Photon autocorrelation function

The photon autocorrelation function was analyzed by the method of cumulants (2.) 9 in which the logarithm of the normalized autocorrelation function, ci,t), is fit to a polynomial using... 

The photon autocorrelation function of single molecules has been shown to be a powerful tool for investigating the kinetics of the optical pmnping cycle [15]. This fluorescence autocorrelation function... 

I will present here the properties of various sources when the random variable considered is the field intensity. In this case, one has access to the mean and variance via a simple photodetector. The autocorrelation function can be interpreted as the probability of detecting one photon at time t + t when one photon has been detected at time t. The measurement is done using a pair of photodetectors in a start stop arrangement (Kimble et al., 1977). The system is usually considered stationary so that the autocorrelation function, which is denoted depends only on r and is defined by ... 

A Fock state is a state containing a fixed number of photons, N. These states are very hard to produce experimentally for A > 2. Their photon number probability density distribution P (m) is zero everywhere except for m = N, their variance is equal to zero since the intensity is perfectly determined. Finally, the field autocorrelation function is constant... 

The autocorrelation function G(t) corresponds to the correlation of a time-shifted replica of itself at various time-shifts (t) (Equation (7)).58,65 This autocorrelation defines the probability of the detection of a photon from the same molecule at time zero and at time x. Loss of this correlation indicates that this one molecule is not available for excitation, either because it diffused out of the detection volume or it is in a dark state different from its ground state. Two photons originating from uncorrelated background emission, such as Raman scattering, or emission from two different molecules do not have a time correlation and for this reason appear as a time-independent constant offset for G(r).58... 

When the number of data points is large (i.e. in the single-photon timing technique, or in phase fluorometry when using a large number of modulation frequencies), the autocorrelation function of the residuals, defined as... 

The phase-dependent directionality of photocurrents produced by such a detector entails advantageous properties of the photocurrents cross correlations in nonoverlapping time intervals or spatial regions (considered in Section 4.2.2). These directional time-dependent correlations are measured with one detector only. They involve solely terms dependent on LO phases, in contrast to similar correlations measured by conventional photocounters, which inevitably contain terms depending on photon fluxes such as the LO excess noise. Owing to these properties, the mean autocorrelation function of the SL quadrature is shown in the schemes considered here to be measurable without terms related to the LO noise. LO shot noise, which affects the degree of accuracy to which this autocorrelation is measured (i.e., its variance) is easily obtainable from zero time delay correlations because the LO excess noise is suppressed. The combined measurements of cross correlations and zero time delay correlations yield complete information on the SL in these schemes. 

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... 

Fig. 15.8. Schematic one-dimensional illustration of electronic predissociation. The photon is assumed to excite simultaneously both excited states, leading to a structureless absorption spectrum for state 1 and a discrete spectrum for state 2, provided there is no coupling between these states. The resultant is a broad spectrum with sharp superimposed spikes. However, if state 2 is coupled to the dissociative state, the discrete absorption lines turn into resonances with lineshapes that depend on the strength of the coupling between the two excited electronic states. Two examples are schematically drawn on the right-hand side (weak and strong coupling). Due to interference between the non-resonant and the resonant contributions to the spectrum the resonance lineshapes can have a more complicated appearance than shown here (Lefebvre-Brion and Field 1986 ch.6). In the first case, the autocorrelation function S(t) shows a long sequence of recurrences, while in the second case only a single recurrence with small amplitude is developed. The diffuseness of the resonances or vibrational structures is a direct measure of the electronic coupling strength.

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

Time- and space-resolved major component concentrations and temperature in a turbulent gas flow can be obtained by observation of Raman scattering from the gas. (1, 2) However, a continuous record of the fluctuations of these quantities is available only in those most favorable cases wherein high Raman scattering rate and/or slow rate of time variation of the gas allow many scattered photons (> 100) to be detected during a time resolution period which is sufficiently short to resolve the turbulent fluctuations. (2, 3 ) Fortunately, in other cases, time-resolved information still can be obtained in the forms of spectral densities, autocorrelation functions and probability density functions. (4 5j... 

In particular, if the number of photons detected during each period is recorded as a sequential record (instead of the simpler data recording mode utilized for this work) then autocorrelation functions and spectral densities of concentration... 

A is the base line, which is obtained either from the long-time asymptote of the measured autocorrelation function or from the square of the average photon flux. 8 is an equipment-related constant, and gfirst-order autocorrelation function, which is easily obtained from the measured function,... 

Photon Correlation. Particles suspended in a fluid undergo Brownian motion due to collisions with the liquid molecules. This random motion results in scattering and Doppler broadening of the frequency of the scattered light. Experimentally, it is more accurate to measure the autocorrelation function in the time domain than measuring the power spectrum in the frequency domain. The normalized electric field autocorrelation function g(t) for a suspension of monodisperse particles or droplets is given by ... 

The random Brownian motion of colloidal particles creates temporal fluctuations in the intensity of the scattered light. The fluctuating intensity signal cannot be readily interpreted because it contains too much detail. Instead, the fluctuations are commonly quantified by constructing an intensity autocorrelation function (ACF) [41J. For this reason, DLS often goes by the name photon correlation spectroscopy (PCS). 

The arrival times of fluorescence photons contain information about correlations in fluorescence signals. Eluorescence correlation spectroscopy (FCS) (26) exploits these correlations to measure the magnitude and time scales of fluctuations in fluorescence. These fluctuations contain information about the dynamic time scales of the system and the concentration of fluorescing molecules. Correlations may span time ranges from nanoseconds to milliseconds, which extends the dynamic time window for fluorescence measurements far beyond what is achievable in fluorescence lifetime measurements. The autocorrelation function is calculated as ... 

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 ). 

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