophysical transition rates is available. By recording the fluorescence intensity autocorrelation function, i.e. by measuring the correlation between fluorescence photons at different instants of time, a more versatile and powerful technique is available which allows the determination of dynamical processes of a single molecule from nanoseconds up to hundreds of seconds. It is important to mention that any reliable measurement with this technique requires the dynamics of the system to be stationary for the recording time of the correlation function. 

When we measure photons emitted by a single molecule using a quantum detector such as a photomultiplier tube, we interpret /(/) to be the photon counting rate (fluorescence intensity at time i) and we can deduce the fluorescence intensity autocorrelation function by counting the number of photon pairs separated by... 

The autocorrelation function can be calculated in real time using a hardware correlator or in software after the collection of a photon count trace using a multichannel scalar card. Details of the instrumentation will be discussed in Chapter 3. Formally, the un-normalized autocorrelation of time series data is given as [6] ... 

Higher order autocorrelation analysis is analogous to the analysis of the higher order moments of the photon count distribution. Such a correlation function is given by. 

A laser source is incident on a sample. The sample is usually a well-dispersed suspension. The scattered radiation containing the Doppler broadening information is incident on a PMT Photon counting signal processing is used. The autocorrelation function of the scattering signal is calculated and used to obtain the translational diffusion coeffl-cienl Oy. which Is then related to particle size. 

Fig. 5A, B Proteolytic cleavage analysed by A cross-correlation analysis B FRET on single-molecule-scale. In A, during the course of a specific proteolytic reaction GFP and DsRed get separated leading to gradually decreasing cross-correlation amplitudes Gx(0) determined in 40-s intervals, in B, alternatively, autocorrelation functions and photon counts per molecule in kHz (inset) for rsGFP and DsRed were determined in parallel during a proteolytic digest. Changes in fluorescence intensity of FRET donor and acceptor were detected immediately after enzyme addition, whereas autocorrelation G(0) values and fluorescent particle numbers remained constant. The monitored increase of rsGFP fluorescence corresponds to approximately 35% FRET in the intact substrate...

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