The Theory of Aberrations
The operation of axially symmetric electron and ion lenses is based o n the paraxial (first-order) theory. In practice, however, the trajectories always have both finite displacements r and finite slopes r’ with respect to the axis. Even if they are small, the omission of the higher-degree terms in the series expansions leading to the paraxial ray equation causes some error. Therefore, the paraxial theory is always an approximation. In fact, a point object will be “imaged” not by a conjugate point but by a blurred spot produced by different rays with different slopes that converge at different image points. These rays intersect the Gaussian (paraxial) image plane at different points; therefore the “image” is not a point but a finite-size spot, which can have quite an irregular shape. This phenomenon is called the geometrical aberration. W e have already seen an example of this effect in Section 2–7–2–1 when we analyzed the operation of the long magnetic lens. We established the fact that a clear image can only be produced if the particles move close to the field lines. Otherwise, different particles will be focused at different points and the image will be blurred.
KeywordsObject Point Spherical Aberration Chromatic Aberration Gaussian Image Magnetic Lens
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