E09 · Electron acquisition / diffraction

Raster Scan & Drift Recovery

Scan a nanograin specimen over a 6 nm grating. Set pixel spacing, dwell, flyback and drift, then compare the reference, recorded-frame average and rigidly aligned output. Switch row order to expose how acquisition time enters every pixel.

Frame time $0\,\mathrm{s}$

Total acquisition $0\,\mathrm{s}$

Within-frame displacement $0\,\mathrm{nm}$

First-to-last frame displacement $0\,\mathrm{nm}$

Incident-count relative noise $0\,\mathrm{\%}$

Common recorded coverage $0\,\mathrm{\%}$

6 nm grating sampling $\text{—}$

Expected image RMS error $0$

Experiment task $\text{—}$

Instrument settings

Raster Scan & Drift Recovery

Reference-assisted frame translationsTranslate recorded frames using the known midpoint drift; retain intra-frame error.Even rows, then odd rowsKeep the same pixel and frame budget; change the time assigned to each row.Counting noiseFixed seeded counting statistics; no detector read noise.Pixel spacing

p

4\,\mathrm{nm}

Pixel dwell

t_p

20\,\mathrm{\mu s}

Line flyback

t_b

250\,\mathrm{\mu s}

Number of frames

N_f

4

Horizontal stage drift

v_x

12\,\mathrm{nm\,s^{-1}}

Vertical stage drift

v_y

4\,\mathrm{nm\,s^{-1}}

Line deflection error amplitude

A_l

0\,\mathrm{nm}

Resolve the 6 nm grating, use at least 8 frames, enable rigid registration and keep within-frame displacement below 1 nm with over 90 percent common coverage.

Analytic specimen with a Gaussian probe of 1 nm standard deviation and fixed 2 pA beam. Count noise uses Poisson statistics below 40 counts and a Gaussian approximation above. Registration uses the known drift at each frame midpoint, resamples recorded frames and masks missing overlap; it is a reference-assisted translation demonstration, not an image-estimated registration algorithm. Within-frame distortion and interlace discontinuities remain. No dose damage or scan-coil dynamics.

Start with the essentials

Focus question: Can frame registration recover a scan-distorted image?
One-sentence intuition: Rigid registration estimates only one displacement per frame. This Lab supplies that displacement from the known drift, keeps within-frame warping and does not recover frequencies lost to sampling.

Core mathematical model

Time belongs to every pixel

t_{f,r,c}=fT_f+\ell(r)T_l+(c+\tfrac12)t_p,\quad T_l=Nt_p+t_b,\quad T_f=NT_l

All times are in seconds. The line order changes under interlacing; flyback follows every line.

Signed specimen coordinates

\mathbf r_{\mathrm{sample}}=\mathbf r_{\mathrm{nominal}}-\mathbf v t+\mathbf e_l

Positive specimen drift moves the sampled coordinate backward. Line error is an additional beam-deflection displacement.

Frame translation and strict sampling

J(\mathbf r)=\frac1{N_f}\sum_f I_f(\mathbf r+\mathbf v t_{f,\mathrm{mid}}),\quad p<\frac{6\,\mathrm{nm}}2

Interpolation uses acquired data only. Missing common coverage is masked. This translation leaves within-frame distortion; the 6 nm grating must be sampled finer than 3 nm.

Common difficulties

Interpretation trap

Typical misconceptionRegistration makes every image distortion disappear.

Better mental modelRigid registration estimates only one displacement per frame. This Lab supplies that displacement from the known drift, keeps within-frame warping and does not recover frequencies lost to sampling.

Run the experiment

01
Predict the error
Compare Slow drifting scan with Recovery target. Predict which change affects frame duration and which only affects averaging.
What to observe: Line flyback contributes to drift even though those intervals collect no specimen counts.
02
Recover what translation can recover
Toggle reference-assisted translations at the same settings; compare the recorded average and output, then increase dwell.
What to observe: Frame offsets can be aligned. Shear within each frame remains, and aligned borders lose common coverage.
03
Separate sampling from noise
Use Aliasing, then reduce pixel spacing to 2 nm. Try interlacing and compare row-time plots.
What to observe: The RMS error readout compares noiseless expectations on the sampled grid; the separate sampling flag checks the grating. More frames cannot resolve an undersampled grating. Interlacing changes time order and may introduce even/odd-row discontinuities.