---
title: "Multi-beam SEM: Calibrate Before Stitching Interactive Lab | Sandbox Physics"
description: "Can a multi-beam SEM scan faster and still stitch its tiles into a seamless image? Only if the beams are calibrated and each pixel still gets enough electrons."
canonical_url: "https://sandboxphysics.com/labs/multibeam-sem/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/multibeam-sem/"
last_modified: "2026-10-27"
---

E22 · Electron acquisition

# Multi-beam SEM: Calibrate Before Stitching

**Can a multi-beam SEM scan faster and still stitch its tiles into a seamless image?** Only if the beams are calibrated and each pixel still gets enough electrons. Every beam has its own gain and its own position error, so before stitching, even out each tile's brightness against a uniform reference and place it using calibrated beam positions. A faster scan leaves fewer electrons per pixel.

Record nine overlapping tiles and a uniform reference image, then correct each beam's gain and calibrated position before stitching the tiles together.

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

Model assumptions

The model counts electrons in nine channels, using a synthetic specimen, normalized Gaussian probes and independent flat-field counts. Fiducial positions are assumed to be known exactly; stitching resamples the recorded pixels and never estimates positions from the true specimen. Channel response is an effective collection probability, not an analog detector gain. Switching between 1, 3 and 9 beams at fixed current per beam changes the scan time, not the dose. Stitching does not remove focus mismatch. Calibration time, stage motion, cross-talk, drift, charging and real multi-beam electron optics are left out. The task covers a single section, not an array-tomography reconstruction. The planes shown are schematic.

Physics tutorial

## Multi-beam SEM: Calibrate Before Stitching

**Background** A multi-beam SEM scans with several beams at once, and each beam records its own tile. Here you record nine overlapping tiles and a uniform reference, then correct each beam's gain and calibrated position before stitching.

**Why it matters** More beams finish the scan sooner, but each beam has its own response and position, so the seams between tiles can disagree.

Start with the essentials

- **Focus question**: Can a multi-beam SEM scan faster and still stitch its tiles into a seamless image?
- **One-sentence intuition**: Keep the recorded tiles and calibration data before you judge a processed result.

### Core mathematical model

#### Counts per pixel and total scan time

$$
\begin{aligned}N_{\mathrm{px}}&=It_d/e\\\mu_{b,j}&=N_{\mathrm{px}}g_b(p*G_{\sigma_b})_j\\T&=\lceil9/B\rceil(1024t_d+t_o)\end{aligned}
$$

The current is per active beam. Each batch adds an assumed overhead of one millisecond, and the time to record the reference is not included.

#### Gain from an independent flat field

$$
\widehat g_b=\frac{\sum_j F_{b,j}}{1024N_{\mathrm{flat}}p_{\mathrm{flat}}}
$$

The uniform reference has a known probability of one quarter. The corrected signal is an estimate that can be fractional, not a new integer count.

#### How much overlapping tiles disagree

$$
\epsilon=\sqrt{\frac{\sum_j\langle(v_{b,j}-\bar v_j)^2\rangle_b}{\sum_j\bar v_j^2}}
$$

Only pixels covered by more than one tile contribute. Bilinear resampling makes the noise correlated, so this number is not a confidence interval.

### Common difficulties

#### What a small residual does not prove

**Typical misconception** A small residual proves the physical experiment is fully resolved.

**Better mental model** The residual only shows agreement inside this simplified model. The model counts electrons in nine channels, using a synthetic specimen, normalized Gaussian probes and independent flat-field counts. Fiducial positions are assumed to be known exactly; stitching resamples the recorded pixels and never estimates positions from the true specimen. Channel response is an effective collection probability, not an analog detector gain. Switching between 1, 3 and 9 beams at fixed current per beam changes the scan time, not the dose. Stitching does not remove focus mismatch. Calibration time, stage motion, cross-talk, drift, charging and real multi-beam electron optics are left out. The task covers a single section, not an array-tomography reconstruction. The planes shown are schematic.

### Run the experiment

1. 01

   #### Predict the seams

   Change channel response and offsets. Predict which boundaries will disagree.

   **What to observe:** The same specimen is measured through nine different channels.

2. 02

   #### Record the tiles and a flat field

   Acquire the tiles and a separate uniform flat field, then move a slider.

   **What to observe:** The stored counts and calibration stay fixed until you acquire again.

3. 03

   #### Stitch the mosaic

   Stitch with and without the gain and position corrections, and inspect the coverage.

   **What to observe:** Blank edges are pixels that were never measured; interpolation cannot add coverage.

4. 04

   #### Test the speed gain

   Compare the serial, blurred and low-count examples. Check the target.

   **What to observe:** Parallel beams save time on the ideal schedule, but blur and dose still limit the data.

Physical conclusion

A faster scan still needs enough counts, a calibration and repeatable results.

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)