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.

Full delivered dose · irreversible $0\,\mathrm{e^{-}\,\mathring{A}^{-2}}$

Included mean counts per pixel $0$

Count-derived whole-image mode SNR $0$

Predicted final contrast retention $0\,\mathrm{\%}$

More measurements and target

Included saved frames $0$

Dose represented by included frames $0\,\mathrm{e^{-}\,\mathring{A}^{-2}}$

Fitted known-mode contrast $0$

Clipped frame-pixel samples $0$

5 nm mode sampling $\text{—}$

Included exposure-averaged retention $0\,\mathrm{\%}$

Predicted per-pixel detail SNR $0$

Full incident expectation per pixel $0$

Full background count expectation $0$

Included background shot-noise estimate $0\,\mathrm{\%}$

Probe peak pulse dose $0\,\mathrm{e^{-}\,\mathring{A}^{-2}}$

Temperature rise proxy $0\,\mathrm{K}$

Contamination proxy $0\,\mathrm{nm}$

Carbon threshold comparison $\text{—}$

64-square series exposure $0\,\mathrm{s}$

Experiment task $\text{—}$

Simulated examples; each plot identifies its data source.

More examples

Beam current

I

50\,\mathrm{pA}

Pixel dwell per frame

\tau

10\,\mathrm{\mu s}

Frames to acquire

N_f

1

Pixel pitch

a

1\,\mathrm{nm}

Advanced settings

Gaussian probe FWHM

d

0.6\,\mathrm{nm}

Counting efficiency

\eta

0.5

Beam energy

E_0

80\,\mathrm{keV}

Assumed contrast decay dose

D_c

60\,\mathrm{e^{-}\,\mathring{A}^{-2}}

Chamber pressure exponent

\log_{10}(p/\mathrm{Pa})

-7

Frames to include from the start, up to the number saved

n

20

Display contrast gain only

G

1

Learning goal and model limits

Acquire, then compare frames

Exposure and saved-frame analysis

Target: a fitted mode SNR of at least 10, contrast of at least 0.1 and at least 100 counts per pixel on average. The predicted final retention must be at least 75 percent, the full dose below 30 percent of the assumed decay dose and the heating below 10 K. Aliased or clipped data fail.

All count images use the same linear scale, normalized to the background. Gain changes only the display. Leaving out late frames changes the sum, but never the full dose the specimen received.

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.

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 misconceptionIf I keep only the early frames, the specimen only received those frames.

Better mental modelEvery 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 misconceptionA high fitted SNR proves the resolution, or gives a calibrated damage dose for the material.

Better mental modelThe 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

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.
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.
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.