---
title: "Ultrafast TEM: Resolve Time Without Losing Counts Interactive Lab | Sandbox Physics"
description: "Can many weak electron pulses capture fast dynamics that one intense pulse would blur? They can, if the process repeats the same way every time."
canonical_url: "https://sandboxphysics.com/labs/ultrafast-tem/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/ultrafast-tem/"
last_modified: "2026-10-27"
---

E49 · Electron acquisition

# Ultrafast TEM: Resolve Time Without Losing Counts

**Can many weak electron pulses capture fast dynamics that one intense pulse would blur?** They can, if the process repeats the same way every time. A weak pulse carries few electrons, so they barely repel each other and the pulse stays short. Summing many repetitions builds up the counts. Every pump cycle has to replay the same dynamics; anything that differs from shot to shot gets averaged away.

Record images at a series of pump–probe delays plus an unpumped reference, then fit the relaxation from the camera counts while you change the charge per pulse and test whether the process repeats.

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

Model assumptions

This is a synthetic 200 kV transmission-image model. A causal exponential feature is blurred by the Gaussian widths of the pump, the electron pulse and the timing jitter. The temporal and spatial broadening from space charge use stated, assumed coefficients; there is no Coulomb solver or instrument calibration. Each delay starts on a fresh, identically prepared specimen. In stroboscopic mode that specimen is then pumped repeatedly, and the irreversible preset keeps a permanent change after its first pump. Single-shot mode uses one pulse at each delay, each on a fresh replica, so it is not a movie of one irreversible event. Fits use a fixed camera region of interest and the recorded unpumped reference; they never see the assigned lifetime. Shot noise, correlation through the common reference and finite sampling remain. The model has no CTF, diffraction, pulse compression, velocity mismatch, heat buildup or damage solver. Planes and beam paths are schematic.

Physics tutorial

## Ultrafast TEM: Resolve Time Without Losing Counts

**Background** In ultrafast TEM an optical pump starts a change in the specimen, and an electron pulse images it a set delay later. Here you record a delay series and an unpumped reference, then fit a relaxation from the camera counts while you change the charge per pulse and test whether the process repeats.

**Why it matters** Packing more electrons into one pulse collects counts faster, but space charge stretches the pulse in time and blurs fast dynamics.

Start with the essentials

- **Focus question**: Can many weak electron pulses capture fast dynamics that one intense pulse would blur?
- **One-sentence intuition**: Know how every frame was acquired before you interpret the fitted result.

### Core mathematical model

#### Time resolution from Gaussian widths

$$
\begin{aligned}\sigma_t^2&=\frac{w_p^2+w_e^2+w_{\mathrm{sc}}^2}{8\ln2}+\sigma_j^2\\w_{\mathrm{sc}}&=0.004\,\mathrm{ps}\,(N_e-1)^{2/3}\end{aligned}
$$

Pulse widths are given as FWHM and the jitter as RMS. The coefficient for broadening by pulse charge is a chosen teaching parameter.

#### Relaxation blurred by the time resolution

$$
R(t)=\int_0^\infty e^{-u/\tau}\frac{e^{-(t-u)^2/(2\sigma_t^2)}}{\sqrt{2\pi}\sigma_t}\,du
$$

A positive delay means the electron reaches the specimen after the pump. The Gaussian has unit area.

#### Contrast from the recorded camera counts

$$
\begin{aligned}c_i&=1-C_i/C_0\\(\widehat a,\widehat\tau)&=\arg\min_{a\ge0,\tau}\sum_i[c_i-aR(t_i;\tau)]^2\end{aligned}
$$

The trace comes from a fixed 20 nm circular region of interest and the separately recorded unpumped image. The least-squares residual describes the fit; it is not an uncertainty on the lifetime.

### 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. This is a synthetic 200 kV transmission-image model. A causal exponential feature is blurred by the Gaussian widths of the pump, the electron pulse and the timing jitter. The temporal and spatial broadening from space charge use stated, assumed coefficients; there is no Coulomb solver or instrument calibration. Each delay starts on a fresh, identically prepared specimen. In stroboscopic mode that specimen is then pumped repeatedly, and the irreversible preset keeps a permanent change after its first pump. Single-shot mode uses one pulse at each delay, each on a fresh replica, so it is not a movie of one irreversible event. Fits use a fixed camera region of interest and the recorded unpumped reference; they never see the assigned lifetime. Shot noise, correlation through the common reference and finite sampling remain. The model has no CTF, diffraction, pulse compression, velocity mismatch, heat buildup or damage solver. Planes and beam paths are schematic.

### Run the experiment

1. 01

   #### Plan the pulses

   Predict what increasing electrons per pulse does to counts and pulse widths.

   **What to observe:** For the same total number of electrons, many gentle pulses can avoid the space-charge blur assumed in the model.

2. 02

   #### Acquire the delay series

   Record 31 delay frames and one unpumped reference, then select one of the recorded frames.

   **What to observe:** The camera stores real-space image counts, and the time trace is computed from them.

3. 03

   #### Fit the stored counts

   Commit a relaxation fit and inspect the trace built from the counts and its residual.

   **What to observe:** The fitted amplitude absorbs the spatial blur, while the response width is known from the pulse calibration.

4. 04

   #### Test whether the process repeats

   Compare a single shot and an irreversible stroboscopic acquisition.

   **What to observe:** No number of counts can rescue a measurement that averages over different histories of the specimen.

Physical conclusion

A faster measurement still needs enough counts, a calibration and a process that repeats.

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)