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E49 · Electron acquisition

Ultrafast TEM: Resolve Time Without Losing Counts

Record a delay series and unpumped reference, then fit a relaxation from camera counts while varying pulse charge and repeatability.

Interactive modelUltrafast TEM: Resolve Time Without Losing Counts
Stored frame count—\text{—}
Total recorded specimen events—\text{—}
Ideal specimen schedule time—\text{—}
Stored incident electrons per frame—\text{—}
Pulses per frame—\text{—}
Calculated response FWHM—\text{—}
Calculated spatial PSF FWHM—\text{—}
Selected recorded delay—\text{—}
Recorded reference ROI events—\text{—}
Fitted relaxation time—\text{—}
Fitted relative RMS—\text{—}
Experiment target—\text{—}

Physics tutorial

Ultrafast TEM: Resolve Time Without Losing Counts

BackgroundRecord a delay series and unpumped reference, then fit a relaxation from camera counts while varying pulse charge and repeatability.

Why it mattersCan many gentle pulses reveal dynamics that one intense pulse blurs?

Start with the essentials

Focus question
Can many gentle pulses reveal dynamics that one intense pulse blurs?
One-sentence intuition
Preserve the acquisition history before interpreting a processed result.

Core mathematical model

Gaussian response width

σt2=wp2+we2+wsc28ln⁡2+σj2wsc=0.004 ps (Ne−1)2/3\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 FWHM; jitter is RMS. The charge broadening coefficient is an assigned teaching parameter.

Convolved relaxation

R(t)=∫0∞e−u/τe−(t−u)2/(2σt2)2πσt duR(t)=\int_0^\infty e^{-u/\tau}\frac{e^{-(t-u)^2/(2\sigma_t^2)}}{\sqrt{2\pi}\sigma_t}\,du

Positive delay means the electron arrives after the pump at the specimen; the Gaussian has unit area.

Recorded camera contrast

ci=1−Ci/C0(a^,τ^)=arg⁡min⁡a≥0,τ∑i[ci−aR(ti;τ)]2\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 fixed 20 nm circular ROI and independently recorded unpumped image define the trace. The least-squares residual is descriptive, not an uncertainty on lifetime.

Common difficulties

Scientific boundary

Typical misconceptionA small residual proves the physical experiment is fully resolved.

Better mental modelSynthetic 200 kV transmission-image model: a causal exponential feature is blurred by Gaussian pump, electron pulse and timing jitter. Space-charge temporal and spatial widths use disclosed assumed coefficients, not a Coulomb solver or instrument calibration. Each delay starts from an identically prepared fresh specimen. Stroboscopy then repeats that specimen; an irreversible preset retains a permanent state after its first pump. Single-shot uses one pulse at each delay on fresh replicas, not a movie of one irreversible event. Fits use a fixed camera ROI and recorded unpumped reference; they do not access the assigned lifetime. Shot noise, common-reference correlation and finite sampling remain; no CTF, diffraction, pulse compression, velocity mismatch, thermal accumulation or damage solver. Planes and beam paths are schematic.

Run the experiment

  1. 01

    Plan pulse strategy

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

    What to observe: At fixed total electrons, many gentle pulses can avoid assigned space-charge blur.
  2. 02

    Acquire the delay series

    Record 31 delay frames and one unpumped reference; select a recorded frame.

    What to observe: The camera carries real-space image counts, not a separately synthesized time plot.
  3. 03

    Fit stored counts

    Commit a relaxation fit and inspect the count-derived trace and residual.

    What to observe: The fitted amplitude absorbs spatial blur; the known response width comes from pulse calibration.
  4. 04

    Test repeatability

    Compare a single shot and an irreversible stroboscopic acquisition.

    What to observe: Many counts cannot rescue a measurement that averages different specimen histories.