Coherence factor

Usually we are only interested in mutual intensity suitably normalised to account for the magnitude of the helds, which is called the complex degree of coherence 712 (r). This quantity is complex valued with a magnitude between 0 and 1, and describes the degree of likeness of two e. m. waves at positions ri and C2 in space separated by a time difference r. A value of 0 represents complete decorrelation ( incoherence ) and a value of 1 represents complete eorrelation ( perfect coherence ) while the complex argument represents a difference in optical phase of the helds. Special cases are the complex degree of self coherence 7n(r) where a held is compared with itself at the same position but different times, and the complex coherence factor pi2 = 712(0) which refers to the case where a held is correlated at two posihons at the same time. 

We are now ready to derive an expression for the intensity pattern observed with the Young s interferometer. The correlation term is replaced by the complex coherence factor transported to the interferometer from the source, and which contains the baseline B = xi — X2. Exactly this term quantifies the contrast of the interference fringes. Upon closer inspection it becomes apparent that the complex coherence factor contains the two-dimensional Fourier transform of the apparent source distribution I(1 ) taken at a spatial frequency s = B/A (with units line pairs per radian ). The notion that the fringe contrast in an interferometer is determined by the Fourier transform of the source intensity distribution is the essence of the theorem of van Cittert - Zemike. 

This effective Q,t-range overlaps with that of DLS. DLS measures the dynamics of density or concentration fluctuations by autocorrelation of the scattered laser light intensity in time. The intensity fluctuations result from a change of the random interference pattern (speckle) from a small observation volume. The size of the observation volume and the width of the detector opening determine the contrast factor C of the fluctuations (coherence factor). The normalized intensity autocorrelation function g Q,t) relates to the field amplitude correlation function g (Q,t) in a simple way g t)=l+C g t) if Gaussian statistics holds [30]. g Q,t) represents the correlation function of the fluctuat-... 

Figure 18. Modulation of an image as a function of the spatial frequency, v for three coherency factors, a 0, 0.7, and >.

It should be note that the coherent factor ft in dynamic LLS should be as high as possible. The ALV instrument can reach 0.95, a rather high value... 

Two different cases can be treated. The first is the case where the energy mismatch is small compared to the available phonon energies so the relevant phonon modes are those of small wave vector, k-Rga << 1. Thus, the phonon wavelength is large compared to the sensitizer-activator separation. A Debye distribution of phonon modes can be used to evaluate the sum in Eq. (30) and the coherence factor can be averaged over all angles. This leads to 2)... 

For coherent state light, each and every coherence factor takes the value of unity, and it may be observed that the result of effecting Eq. (70) is that a time-dependent irradiance / ,(/) now appears, properly defined through... 

The result embodies the coherence factor r w to account for the phase-matching characteristics of the process, leading to the familiar sine2 behavior, which... 

C is a coherence factor and depends on the experimental conditions. For an ideal solution of mono-disperse particles the function g1 (t ) is represented by a single exponential... 

Figure 1. The coherence factor f(A) determined for several values of the pinhole diameter D. The curve is a theoretical estimate, fitted to the data by use of an arbitrary proportionality between and the coherence area A.

The coherence factor depends, as the name suggests, on the coherence of the light falling on the photodetector. The beam has a finite cross section, and different parts of the beam may not have the same phase. If they have the same phase, the number of photons will be distributed with a Poisson distribution. The variance of I is then equal to the square of the mean, i.e., /c = 1. In general, 0 [Pg.171]

It is thus necessary to use the correlation technique. In our horaodyne correlation experiment, we directly obtain C(t)"a(l+b02(t)), in which b is a spatial coherence factor and a depends on the average number of photocounts in the sampling time. The 0(t) correlation function is the Fourier Transform of the central line of Fig. 1. This correlation function will be supposed latter to have a particular form depending on two parameters characterizing the relaxation process. 

K K coherence factor = 100 0.16 K K average relative strong phase = (26 16)° CP-vloladon decay-rate asymmetries (labeled by the 0° decay)... 

In this equation, ki describes a coherence factor, which depends on exposure wavelength and varies between 0.55 and 0.8. In the case of an Airy-function (i.e., a point light source) one finds k = 0.61. The factor NA is called the numerical aperture,... 

A straightforward approach with heterodyne treatment was proposed by Fang and Brown, which is a modification of the partial heterodyne method, where the instmmental coherent factor p is taken into account. Then, we can rewrite eqn [140] as... 

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