Astigmatism

If the object is a radial line, its image is sharp at F and blurred at Fj. If the line object is rotated about the axis and a series of successive images are 

Radial line object of rotational symmetry (top), tangential Une object (center), and astigmatic image of spoked wheel (bottom). 

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Once the primary electron beam is created, it must be demagnified with condenser lenses and then focused onto the sample with objective lenses. These electron lenses are electromagnetic in nature and use electric and magnetic fields to steer the electrons. Such lenses are subject to severe spherical and chromatic aberrations. Therefore, a point primary beam source is blurred into a primary beam disk to an extent dependent on the energy and energy spread of the primary electrons. In addition, these lenses are also subject to astigmatism. AH three of these effects ultimately limit the primary beam spot size and hence, the lateral resolution achievable with sem. 

AAST angular diameter of astigmatic blur circle... 

Lastly, it is possible to correct for all three major aberrations. Spherical, coma and astigmatism. This gives a system with very large FOV, but with other less desirable features. Examples are ... 

As the relative size of segments shrink, the higher order terms become smaller quickly, and for small segments, the astigmatic term is the only term that matters. 

Following similar reasoning, the error in the astigmatism component of the departure is... 

Figure 10. Eigenvalues of a 4 LGSs 3D mapping system with a /O field. Neither piston nor tilts are measured from the LGSs. Dashed line without natural guide star. Solid line with a NGS to measure tilts, defocus and astigmatisms (Le Louam and Tallon, 2002).

When neither the piston nor the tilts are measured from the LGSs, there are 5 more 0 eigenvalues the two even tilt modes, and the odd defocus and astigmatism modes. These last modes result from combinations of not measured tilts in front of the LGSs. 

Figure 2. Schematic drawing of a control apparatus. A laser of frequency coi is focused by lens L into a cell containing a tripling medium such as Hg vapor. Mirrors Ml and M2 are mounted inside a phase tuning cell (not shown) containing a refractive medium such as H2. The folded mirror geometry produces a pair of elliptical astigmatic foci, one of which overlaps the molecular beam (MB) at a distance zm from the beam axis. (Reproduced with permission from Ref. 62, Copyright 2006 American Physical Society.)...

In the quest for optimal FRET resolution in three dimensions [48, 49], one requires sophisticated algorithms for analyzing complex distributions [48, 50, 51], An issue of particular relevance when multiple probes [52-54] and multiparametric detection [26, 55] are employed. Strategies for spatial superresolution [56] have spawned a family of acronyms RESOLFT, STED, STORM, astigmatic STORM, PALM, fPALM, sptPALM, PALMIRA ([57-59] and other references), some of which involve systematic photoconversion or destruction. Undoubtedly, these techniques will be applied systematically to FRET imaging, and, conversely, one can anticipate that FRET mechanisms will be exploited for achieving superresolution. 

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