Fringe visibility coherence

The fundamental quantity for interferometry is the source s visibility function. The spatial coherence properties of the source is connected with the two-dimensional Fourier transform of the spatial intensity distribution on the ce-setial sphere by virtue of the van Cittert - Zemike theorem. The measured fringe contrast is given by the source s visibility at a spatial frequency B/X, measured in units line pairs per radian. The temporal coherence properties is determined by the spectral distribution of the detected radiation. The measured fringe contrast therefore also depends on the spectral properties of the source and the instrument. 

Distances between scatterers of (0.60 0.06) A estimated from the interference fringes do not correspond to any visible distance between protons in the crystal structure. However, they correspond closely to distances between projections of proton positions onto directions corresponding to normal coordinates (namely, x, y or z as shown in Fig. 1). It appears that neutrons are scattered coherently by lines of protons quite visible in the crystal structure (see Fig. 17). The elastic scattering function presented in Fig. 16 corresponds to a double-quantum-slits experiment. The interference fringes are quite different from those observed for neutrons scattered by double-classical-slits [Zeilinger 1988]. It can be concluded that quantum entanglement is not limited to single pairs. 

The visibility (or contrast) of the fringes detected depends, in addition, on a number of factors including the relative intensities of the two beams, incoherent background light within the bandpass of the detection system, and coherent scattered light. 

Referring to Young s experiment (Fig. 2.24) with a narrow bandwidth but extended source, spatial coherence effects will predominate. The fringe pattern in the plane B will depend on IXSx, S2, t) = Pnit). In the region about the central fringe (r2 — ri) = 0, t = 0, the values of ri2(0) and yi2(0) can be determined from the visibility of the interference pattern. 

The visibility is then equal to the degree of coherence. Figure 2.28a depicts the visibility V of the fringe pattern in P as a function of the slit separation d, indicated in Fig. 2.24, when these slits are illuminated by monochromatic light from an extended uniform source with quadratic size bxb that appears from Si under the angle 0, Figure 2.28b illustrates the visibility as a function of path difference A5 in a Michelson interferometer which is illuminated with the Doppler-broadened line X = 632.8 nm from a neon discharge lamp. 

This yields the desired information about the spatial coherence of the source which depends on the size of the source. The visibility of the fringes at P is defined to be... 

---