Skip to main content
Sandbox Physics

E22 · Electron acquisition

Multi-beam SEM: Calibrate Before Stitching

Acquire nine overlapping tiles, measure a uniform reference, then correct gain and calibrated position before stitching.

Interactive modelMulti-beam SEM: Calibrate Before Stitching
Stored frame count—\text{—}
Total recorded specimen events—\text{—}
Ideal specimen schedule time—\text{—}
Stored incident electrons per pixel—\text{—}
Recorded active channels—\text{—}
Ideal schedule speedup—\text{—}
Calculated widest probe sigma—\text{—}
Committed overlap disagreement—\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

BackgroundAcquire nine overlapping tiles, measure a uniform reference, then correct gain and calibrated position before stitching.

Why it mattersDoes a faster scan preserve continuity between beams?

Start with the essentials

Focus question
Does a faster scan preserve continuity between beams?
One-sentence intuition
Preserve the acquisition history before interpreting a processed result.

Core mathematical model

Counting and 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}

Current is per active beam. The assumed overhead is one millisecond per batch; reference acquisition time is excluded.

Independent flat field

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

The known uniform reference probability is one quarter. Corrected signal is a fractional estimate, not a new integer count.

Overlap disagreement

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 multiply covered pixels contribute. Bilinear resampling correlates noise; this diagnostic is not a confidence interval.

Common difficulties

Scientific boundary

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

Better mental modelNine-channel counting model with a synthetic specimen, normalized Gaussian probes and independent flat-field counts. Fiducial positions are assumed known exactly; stitching resamples recorded pixels and does not estimate positions from specimen truth. Channel response is an effective collection probability, not an analog detector gain. The 1/3/9-beam schedule changes time at fixed current per beam; it does not lower dose. Focus mismatch is not removed by stitching. Calibration time, stage motion, cross-talk, drift, charging and physical multi-beam electron optics are omitted. This is a single-section task, not array-tomography reconstruction. Planes 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 passes through nine different measurement channels.
  2. 02

    Record independent data

    Acquire tiles and a separate uniform flat field. Move a slider afterwards.

    What to observe: Stored counts and calibration remain fixed until reacquisition.
  3. 03

    Commit a mosaic

    Stitch with and without gain and position corrections. Inspect coverage.

    What to observe: Blank edges indicate unmeasured pixels; interpolation never creates extra coverage.
  4. 04

    Challenge throughput

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

    What to observe: Parallel acquisition saves ideal schedule time while blur and dose still constrain data.