E21 · Serial volume electron microscopy

Block-face SEM: Between the Cuts

Can sharp block-face images still miss structures that lie between two cuts? It can. Each image shows only the freshly cut face of the block. A structure thinner than the cut spacing can fall between two faces, and anything the knife damages is lost too. Neither ever appears in the image stack, and no amount of alignment can put it back.

Cut a resin block with a diamond knife inside the microscope chamber, pull the knife back and image the new face. Compare section spacing, counting noise, drift and knife damage before you reconstruct the volume.

Volume error against known input $\text{—}$

Count-derived segmented volume $\text{—}$

End-of-frame negative-potential magnitude $\text{—}$

Lateral sampling pitch $\text{—}$

More measurements and target

Overlap with known sampled input $\text{—}$

Known sampled input volume $\text{—}$

Mean central pixel counts $\text{—}$

Recorded depth coverage $\text{—}$

Section to lateral pitch ratio $\text{—}$

Selected exposed-face depth $\text{—}$

Total section positions $\text{—}$

Selected image status $\text{—}$

Summed incident dose over new faces $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Physical section thickness

h

60\,\mathrm{nm}

Dwell per pixel

\tau

2\,\mathrm{\mu s}

Assigned heavy-metal loading

s

1

Field width at 48 pixels

L

1200\,\mathrm{nm}

Advanced settings

Horizontal drift per cut

d_x

3\,\mathrm{\frac{nm}{\mathrm{cut}}}

Prescribed knife-damage band fraction

a

0.15

Lose every nth image: 0 none

n_{\rm gap}

0

r

0

Incident-normalized response threshold

q

0.4

Actual depth spacing: 1 on; 0 assumes 25 nm

c

1

Stored image index: values past the end show the last image

k

10

Knife travel: 0 retracted, 1 across face

s

0

Assigned charge-drain multiplier

g

1

Learning goal and model limits

Predict · cut · record · reconstruct

Can sharp block-face images still miss structures that lie between two cuts?

Target: reach at least 80 percent overlap with a volume error of at most 12 percent. Record at least 95 percent of the depth, with at least 12 mean counts in the central pixels. Use the actual depth spacing and sections at most 50 nm thick. The known input is used only to check the result; the reconstruction never sees it.

Model assumptions

The face of the resin block is perpendicular to the SEM axis. A diamond knife moves sideways across the face while the electron beam is blanked, then retracts before imaging. The stage advances so the face stays at a fixed working position. The BSE information length is assumed to be 30 nm, and sections can be 50 to 160 nm thick. Knife damage is an assumed horizontal band of low signal that moves from cut to cut; it is not a calculation of mechanical fracture or chatter. An assigned heavy-metal loading scales occupied-region contrast and the conductance of a lumped charging face. An effective dielectric backing with relative permittivity 3 and a fixed 1 micrometre charge-drain path sets its capacitance; 40 percent of the fixed 50 pA current charges it, and linear leakage drains it. Row-dependent negative potential deflects sampling positions with an assigned spatial-gradient law before counts are drawn. Each fresh face starts discharged. This illustrates staining, charging and sampling together; it does not model a cell, membrane, staining chemistry, spatial Poisson field, inter-face trapped charge, tissue preparation, knife force, environmental pressure, throughput or real material calibration. The SEM current is fixed at 50 pA, and each image has 48 by 48 pixels across a selectable 900–2400 nm field and 960 nm total depth. The field sets the lateral pitch; a wider view trades finer sampling and dose density for coverage. The apparatus shows the viewed specimen column at an independently enlarged scale. The synthetic specimen is a sphere plus a curved tube, with three fiducial marks near the edge that run through the whole depth. The BSE response is an assumed linear mix: 0.18 for background, plus 0.44 times the loading for the occupied region and 0.65 for the fiducials, with 8 percent detector efficiency. It does not identify materials or represent a calibrated biological structure. The forward model averages four normalized exponential depth bins, adds horizontal drift and cutting artefacts, then stores electron counts drawn from a fixed random seed: Poisson below 40 expected counts and a normal approximation above. The fixed linear color scale clips only the display. The reconstruction receives only the stored counts and calibration metadata, never the known specimen or the imposed drift. Registration cross-correlates the recorded fiducials with those in the first recorded image, in whole-pixel horizontal steps up to eight pixels either way. Vertical, affine and subpixel shifts are not corrected. A threshold segments the central 700 nm square and leaves out the fiducials. Missing layers and pixels with no data stay marked as unknown. Each mask becomes a slab with its recorded thickness; nothing is interpolated, and there is no tomography solver. The known input, shown separately, is used only to check overlap and volume error on the same sampling grid. The cumulative incident dose adds up the exposures of each new face; it is not the dose received by any one surviving voxel. The presentation phase and camera motion never change the stored data.

Physics tutorial

Block-face SEM: Between the Cuts

BackgroundIn block-face SEM, a diamond knife inside the microscope chamber shaves a thin layer off a resin block and pulls back, and the SEM images the new face. You compare section spacing, counting noise, drift and knife damage before reconstructing the volume.

Why it mattersThe task is to reach at least 80 percent overlap with the known sampled input, at most 12 percent volume error, at least 95 percent recorded depth coverage and at least 12 mean counts per central pixel. Keep the actual depth spacing turned on, and keep sections no thicker than 50 nm.

Start with the essentials

Focus question: Can sharp block-face images still miss structures that lie between two cuts?
One-sentence intuition: A sharp face image shows detail across the face, not what lies between the cuts. Registration can fix drift it measures, but it cannot bring back a section that was destroyed or never recorded, and the right voxel spacing matters as much as a good segmentation.

Core mathematical model

Expected electron counts

N_0=\eta\frac{I\tau}{e}

The beam current and dwell time set the count scale, and the BSE response at each point scales it further.

Depth sampling

\begin{aligned}\mathcal T&=\sum_{j=0}^{3}w_j\rho_j\\\rho_j&=\rho(x,y,z_j)\\z_j&=z+(j+\tfrac12)\ell\\w_j&=\frac{e^{-j}-e^{-j-1}}{1-e^{-4}}\end{aligned}

The signal averages four depth bins below the face, weighted by an assumed exponential fall-off. This is a fixed numerical sum, not an electron transport calculation.

Volume from the recorded counts

\begin{aligned}\widehat V&=p^2\sum_k h_k\sum_{x,y}\widehat M_k(x,y)\\\mathrm{IoU}&=\frac{|\widehat M\cap M_*|}{|\widehat M\cup M_*|}\end{aligned}

The threshold mask comes from the recorded counts. Each slab has its actual thickness, including the thinner last section. Unknown voxels add no made-up volume, and the overlap with the known input is a separate check.

Common difficulties

A reconstruction is not the known input

Typical misconceptionThe reference shape is right there, so the algorithm must have recovered it.

Better mental modelThe gold reference is used only for a separate check. The teal reconstruction comes from thresholding the recorded counts, so its noise, damage and gaps are still there.

Smaller voxels do not create resolution

Typical misconceptionIf I set every voxel edge to 25 nm, the volume gets the same resolution in every direction.

Better mental modelChanging the metadata can distort the shape and volume, and it adds no measured detail. Use the real section spacing.

Run the experiment

01
Compare staining and field width
Compare Stained and resolved with Weak stain, charging face. Watch the stored image and charging curve. Restore the stained preset, then choose Wide field, coarse pixels.
What to observe: Weak staining reduces contrast and charge drainage. A wider field covers more specimen with the same 48 pixels, so fine structures have fewer samples.
02
Predict what the cuts miss
Compare Structures between cuts with Stained and resolved. Look at the face image, the orthogonal reslices and the known input.
What to observe: A sharp face image cannot show structure that lies between the cuts.
03
Reprocess the same data
Choose Stained and resolved, set Horizontal drift per cut to 4, then compare Register counted fiducials off and on. Change the threshold and the depth-spacing calibration.
What to observe: These controls reprocess the same stored counts, so a different reconstruction does not mean new data were taken.
04
Look at a missing layer
Load the Missing sections preset and select the fifth stored position. Look at the dark image tile and the row marked unknown in the reslice.
What to observe: A missing layer means there are no data there, not that the specimen is empty.
05
Reach the target
Make the sections thinner, reduce the artefacts, raise the dwell for enough counts, register the measured fiducials and turn on actual depth spacing. Then press Check target.
What to observe: The target checks overlap, volume error, depth coverage and whether there are enough counts.

Core mathematical model

Expected electron counts

Depth sampling

Volume from the recorded counts

Common difficulties

A reconstruction is not the known input

Smaller voxels do not create resolution

Run the experiment

Compare staining and field width

Predict what the cuts miss

Reprocess the same data

Look at a missing layer

Reach the target