---
title: "TEM Mass–Thickness Contrast Interactive Lab | Sandbox Physics"
description: "Why does a denser inclusion look dark in bright-field TEM? It scatters more electrons to large angles, and the objective aperture blocks those electrons from the bright-field image. Open a wider aperture and some of the scattered electrons get back in, weakening this mass-thickness contrast."
canonical_url: "https://sandboxphysics.com/labs/tem-mass-thickness/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/tem-mass-thickness/"
last_modified: "2026-10-25"
---

E26 · Electron imaging / spectroscopy

# TEM Mass–Thickness Contrast

**Why does a denser inclusion look dark in bright-field TEM?** It scatters more electrons to large angles, and the objective aperture blocks those electrons from the bright-field image. Open a wider aperture and some of the scattered electrons get back in, weakening this 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 simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Contrast comes from an incoherent amplitude model. The elastic and inelastic mean free paths are assumed, and the angular distribution is a direct beam plus a Gaussian spread. The zero-loss filter removes every electron that has lost energy. Defocus only blurs the image geometrically; Fresnel phase contrast, diffraction, multislice and dynamical scattering are not modeled. The mean free paths are illustrative, not tabulated material data.

Physics tutorial

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

**Background** 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.

**Why it matters** Before drawing conclusions about the specimen, see how each instrument setting shapes the measured result.

Start with the essentials

- **Focus question**: Why does a denser inclusion look dark in bright-field TEM?
- **One-sentence intuition**: The objective aperture turns a change in scattering angle into a change in brightness. A wide aperture lets scattered electrons back in and weakens mass contrast. Zero-loss electrons and unscattered electrons are not the same group.

### Core mathematical model

#### Direct and zero-loss fractions

$$
P_{\mathrm{dir}}=e^{-t/\lambda_{\mathrm{el}}},\quad P_0=e^{-t/\lambda_{\mathrm{in}}}
$$

Elastic and inelastic events are independent in this teaching model.

#### Fraction passing the aperture

$$
T_{\alpha}=P_{\mathrm{dir}}+(1-P_{\mathrm{dir}})\left(1-e^{-\alpha^2/(2\sigma_\theta^2)}\right)
$$

The width of the diffuse part is chosen to keep the assumed mean-square scattering angle.

#### Filtered intensity

$$
T_{\mathrm{filtered}}=T_{\alpha}P_0,\quad P_{\ge2}=1-(1+t/\lambda_{\mathrm{in}})P_0
$$

The rejected intensity is kept as its own fraction; no absorption is calculated.

### Common difficulties

#### Missing electrons and absorption

**Typical misconception** Every electron missing from a bright-field image was absorbed by the specimen.

**Better mental model** The model splits the incident electrons into three parts: recorded, stopped by the aperture and removed by the filter. Scattering electrons to other angles can darken the image on its own, without any absorption term.

### Run the experiment

1. 01

   #### Predict the aperture effect

   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 turns a change in scattering angle into a change in brightness. Opening it lets scattered electrons back in, which weakens the mass contrast. Zero-loss and unscattered electrons are different groups.

2. 02

   #### Meet the contrast target

   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:** Check the numbers against the target, then compare the instrument view with the data it produces.

3. 03

   #### Separate the losses

   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:** Contrast comes from an incoherent amplitude model. The elastic and inelastic mean free paths are assumed, and the angular distribution is a direct beam plus a Gaussian spread. The zero-loss filter removes every electron that has lost energy. Defocus only blurs the image geometrically; Fresnel phase contrast, diffraction, multislice and dynamical scattering are not modeled. The mean free paths are illustrative, not tabulated material data.

Physical conclusion

The objective aperture turns a change in scattering angle into a change in brightness. A wide aperture lets scattered electrons back in and weakens mass contrast. Zero-loss electrons and unscattered electrons are not the same group.

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)