off-axial astigmatism and curvature of image field

When electron beams exiting from a circular object centered on the optical axis do not form a perfect circle but form an ellipse on the image plane, this defect is called "off-axial astigmatism." This astigmatism arises from the fact that the lens action (curvature of the lens) is different for the rays in the two orthogonal planes, that is, for the rays in the plane including the optical axis (tangential plane) and for the rays in the plane normal to the tangential plane but not including the optical axis (sagittal plane). "Curvature of image field" is the aberration that the image plane is deformed from a flat plane to a curved plane. The distance from an off-axis object point to the principal point of the lens (the center of the lens) is longer than the distance from the point on the optical axis at the object plane to the principal point. Thus, the distance from the principal point to the image point for the former ray becomes shorter than that for the latter ray. As a result, the image plane deviates from the Gaussian (flat) plane to a curved plane as the image point goes away from the optical axis. The curvature of image field is different for the two orthogonal directions or for the tangential and sagittal directions due to the off-axial astigmatism.

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