Field autocorrelation

Finally, the field autocorrelation function is constant equal to 1. 

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 different behaviors for the field autocorrelation function are summarized on Fig. 1. 

Figure 10 Polarized field autocorrelation function g(1) for poly(p-phenylene)...

DLS is a versatile experimental technique, which is readily available in many laboratories. As discussed in Section 5.2, the field autocorrelation function g (r)... 

Here <( t ) f(t")> is the autocorrelation function of the electromagnetic field. For the case of excitation by a conventional light source, where the amplitudes and the phases of the field are subject to random fluctuations, the field autocorrelation function differs from zero for time intervals shorter than the reciprocal width of the exciting source. In the limit 8v A, that is when the spectral width, 8v, of the source exceeds the inhomogenously broadened line width, the field autocorrelation function can be represented as a delta function... 

In this section it will be outlined how the different molar masses contribute to the TDFRS signal. Of especial interest is the possibility of selective excitation and the preparation of different nonequilibrium states, which allows for a tuning of the relative statistical weights in the way a TDFRS experiment is conducted. Especially when compared to PCS, whose electric field autocorrelation function g t) strongly overestimates high molar mass contributions, a much more uniform contribution of the different molar masses to the heterodyne TDFRS diffraction efficiency t) is found. This will allow for the measurement of small... 

The normalized electric field autocorrelation function gift), which can be calculated from the normalized intensity autocorrelation function g2(t) = (1(0) 7(f)) (I(0)/2 according to the Siegert relation [56]... 

The intensity distribution of particle size, G(a), is related to the experimentally observed electric field autocorrelation function, g[Pg.107]

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 ... 

Since DLS does not detect single particles, the interpretation of data on polydisperse samples is quite a bit more complex than that for monodisperse samples. In essence, the expression for the field autocorrelation function gg given in Eq. (8) must be generalized to... 

For pulses much longer than T2, the expression for the scattered energy is simply the envelope of the electric field autocorrelation squared for both the homogeneous and inhomogeneous cases ... 

Equation (8.159) is strictly valid for a Gaussian distribution of electric fields. The electric field autocorrelation function is related to the dynamic structure factor S q, t) [compare it with the static scattering function S q) in Eq. (3.121)] ... 

In the homodyne mode, G2(t) can be related to the normalised field autocorrelation function gj (t) by. 

The field autocorrelation function gi(r) for a monodisperse suspension decays exponentially with r,... 

For the purpose of discussing the differences between heterodyne and homodyne scattering we define the two scattered field autocorrelation functions... 

In light-scattering experiments one measures the spectral density of the electric field autocorrelation function of the scattered light wave, given as... 

The function G(K, t) is the Fourier transform of S(K, interacting particles, G(K, t) is simply a self-correlation function, and the absolute value of the normalized field autocorrelation function takes the form ... 

Figure 33. BaseUne-subtracted, normalized intensity antocorrelation function g2(t) (a) and the absolute value of the baseline-subtracted, normalized electric-field autocorrelation function, gi(i) (b).

Electric-Field Autocorrelation Function We consider the autocorrelation function of the electric field E,(t) of the light scattered by solutes. As we have seen in Section 2.4, is a complex quantity. We introduce another normalized autocorrelation function gi(r), which is defined as... 

The electric field autocorrelation function can be obtained in a heterodyne system, in which the scattered light is mixed with unscattered light from the laser source, thus obtaining a beat frequency. The characteristic exponential decay rate for the heterodyne correlation function is q DI2 that is, one-half the decay rate of the homodyne autocorrelation function. Sometimes there will be a partial heterodyne character to the autocorrelation function if unwanted stray light from the incident laser mixes with the scattered light, termed accidental heterodyning [16]. 

In most PCS experiments the intensity autocorrelation function G2(0,t) is measured at one or several scattering angles 0 as a function of time delay x. In the first step of the interpretation procedure G2(0,x) is related to the modulus of the normalized field autocorrelation function gi(0,x) by a Siegert relation ... 

In eq. (1) A is a, in principle constant, background signal and B is an instrumental factor. Note that eq. (1) applies only to scattered fields with Gaussian statistics an hypothesis which is not always fulfilled experimentally. Especially for particles larger than roughly 0.5 to 1 im additional time delay dependent factors can be distinguished in eq. (1) In a second step the time decay of the field autocorrelation function is related to the particles Brownian motion. Thereby it is assumed that the particles scatter independently. In particular for monodisperse samples gi(0,x) is an exponentially decaying function ... 

The normalized electric field autocorrelation function for a nematic medium see Eq. 85... 

The rate of decay of g x) is indicative of the typical fluctuation time of the scattering signal and of the rate of diffusion of the scatterers. Quantitatively, g( )(r) can be related to the electric field autocorrelation function through the relation... 

Thus, for such a system, diffusion coefficients can rapidly be obtained by simple least-squares fits of Equation [3] to electric field autocorrelation functions recovered from the experimental intensity autocorrelation functions, or by linear fits to the natural logarithm of ( (r). 

We independently measured the transmittance of the sample that is directly related to the photon transport mean free path when the diffusing particles are not interacting. From the field autocorrelation function, g (t) = yjg2(t)-l, we were able to deduce the mean square displacement Ar (t) of the diffusing particles. In the case of backscattering geometry, the field autocorrelation function is linked to the mean square displacement of the particles through... 

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