---
title: "Electron Dose, Noise & Damage Interactive Lab | Sandbox Physics"
description: "When does more exposure stop revealing more detail? Once beam damage wipes out detail faster than the extra electrons reveal it. The early frames hold the specimen's original contrast, and adding later frames to the sum dilutes it. You can leave the late frames out of the sum, but the specimen has already received that dose and the damage stays."
canonical_url: "https://sandboxphysics.com/labs/electron-dose/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/electron-dose/"
last_modified: "2026-10-25"
---

E08 · Electron microscopy / specimen physics

# Electron Dose, Noise & Damage

**When does more exposure stop revealing more detail?** Once beam damage wipes out detail faster than the extra electrons reveal it. The early frames hold the specimen's original contrast, and adding later frames to the sum dilutes it. You can leave the late frames out of the sum, but the specimen has already received that dose and the damage stays.

Record a series of frames on a fresh area of the specimen. Compare the first frame, the last frame and a sum of the early frames, and fit a known periodic detail from the saved counts. Find an exposure that gives a usable image before the contrast fades.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Each frame is a simulated 64 by 64 raster scan of a prescribed pattern with a 5 nm period. The model includes a Gaussian probe and pixel integration, and the contrast decays exponentially with incident dose. Each frame integrates over its own dose interval. The SNR from the known-template fit is a statistic over the whole image; it does not measure resolution or a material property. The decay dose, the carbon threshold and the laws for heating and contamination are teaching assumptions. Poisson sampling switches to a normal approximation above 40 expected counts, and each frame pixel saturates at 65,535. Specimen motion, recovery, read noise, real detector calibration and frequency-dependent damage are not modeled. Each acquisition assumes a fresh, equivalent area, and the series assumes repeated uniform scans.

Physics tutorial

## Can discarding late frames undo radiation damage?

**Background** Every electron that forms an image also adds to the damage in the specimen. Record a series of frames on a fresh area, compare the first frame, the last frame and a sum of the early frames, and estimate a known 5 nm detail directly from the stored counts.

**Why it matters** The signal you keep in an image and the damage the specimen has already taken are two different things. This Lab helps you keep them apart.

Start with the essentials

- **Focus question**: Can discarding late frames undo radiation damage?
- **One-sentence intuition**: Early frames record the contrast from earlier in the exposure; dropping late frames changes the summed image, but the specimen still received every recorded frame.

### Core mathematical model

#### Incident dose per frame

$$
\delta D=\frac{I\tau}{100ea^2},\quad D_{\mathrm{full}}=N_f\delta D
$$

Pixel pitch is in nanometres, and dose is in incident electrons per square angstrom. Detector efficiency changes the recorded counts, not the dose the specimen receives.

#### Each frame averages over its own dose interval

$$
\overline S_j=\frac{1}{\delta D}\int_{(j-1)\delta D}^{j\delta D}e^{-ku}\,du
$$

The decay rate adds up assumed terms for radiolysis, knock-on damage above a threshold and contamination. It weakens the contrast but leaves the mean background count unchanged.

#### Expected Poisson counts in each pixel

$$
\mu_{ij}=B\left[1+0.3H\overline S_j h_i\right],\quad h_i=\tfrac12\left[\cos(2\pi x_i/\Lambda)+\cos(2\pi y_i/\Lambda)\right]
$$

The pattern period is 5 nm. The background count is the efficiency times the expected incident count, divided by 1.3 so that the collection probability never exceeds one. The transfer includes the Gaussian probe and pixel integration, and the known template uses calibrated pixel centers. A larger pixel pitch can alias the pattern.

#### Fitting a known pattern to the counts

$$
\widehat A=\sum_i w_iY_i,\quad w_i=\frac{h_i-\overline h}{\sum_l(h_l-\overline h)^2},\quad \widehat{\mathrm{SNR}}=\frac{\widehat A}{\sqrt{\sum_iw_i^2Y_i}}
$$

The summed counts of the included frames are fitted with a free background plus one known mode. The result is a signed amplitude statistic for the whole image; it is not a resolution estimate or a confidence guarantee. Clipped, empty or aliased data give no result.

#### Average contrast versus final contrast

$$
\overline S(D)=\frac{1-e^{-kD}}{kD},\quad S(D)=e^{-kD}
$$

The predicted per-pixel figure uses the contrast averaged over the exposure. The specimen view and the final-retention readout use the full delivered dose.

### Common difficulties

#### Processing an image does not undo damage

**Typical misconception** If I keep only the early frames, the specimen only received those frames.

**Better mental model** Every saved frame irradiated this area. The dose of the included frames describes your data; the full delivered dose describes the specimen. Each new acquisition assumes a fresh, equivalent area.

#### What the known-pattern fit can show

**Typical misconception** A high fitted SNR proves the resolution, or gives a calibrated damage dose for the material.

**Better mental model** The fit is given the spatial pattern and the calibration in advance. The Lab does not recover unknown structure, identify materials, correct for motion, apply frequency-dependent dose weighting or calibrate a real detector.

### Run the experiment

1. 01

   #### Predict and acquire

   Load Safe recorded series and press Check target. Change the beam current, and confirm that the saved counts stay the same until you press Acquire fresh area.

   **What to observe:** Acquisition settings apply to the next record. Each fresh acquisition comes with new random noise.

2. 02

   #### Compare the same saved frames

   Load Fading over 20 frames. Include the first four frames, then all of them, and compare the count-derived mode SNR, the mean counts and the first and last images.

   **What to observe:** Counts rise as the contrast fades. Summing only the early frames cannot reduce the full delivered dose or bring back the predicted final retention.

3. 03

   #### See what makes a record fail

   Compare the Count starved, Aliased sampling and Detector clipping records. Raise the display gain and check again.

   **What to observe:** A brighter display cannot make up for missing counts, poor sampling or detector clipping. The target also requires the full recorded exposure to stay safe.

Physical conclusion

Adding frames adds counts but can wash out a fading detail. Choose the dose you deliver and the frames you sum as two separate decisions.

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)