Lens aberrations spherical aberrations

There are three common types of lens aberrations. An aberration is the failure of a lens to produce an exact point-to-point correspondence between an object point and an image point, or in other words, an image distortion. The types of aberrations are spherical, chromatic, and curvature of field as illustrated in Figure 22A-22C. Spherical aberration is the failure of the lens to focus light onto the same focal plane (Fig. 22A). Chromatic aberration is when the different colors focus on different focal planes (Fig. 22B), which makes the image appears blurry. Curvature of field is when the plane of sharpest focus is curved due to this image curvature the whole image cannot be in focus (Fig. 22C). 

The ratio F/d is the F number of the lens. For F numbers much less than unity, spherical aberration precludes reaching the ultimate diffraction-limited spot size. Therefore a practical limit for the minimum spot size obtainable is approximately the wavelength of the light. Commonly this is expressed as the statement that laser light may be focused to a spot with dimensions equal to its wavelength. 

The specimen is immersed in the next lens encountered along the column, the objective lens. The objective lens is a magnetic lens, the design of which is the most crucial of all lenses on the instrument. Instrumental resolution is limited primarily by the spherical aberration of the objective lens. 

The use of a laser beam expander as a spatial filter has also been found to be satisfactory 42). The beam expander consists of an interchangeable negative input lens and a positive output lens. Both the input and output lenses are designed for minimum spherical aberration. The expansion power may be varied by using a different input lens (Fig. 23.) The laser beam... 

Spherical aberration Inacccurate focusing of light due to curved surface of lense whereby light rays passing through the lens at different distances from its center are focused to different positions in the Z-axis. 

The point resolution of an electron microscope is limited by the spherical aberration of the objective lens. Haider et al. (1995 1998) developed a corrector to be implemented into a standard transmission electron microscope to correct the spherical aberration. They showed that the point resolution could be improved from 2.4 A to 1.4 A. 

Figure 1. Ray optical description of lens aberrations, (a) Perfect lens imaging a point P in the object plane onto a sharp point in the image plane, (b) Lens affected by spherical aberration, (c) Lens underfocused by a distance Z. (d) Lens overfocused by a distance Z. Spherical aberration and defocusing cause a blurring of the point P in the image plane.

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. 

In geometrical optics the numerical aperture of a lens is given by first-order theory and spherical aberrations are given by third-order theory (Jenkins and White 1976 Hecht 2002). In first-order theory the approximation is made... 

In the preceding Figs, c denotes crown, f flint-glass. Both forms have equal radii of the front and bach surfaces, equal focal lengths, equal curvature of the image, and an equal distortion hut the plan shown in Fig. 409 is the best, because there is rather less spherical aberration. Even this is very bad, and should he superseded by the view-lens, which has recently been invented by Professor Petzyal, and which will be described presently. 

A laser lens for electrons has spherical aberration, which has a negligible effect on estimate (6), and also chromatic aberration, which is a more serious matter. For the particular numerical example we are discussing here, the electrons would have to be monochromatic within something on the order of 0.01%. 

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