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.

Total recorded specimen events $\text{—}$

Calculated response FWHM $\text{—}$

Fitted relaxation time $\text{—}$

Fitted relative RMS $\text{—}$

More measurements and target

Stored frame count $\text{—}$

Ideal specimen schedule time $\text{—}$

Stored incident electrons per frame $\text{—}$

Pulses per frame $\text{—}$

Calculated spatial PSF FWHM $\text{—}$

Selected recorded delay $\text{—}$

Recorded reference ROI events $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Mean electrons per pulse

N_e

20

Repeated pulses per delay

M

100000

Uncharged electron pulse FWHM

w_e

0.2\,ps

Strategy: 0 single, 1 stroboscopic

1

Advanced settings

Repetition rate

f

50\,kHz

Pump pulse FWHM

w_p

0.1\,ps

Timing jitter RMS

\sigma_j

0.05\,ps

Assigned synthetic relaxation time

\tau

1.5\,ps

Specimen: 0 unrecovered, 1 resets

1

Counts: 0 expectation, 1 seeded statistics

1

Selected recorded delay

j

30\,\%

Display gain only

G

1

Learning goal and model limits

Predict · acquire · interpret

Separate pulse width from lifetime

Target: make the acquisition repeatable, keep the calculated response FWHM below 0.6 ps, record at least 10000 reference events in the ROI and fit with a relative RMS below eight percent. The fitted lifetime must fall inside the search range. Meeting the target does not prove the resolution or that the fit is unique.

The sliders set up the next operation. Acquire first, then run the processing. Stored results stay fixed, and presets load finished examples. Frame and gain only change the display.

A positive delay means the electrons reach the specimen after the pump. Single-shot mode ignores the repeated-pulse setting, and each delay starts with a fresh specimen.

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

BackgroundIn 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 mattersPacking 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 misconceptionA small residual proves the physical experiment is fully resolved.

Better mental modelThe 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

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.
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.
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.
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.

Core mathematical model

Time resolution from Gaussian widths

Relaxation blurred by the time resolution

Contrast from the recorded camera counts

Common difficulties

What a small residual does not prove

Run the experiment

Plan the pulses

Acquire the delay series

Fit the stored counts

Test whether the process repeats