Lens aberrations distortion

Aberration—distortion or defect in an image formed by a lens. 

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). 

Due to the finite aperture size and phase of lens aberrations the distribution of intensity at the back focal plane in the real optical system of a TEM introduces modifications, or phase distortion, given by the expression ... 

Spherical Aberration Distortion or blurriness of image caused by the geometrical formation of a spherical lens or mirror. 

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 Even this is very bad, and should he superseded by the view-lens, which has recently been invented by Professor Petzyal, and which will be described presently. 

There is an optimum angle, as indicated by wave optics. For example, the effect of spherical aberration of the objective is to distort the wave leaving the specimen from the spherical shape produced by a perfect lens. This vmwanted extra pathlength PD inserted into the wave is given by... 

In order to reach a minimum beam waist, diffraction should be small. This means the beam should have a large diameter before the lens. With unconected lenses such a large beam diameter will cause spherical aberration which distorts the focus and widens the beam waist. Therefore corrected microscope objectives should be used to reach the diffraction limited focus diameter. 

Distortion, similar to coma, is not a primary aberration but results from other aberrations. In distortion, the transverse linear magnification in the image varies with the distance from the optical axis, which results in distortion and causes a square object to look like a barrel or a pincushion, as shown in Figure 2.11. Distortion cannot change the resolution of the image, but it changes the locations of image points. For a sufficiently thin lens there is no distortion. 

The second approach to measuring aberrations is by interferometry. The aberrations are, after all, essentially imperfections that appear when the lens focuses the incoming light and causes distortion in the output wavefront. Such deformation would be reflected from the interference patterns between the output wave and a reference wave (usually a plane wave). The measured interference patterns can be used in turn to determine the aberrations, usually using Zemike pol5momials [8-10]. 

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