ザイデルの5収差

Five Seidel aberrations

電子線（光線）が完全な結像をすると仮定したときの軌道からのずれの量を収差という。単色電子線（光線）が近軸電子（光）線でないために生じる3次(光線が光軸となす角度αと光線の光軸からの距離rの積について3次)の収差の総称をザイデルの5収差という。5つの収差は、球面収差(α³に比例)、(軸外)コマ収差(ｒα²に比例)、非点収差と像面湾曲収差（r²αに比例）、歪曲収差(r³に比例)である。電子顕微鏡の場合、像拡大の初段、すなわち対物レンズに対しては、物体の拡大する範囲は小さいので、光軸上を通る電子線(r = 0)を考えればよい。したがって像のボケにはα³に比例する球面収差が最も重要である。理論上は次にコマ収差が重要である。(軸外)コマ収差補正の例はあるが、高倍率の像については(軸外)コマ収差の効果は小さい。後段にある中間レンズおよび投影レンズでは、物体（対物レンズで拡大された像）は大きいので、光軸から離れた場所を通る電子線による収差、すなわち距離rの次数の高い収差、非点収差、像面湾曲収差、歪曲収差が重要になる。最近は球面収差補正ができるようになっている。

図1. 収差の分類。 ⇒ 図1

図2. ザイデルの5収差: 各収差の模式図。 ⇒ 図2

Aberrations are departures of the path of electron beams from the path of the ideal (Gaussian or paraxial) imaging. The term, "(five) Seidel aberrations," is the generic name of the third-order aberrations (third order with respect to the product of α (angle between the electron beam and optical axis) and r (distance of the electron beam from the optical axis)), which occurs for a monochromatic but non-paraxial electron beam. The five aberrations are (1) spherical aberration (proportional to α³), (2) (off-axial) coma aberration (proportional to rα²), (3) off-axial astigmatism (proportional to r²α), (4) curvature of image field (proportional to r²α), and (5) distortion (proportional to r³). In the case of an electron microscope, since the specimen area magnified by the objective lens, the first-stage lens, is very small (r ～0), it is enough to consider the beams passing through the optical axis. Thus, the spherical aberration is most important for the objective lens. The (off-axial) coma aberration is next most important theoretically. Although an example of coma correction has been reported, the effect of coma aberration is small for high magnification images. Since the magnified images or the objects for the intermediate and projector lenses are not small, the aberrations produced by the beams passing through the positions distant from the optical axis give definite contributions. That is, off-axial astigmatism, curvature of image field and distortion are more important for the lenses at successive stages. In recent years, the spherical aberration has been successfully corrected.

Fig. 1. Classification of aberrations.

Fig. 2. Ray paths with each Seidel aberration are descried in the left side. Shapes of the electron beam with each Seidel aberration (spherical aberration, coma, and astigmatism) are descried in the right side. Distortions on the screen with each Seidel aberration (curvature of field and distortion) are descried in the right side.