Mirror electron microscopy

Models WDn in the presence of disorder and the coupled models

“…To make our presentation self-contained, and also because the models {W D (p) n } have not much been used so far in the statistical physics applications, we shall reproduce in this Section the results of the paper [1], by giving the details on a particular model of our…”

“…These models are based on the corresponding W -chiral algebras. They have been defined in the paper [1].…”

Addendum. Laplacian image contrast in mirror electron microscopy

“…An electrostatic MEM immersion lens is shown schematically in figure 1, which illustrates the divergent MEM illumination geometry considered by Kennedy et al (2010), Luk'yanov et al (1974), Dyukov et al (1991), Godehardt (1995), Nepijko & Sedov (1997), Nepijko et al (2001aNepijko et al ( ,b, 2003Nepijko et al ( , 2007 and Nepijko & Schönhense (2010). Here, an electron beam of energy U travels parallel to the optical axis z of the immersion lens and passes through the grounded anode aperture A.…”

“…The overall effect of the electric field in the vicinity of the grounded aperture is approximated by replacing the aperture with a thin diverging lens (Grant & Phillips 1990;Lenc & Müllerová 1992;Rempfer & Griffith 1992;Nepijko & Sedov 1997;Kennedy et al 2010), so that the electron beam is deflected away from the optical axis z. The electron beam is therefore diverging as it interacts with the electric field above the specimen surface C, which is located a distance of L from the anode and acts as the cathode of the immersion objective lens (Barnett & Nixon 1967b;Luk'yanov et al 1974;Bok 1978;Bauer 1985Bauer , 1998Kennedy et al 2010). The cathode C is held at a negative potential V < −U /e < 0 relative to the grounded anode, where −e is the electronic charge, so that the electron beam is reflected in the vicinity of z = L M , a distance of d above the specimen surface,…”

“…This arrangement has been considered by several authors (Dyukov et al 1991;Nepijko & Sedov 1997;Nepijko et al 2001aNepijko et al ,b, 2003Nepijko et al , 2007Nepijko & Schönhense 2010). It is a subset of non-parallel MEM specimen illumination considered in the literature (Barnett & Nixon 1967a;Luk'yanov et al 1974;Someya & Kobayashi 1974;Dupuy et al 1984;Godehardt 1995). Modern low energy electron microscopes (LEEMs) are, however, equipped with a magnetic objective lens and it is customary to slightly converge the incident illumination to compensate for the diverging effect of the anode aperture, resulting in collimated illumination of the sample (Altman 2010;Tromp et al 2010), within the domain of validity of the aperture lens approximation.…”