Retrieving the complex degree of spatial coherence of electron beams

An experiment on the particle–wave nature of electrons

“…The cosine-like distribution of the dark and bright fringes is produced by the Young experimental arrangement. A further property of the electron wavefunction reported neither by Davisson and Germer nor by G P Thomson regards the correlation on pairs of points in space that determines the spatial coherence degree of the electron beam [12]. A highly correlated wavefunction is required at the aperture on the BF plane to produce highly contrasted or visible fringes at the detector plane.…”

“…This effect is demonstrated by changing the spot size of the primary electron beam that illuminates the crystal, as shown in figure 7. The correlation of the electron wavefunction determines its spatial coherence properties and is related to the joint probability of finding an electron at any of two points in space [12]. Therefore, non-null joint probability is a requirement for producing interference patterns, and in this sense, this condition is connected with the above-mentioned redistribution mechanism of the probability of the electron beam.…”

“…The spatial (transverse) coherence length at the crystal plane, l s = λ/α, depends on the electron wavelength λ and the illumination angle α which is subtended by the diameter of the source S at a crystal point. For example, by exciting the condenser lens system so that α is 10 −5 rad (actually it can electron beams, based on the centred reduced moments of the beam spot [12]. This value is far larger than the distance between the lattice planes, so that adjacent crystal planes are coherently illuminated.…”

The Optics of Spatial Coherence Wavelets

“…Such supports distribute as follows on mask plane (the AP): (1) two supports of the first type, centered at the extreme pinholes of the mask; (2) two supports of the second type, centered at the midpoints of the opaque segments; each encloses two consecutive pinhole pair and the both share the middle pinhole of the mask; (3) one support of the third type, centered at the middle pinhole of the mask and enclosing the pair of extreme pinholes. After placing the mask at the AP, let us analyze the Fraunhofer diffraction of a uniform plane wave of power S 0 n ð Þ at frequency n, so that the phase argument k z x A x D is negligible (Castaneda and Carrasquilla, 2008), and adjust the setup to ensure the calibration C ¼ 1. After placing the mask at the AP, let us analyze the Fraunhofer diffraction of a uniform plane wave of power S 0 n ð Þ at frequency n, so that the phase argument k z x A x D is negligible (Castaneda and Carrasquilla, 2008), and adjust the setup to ensure the calibration C ¼ 1.…”

“…A mask with three pinholes cannot illustrate the concept of polarization domains (Castaneda et al, 2006(Castaneda et al, , 2008 because there is a dominant polarization state in any of the possible configurations at the OP. More pinholes are needed to regard configurations in which there is no dominant state at the OP.…”