Astigmatism objective

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. 

Amplitudes of the structure factors are sampled by D(u)sinx(u) when they are transferred to the image. The most significant effect of the lens to the amplitudes is caused by the sinx(u) part, which oscillates with u. Reflections in the resolution regions where sinx(u) 1 are maximally transferred by the lens, while those at resolutions where sinx(u) 0 are not transferred at all. This can be seen in the Fourier transform of HREM images from amorphous materials (Fig. 6), where the highest amplitudes (brightest areas) correspond to sinx(u) 1, while the lowest amplitudes (darkest areas) correspond to sinx(u) 0. If there is no astigmatism in the objective lens, a... 

So far, only defocus and spherical aberration have been considered as aberrations affecting the image contrast. Both depend only on the magnitude of the spatial frequency g[ but not on the diffraction direction, thus resulting in rotationally symmetric phase shifts (Equation 11). However, the objective lens may exhibit further aberrations resulting in additional phase shifts, which are not necessarily rotational symmetric. The most important of these additional aberrations are astigmatism and coma. 

The only practical difficulty comes from determining the appropriate aberration correction. In Truelmage, this has been automated, e.g. for the defocus and the 2-fold astigmatism. For a weak phase object, the real part of exit wave function should be constant (Equation 2). Thus, the defocus and 2-fold astigmatism can be determined by minimizing the contrast of the real part of the exit-wave function. 

Alignment of the electron microscope. It is absolutely essential that the microscope be accurately aligned and that the astigmatism of the objective lens be fully corrected with the same objective aperture as used for the high-resolution imaging. 

The object of an ideal optical configuration is that there are no optical aberrations, no stray light, and no energy loss through the system. In practice, various compromises have to be made to minimize the effect of the various variables. Within a practical optical system, five types of optical aberration are possible which give rise to image distortion, namely primary spherical aberration, coma, astigmatism (anamorphism), field curvature, and distortion. 

Finally, astigmatism is a lens error similar to coma this type of lens error is found at the outer portions of the field of view (far off-centre object points) in uncorrected lenses. It causes the image of such an object point, which in an ideal system would be a circular point image, to blur into a diffuse circle, elliptical patch, or line, depending upon the location of the focal plane. 

FIGURE 14.14 Focus control system (a) the quad detector, (b) the spot of light focused on the quad by the astigmatic lens (circular implies objective lens is in focus), and (c) the spot of light on the quad when the objective lens is out of focus. 

Electron lenses have serious aberrations that control the resolution of the instrument. The off-axis Seidel aberrations vanish for rays parallel to the axis. In the TEM, the angular range of the rays is severely restricted, so these aberrations will not be important. The axial astigmatism can be corrected by adjustment of stigmators that cancel the residual non-circularity of the objective. This leaves chromatic and spherical aberration as the most important. 

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

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