Off-axis aberrations

Curvature of field is an off-axis aberration. It occurs because the focal plane of an image is not flat but has a concave spherical surface, as shown in Figure 1.10. This aberration is especially troublesome with a high magnification lens with a short focal length. It may cause unsatisfactory photography. 

Please note that these rules apply only to beams parallel to the optical axis. If off-axis aberration must be taken into account, the optimum lens shapes can be different. An introduction to basic lens design is given in [252]. 

The off-axis aberrations (off-axis astigmatism, coma, field curvature, and distortion) all vanish for rays parallel to the optical axis. All rays in the TEM are at such small angles to the optical axis that these aberrations are not usually important. The axial astigmatism can be corrected by adjustment of stigmators that cancel the residual non-circularity of the objective. This can be difficult, but assuming that it is done correctly, the remaining effective aberrations are chromatic and spherical. 

The idea to produce a converging objective from a reflecting, concave surface, instead of a refractive lens, was recognised by Galileo himself, and tried by Zucchi in 1616 (Fig. 4). Such arrangement, however, does not deliver acceptable image quality as a spherical surface used off-axis produces strong aberrations, and Zucchi s attempt was doomed for reasons he could not know. 

Several other approaches have been followed towards quantitative HRTEM imaging. One approach is the development of new hardware to correct for or alleviate some of the aberrations in the image, e.g. spherical aberration corrector (Rose 1990, Haider et al. 1995) and three-fold astigmatism corrector (Overwijk et al. 1997). An alternative approach is the development of new methods to retrieve the exit wave function, e.g. off-axis holography (Eichte 1986, Lichte and Rau 1994) and focal-series reconstruction (FSR) (Coene et al. 1992, 1996, Thust et al. 1996a). While each approach has its distinct advantages, we are only going to discuss focal-series reconstruction in this paper. 

Sims K. W. W., Blichert-Toft J., Fornari D. J., Perfit M. R., Goldstein S. J., Johnson P., DePaolo D. J., Hart S. R., Murrell M. T., Michael P., Layne G., and Ball L. (xxxx) Aberrant youth chemical and isotopic constraints on the origin of off-axis lavas from the East Pacific Rise, 9°- 10°N. Geochem. Geophys. Geosys. (in press). 

It should be pointed out that, in good part because of the use of large off-axis mirrors, optical aberrations can lead to significant curvature of the images under certain instrumental configurations. This has a detrimental impact on spectral resolution when multiple rows are birmed. Pelletier et al. have reported a data processing procedure to minimize this effect for situations where experimental limitations prevent improving the optical set-up [9]. In future commercial... 

The field of view of the instrument was also investigated. It results to be about 40 arcmin. The off-axis images show aberration defects (coma). 

Spherical aberration appears both on the axis and off the axis. It does not depend on the distance off-axis. In the absence of other aberrations, an image of a point is not compact but rather is surrounded by a diffuse halo. The diameter of the halo is a measure of the spherical aberration the spherical aberration of a thin lens increases as the cube of the diameter of the lens. The other third-order aberrations begin to appear off-axis and become more severe as the distance from the axis increases. 

Coma is a lens error restricted to off-axis image points. Conceptually, one can consider this effect as spherical aberration of an oblique bundle of rays. However, since the lens has no symmetry about a line passing through the centre of the lens and an off-axis point in the image, the effects of coma are complex and unsymmetrical and will not be elucidated further. 

Electron lenses are not corrected for aberrations, so their effects must be calculated. The off axis Seidel aberrations vanish for rays parallel to the axis. In the TEM, the angular range of rays is severely restricted, so these aberrations will not be important. The axial astigmatism can be corrected by adjustment of stigmators which cancel out the residual noncircularity of the objective. This leaves chromatic and spherical aberrations. 

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