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Comaaberration

Electron beams which exit from a point on the object plane with a distance r from the optical axis at various angles α with respect to the optical axis, do not come to a single point on the image plane after passing through the lens but produce a cone-shaped (comet-shaped) image. This phenomenon is called the off-axial coma aberration. The name of “coma” originates from “comet”. This aberration is proportional to rα2. The vertex angle of the cone is 60°. The off-axial coma aberration is inherent to the lens and is one of “Five Seidel aberrations”. In the case of the objective lens, the spherical aberration which is proportional to α3 has the largest contribution to the image blur. The off-axial coma aberration theoretically has the second largest effect on the blur among Five Seidel aberrations. However, in fact, the blurring of images due to the coma aberration can be ignored not only in high-resolution imaging but also in low-magnification imaging. It is noted that the off-axial coma aberration is a different aberration from the axial coma aberration (proportional to α2), which is one of parasitic aberrations. The off-axial coma aberration is equivalent to the axial coma aberration (proportional to α2) at the distance r from the optical axis. The magnitude and direction of the off-axial coma aberration can be measured using Diffractogram Tableaus (Fig. (a), (b)) taken by changing α at a unit distant (e.g. 1 µm) from the optical axis. Fig. (c) and (d) show the radial (isotropic) components and the azimuthal (anisotropic) components of the off-axial coma aberration (These are not measurement results but computed examples for ease of understanding). Fig. (e) and (f) schematically show the image blurs (cone-shaped beam broadenings) in the real space corresponding respectively to Fig. (c) and (d). In the case of an axially symmetric magnetic-field lens, the off-axial comma aberration contains the radial components (Fig. (c)), and the azimuthal components arising from a rotation effect (Larmor rotation) of the electron beam due to the magnetic field (Fig. (d)). In the case of an electric-field lens (including visible-light lens), the off-axial coma aberration contains only the radial components because there is no rotation effect of the electron beam in the electric field (Fig. (c)). An example of correction of the off-axial coma aberration has been reported. However, in the case of low-magnification imaging (large-field imaging with a large r) in transmission electron microscopy (TEM), the magnification rate is low and thus, image blur due to the off-axial coma aberration is small. For example, when the size of the observation area is 4 µm (the distance from the optical axis being ±2 µm) and an imaging camera with 4000 × 4000 pixels is used, the image size at one pixel is 1 nm, and the image blur due to the off-axial coma aberration becomes less than one to two pixels. Thus, the effect of this aberration is small on the low magnification image. In the case of high-resolution imaging, the observation area or the distance r is small. Thus, the off-axial coma aberration becomes very small. For example, when the size of the observation area is 50 nm (the distance from the optical axis being ±25 nm), the off-axial coma aberration becomes to be 0.1 nm or less. Thus, the effect of this aberration is very small on the high magnification image. In the case of STEM, aberrations cause blurring of the probe or the probe blur, which reduces the resolution of STEM image. However, at low magnification STEM imaging (large scanning area with a large r), the amount of the probe blur due to the off-axial coma aberration is small compared to the image size at a single pixel of the imaging camera, thus blurring of the image hardly appears. At high-resolution (atomic resolution) STEM imaging, as the scanning distance r or the observation area is small, the image blur due to the off-axial coma aberration is not large enough to reduce the image resolution. However unlike the above-mentioned cases, the off-axial coma aberration can decrease image quality at image acquisition in single particle analysis and semiconductor failure analysis. For those analyses, a great number of high-resolution TEM images are acquired while varying the field-of-view. During the acquisition, mechanical moving of the specimen requires a waiting time until the specimen drift stops. To avoid such a waiting time, the field-of-view is often moved using the deflector beneath the specimen (For example in Fig. (b), the field-of-view “5” at an off-axial location is moved to the optical axis or the position “0”). If the field-of-view is distant (about a few µm) from the optical axis, the off-axial coma aberration can degrade the image quality. When the aberration effect arises, alignment of the coma-free axis of the illumination lens system is carried out for the field-of-view moved to the optical axis to reduce the aberration effect.

Comaaberration in eye

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Comaaberration example

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Comaaberration correction

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Comaaberration Definition

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