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E22 · Electron acquisition

Multi-beam SEM: Calibrate Before Stitching

Can a multi-beam SEM scan faster and still stitch its tiles into a seamless image? Only if the beams are calibrated and each pixel still gets enough electrons. Every beam has its own gain and its own position error, so before stitching, even out each tile's brightness against a uniform reference and place it using calibrated beam positions. A faster scan leaves fewer electrons per pixel.

Record nine overlapping tiles and a uniform reference image, then correct each beam's gain and calibrated position before stitching the tiles together.

Interactive modelMulti-beam SEM: Calibrate Before Stitching
Total recorded specimen events—\text{—}
Ideal specimen schedule time—\text{—}
Ideal schedule speedup—\text{—}
Committed overlap disagreement—\text{—}
More measurements and target
Stored frame count—\text{—}
Stored incident electrons per pixel—\text{—}
Recorded active channels—\text{—}
Calculated widest probe sigma—\text{—}
Multiply covered mosaic pixels—\text{—}
Committed corrections: 0 none, 1 gain, 2 position, 3 both—\text{—}
Experiment target—\text{—}

Physics tutorial

Multi-beam SEM: Calibrate Before Stitching

BackgroundA multi-beam SEM scans with several beams at once, and each beam records its own tile. Here you record nine overlapping tiles and a uniform reference, then correct each beam's gain and calibrated position before stitching.

Why it mattersMore beams finish the scan sooner, but each beam has its own response and position, so the seams between tiles can disagree.

Start with the essentials

Focus question
Can a multi-beam SEM scan faster and still stitch its tiles into a seamless image?
One-sentence intuition
Keep the recorded tiles and calibration data before you judge a processed result.

Core mathematical model

Counts per pixel and total scan time

Npx=Itd/eμb,j=Npxgb(p∗Gσb)jT=⌈9/B⌉(1024td+to)\begin{aligned}N_{\mathrm{px}}&=It_d/e\\\mu_{b,j}&=N_{\mathrm{px}}g_b(p*G_{\sigma_b})_j\\T&=\lceil9/B\rceil(1024t_d+t_o)\end{aligned}

The current is per active beam. Each batch adds an assumed overhead of one millisecond, and the time to record the reference is not included.

Gain from an independent flat field

g^b=∑jFb,j1024Nflatpflat\widehat g_b=\frac{\sum_j F_{b,j}}{1024N_{\mathrm{flat}}p_{\mathrm{flat}}}

The uniform reference has a known probability of one quarter. The corrected signal is an estimate that can be fractional, not a new integer count.

How much overlapping tiles disagree

ϵ=∑j⟨(vb,j−vˉj)2⟩b∑jvˉj2\epsilon=\sqrt{\frac{\sum_j\langle(v_{b,j}-\bar v_j)^2\rangle_b}{\sum_j\bar v_j^2}}

Only pixels covered by more than one tile contribute. Bilinear resampling makes the noise correlated, so this number is not a confidence interval.

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. The model counts electrons in nine channels, using a synthetic specimen, normalized Gaussian probes and independent flat-field counts. Fiducial positions are assumed to be known exactly; stitching resamples the recorded pixels and never estimates positions from the true specimen. Channel response is an effective collection probability, not an analog detector gain. Switching between 1, 3 and 9 beams at fixed current per beam changes the scan time, not the dose. Stitching does not remove focus mismatch. Calibration time, stage motion, cross-talk, drift, charging and real multi-beam electron optics are left out. The task covers a single section, not an array-tomography reconstruction. The planes shown are schematic.

Run the experiment

  1. 01

    Predict the seams

    Change channel response and offsets. Predict which boundaries will disagree.

    What to observe: The same specimen is measured through nine different channels.
  2. 02

    Record the tiles and a flat field

    Acquire the tiles and a separate uniform flat field, then move a slider.

    What to observe: The stored counts and calibration stay fixed until you acquire again.
  3. 03

    Stitch the mosaic

    Stitch with and without the gain and position corrections, and inspect the coverage.

    What to observe: Blank edges are pixels that were never measured; interpolation cannot add coverage.
  4. 04

    Test the speed gain

    Compare the serial, blurred and low-count examples. Check the target.

    What to observe: Parallel beams save time on the ideal schedule, but blur and dose still limit the data.
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