Aberration Visualisation

3D Wavefront

2D Wavefront Map

Aberration Type

Amplitude: 0.5

Rotation (°): 0°

Visualization Options

Resolution: 40

Zoom: 100%

Point Spread Function

3D Intensity Profile

Aberration Type

Amplitude: 0.5

Rotation (°): 0°

Display Options

Contrast: 50%

2-fold Astigmatism

3-fold Astigmatism

Coma

Spherical Aberration

Comparison View

Amplitude: 0.7

Examples of Aberrations in TEM Images

2-fold Astigmatism

Elongation of features along two perpendicular directions. Notice how circular features appear elliptical.

3-fold Astigmatism

Threefold symmetry distortion that can appear as triangular features or a cloverleaf pattern.

Coma

Asymmetric tail-like distortion, causing features to have comet-like appearance.

Spherical Aberration

Radially symmetric blurring that increases with distance from the center.

No Aberration (Reference)

Perfect imaging condition for comparison.

Multiple Aberrations

Real TEM images often contain combinations of different aberrations.

Understanding Electron Microscope Aberrations

Aberrations in electron microscopy cause distortions in the electron wavefront, which lead to degradation of image quality. The interactive visualizations above demonstrate how different types of aberrations affect both the wavefront shape and the resulting image formation (point spread function).

Two-fold Astigmatism (A₁)

Two-fold (or primary) astigmatism is the most common form, characterized by different focal planes in two perpendicular directions. The mathematical form in polar coordinates (r, θ) is:

χ(r,θ) = A₁r²cos(2(θ-θ₀))

This creates two perpendicular directions with different focal points, causing point objects to appear as ellipses. Two-fold astigmatism is the most common aberration encountered in TEM and can be corrected using stigmator controls.

Three-fold Astigmatism (A₂)

Three-fold astigmatism introduces a three-lobed distortion to the wavefront with threefold rotational symmetry. Its mathematical representation is:

χ(r,θ) = A₂r³cos(3(θ-θ₀))

This aberration generally appears due to mechanical imperfections in the lens or apertures, producing triangular distortion patterns that are more difficult to correct than two-fold astigmatism.

Coma (B₂)

Coma is an off-axis aberration that causes asymmetrical distortion. Points appear as comet-like shapes with tails pointing away from the optical axis. The mathematical form is:

χ(r,θ) = B₂r³cos(θ-θ₀)

Coma occurs when the electron beam is not centered on the optical axis or when there's misalignment in the column. It results in directional blurring across the field of view.

Spherical Aberration (C_s)

Spherical aberration is a radially symmetric aberration where electrons passing through different zones of the lens focus at different points. Its mathematical form is:

χ(r,θ) = C_sr⁴/4

This aberration is intrinsic to round electromagnetic lenses and causes a uniform blurring that increases with distance from the optical axis. Modern aberration-corrected microscopes use multipole correctors to compensate for spherical aberration.