astigmatism

The astigmatism is an aberration which arises from the difference in the focal positions between the electron beams passing on two axes orthogonal to the optical axis when the beams pass through an electron lens.
As shown in Fig. 1, an electron beam which runs at a distance r on the X axis from the optical axis of the lens is focused at position a, which is in the front of the exact focus point (overfocus). On the other hand, an electron beam which runs at a distance r on the Y axis from the optical axis of the lens is focused at position b, which is at the rear of the exact focus point (underfocus). As a result, the electron beam forms a line in the Y direction at position a, but forms a line in the X direction at position b. The distance between the positions a and b is called the astigmatic difference. The minimum circle of confusion is produced between the positions a and b (at the original focus position) even astigmatism exists.
The astigmatism is caused by the axial asymmetry of the lens due to magnetic non-uniformity of the lens material and insufficient precision of machining and assembly. The astigmatism treated here is different from the off-axial astigmatism or one of Seidel’s five aberrations inherent to electron optics.
Fig. 2(a-c) show SEM images which contain the astigmatism. The SEM images taken at an overfocus position (a) and an underfocus position (c) show blur in the two orthogonal directions to each other. At the exact focus position (b), the image shows isotropic blur, which is because the electron beams emitted from one point of the specimen do not form a size smaller than the size of the minimum circle of confusion due to the astigmatism.
The astigmatism can be removed using a stigmator.

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