Transverse Spherical Aberration
- Practical Electron Microscopy and Database -
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


Spherical aberration is the only form of monochromatic axial wavefront aberration produced by rotationally symmetrical surfaces centered and orthogonal in regard to the optical axis. The spherical attribute is due to this aberration being inherent to the basic optical surface - spherical - for object at infinity. Spherical aberration affects the entire image field, which makes its correction first priority. As shown in Figure 3631a, the light or electrons passing through the periphery of the lens are focused more strongly than those passing through the centre and the circle of the least confusion (the best focus point) is located within the range of longitudinal spherical aberration.

Schematic diagram of longitudinal spherical aberration

Figure 3631a. Schematic diagram of spherical aberration (SA), indicating transverse spherical aberration.

Figure 3631b shows typical Ronchigrams taken at the edge of an amorphous carbon film. At defoci (defined by z-height), there is a distance between the electron cross-over and the point on the specimen along the optic axis. At large underfocus, electron rays at all angles cross the optic axis after the specimen and it shows a shadow image of the specimen edge. At small underfocus, low-angle rays cross the optic axis after the specimen, while high-angle rays cross before the specimen due to spherical aberration. Therefore, the shadow image changes in magnification as a function of the angle. The low-angle asymmetry indicates the presence of astigmatism. At Gaussian focus, the lowest-angle rays cross the axis at the specimen, while higher-angle rays cross before the specimen due to the spherical aberration. The coma free axis is defined at this focus and all alignment and positioning of detectors and apertures can be performed with respect to the low-angle “disk”. Defocus and spherical aberration can effectively cancel each other at those lowest angles. Axial astigmatism can be accurately corrected by using the stigmator coils, resulting in circularly symmetric Ronchigram features. At overfocus, rays at all angles cross the axis before the specimen.

Ronchigrams of a thin amorphous carbon (C) film at: (a) Large underfocus, (b) Small underfocus, (c) Gaussian focus, and (d) Overfocus.

Figure 3631b. Ronchigrams of a thin amorphous carbon (C) film at: (a) Large underfocus, (b) Small underfocus, (c) Gaussian focus, and (d) Overfocus. [1]


[1] E.M. James, N.D. Browning, Practical aspects of atomic resolution imaging and analysis in STEM, Ultramicroscopy 78 (1999) 125-139.




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