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Sandbox Physics

E26 · Electron imaging / spectroscopy

TEM Mass–Thickness Contrast

Pass a parallel beam through an amorphous wedge with denser inclusions. Open the objective aperture, select zero-loss electrons and defocus the image. Follow the direct, scattered and excluded electrons all the way to the recorded image.

Interactive modelTEM Mass–Thickness Contrast
Recorded intensity0 %0\,\mathrm{\%}
Aperture rejected0 %0\,\mathrm{\%}
Filter rejected0 %0\,\mathrm{\%}
No elastic scattering0 %0\,\mathrm{\%}
Zero-loss fraction0 %0\,\mathrm{\%}
Plural inelastic scattering0 %0\,\mathrm{\%}
Dense-inclusion contrast0 %0\,\mathrm{\%}
Geometric blur0 nm0\,\mathrm{nm}
Counts per 4 nm pixel00
Experiment task—\text{—}

Physics tutorial

Why does a denser inclusion look dark in bright-field TEM?

BackgroundPass a parallel beam through an amorphous wedge with denser inclusions. Open the objective aperture, select zero-loss electrons and defocus the image. Follow the direct, scattered and excluded electrons all the way to the recorded image.

Why it mattersConnect the instrument setting to a measured result before interpreting the specimen.

Start with the essentials

Focus question
Why does a denser inclusion look dark in bright-field TEM?
One-sentence intuition
The objective aperture converts redistribution in angle into intensity contrast. A wide aperture recovers scattered electrons and weakens mass contrast; zero loss and unscattered are different populations.

Core mathematical model

Ballistic and zero-loss fractions

Pdir=e−t/λel,P0=e−t/λinP_{\mathrm{dir}}=e^{-t/\lambda_{\mathrm{el}}},\quad P_0=e^{-t/\lambda_{\mathrm{in}}}

Elastic and inelastic events are independent in this teaching model.

Aperture acceptance

Tα=Pdir+(1−Pdir)(1−e−α2/(2σθ2))T_{\alpha}=P_{\mathrm{dir}}+(1-P_{\mathrm{dir}})\left(1-e^{-\alpha^2/(2\sigma_\theta^2)}\right)

The diffuse width preserves the assumed mean-square scattering angle.

Filtered intensity

Tfiltered=TαP0,P≥2=1−(1+t/λin)P0T_{\mathrm{filtered}}=T_{\alpha}P_0,\quad P_{\ge2}=1-(1+t/\lambda_{\mathrm{in}})P_0

Rejected intensity is accounted for separately; this is not an absorption calculation.

Common difficulties

Interpretation trap

Typical misconceptionEvery electron missing from a bright-field image was absorbed by the specimen.

Better mental modelThe model partitions incident electrons into recorded, aperture-rejected and filter-rejected fractions. Angular redistribution alone can darken the image without an absorption term.

Run the experiment

  1. 01

    Predict the result

    Predict whether opening the objective aperture makes the dense inclusion brighter or darker. Compare Contrast target and Open aperture at the same specimen thickness.

    What to observe: The objective aperture converts redistribution in angle into intensity contrast. A wide aperture recovers scattered electrons and weakens mass contrast; zero loss and unscattered are different populations.
  2. 02

    Operate and check

    Keep recorded intensity above 15 percent, inclusion contrast at least 15 percent, plural inelastic scattering below 30 percent, and geometric blur below 4 nm.

    What to observe: Use the numerical target, then compare the linked instrument and data views.
  3. 03

    Explain the limitation

    Compare the zero-loss filtered and unfiltered cases. Then thicken the specimen and defocus it. Explain lost counts, plural scattering and blur separately.

    What to observe: Incoherent amplitude-contrast model with assumed elastic/inelastic mean free paths and a direct-plus-Gaussian angular distribution. Filtering removes nonzero-loss electrons. Defocus produces geometric blur only: no Fresnel phase contrast, diffraction, multislice or dynamical scattering. Mean free paths are illustrative, not tabulated material data.