E20 · Serial volume electron microscopy

FIB-SEM: From Slices to Volume

When can clear slices produce a wrong volume? When the slices do not sample the depth properly: some depths are skipped, or the stack is built with the wrong slice spacing. A crisp image shows only that contrast within each slice is good. Registration can correct drift you have measured, but it cannot bring back a slice that is missing or was destroyed.

Mill away a thin layer with the ion beam, image the new face with backscattered electrons, and repeat. Adjust the section spacing, dwell, drift and curtaining, then align and threshold the recorded counts to build a calibrated volume.

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

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

Recorded depth coverage $\text{—}$

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

More measurements and target

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

Known sampled input volume $\text{—}$

Mean central pixel counts $\text{—}$

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.

More examples

Physical section thickness

h

40\,\mathrm{nm}

Dwell per pixel

\tau

2\,\mathrm{\mu s}

Horizontal drift per cut

d_x

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

r

0

Advanced settings

Prescribed curtaining amplitude

a

0.15

Lose every nth image: 0 none

n_{\rm gap}

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

Presentation phase: 0 image, 1 cut

s

0

Learning goal and model limits

Predict · cut · record · reconstruct

When can clear slices produce a wrong volume?

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 25 nm thick. The known input is used only to check the result; the reconstruction never sees it.

Model assumptions

The angle between the SEM and FIB columns is 54 degrees, following the ZEISS Crossbeam convention. The ion beam mills a face perpendicular to its own axis, so the SEM sees that face at an angle and the image height is foreshortened; the reconstruction uses calibrated face coordinates. The specimen is advanced schematically so the viewed face stays in place. The BSE information length is assumed to be 8 nm, and sections can be 20 to 120 nm thick. Curtaining is an assumed sinusoidal change in gain, not a sputter-yield or redeposition calculation. The electron beam is blanked during milling, and the ion beam is blanked during imaging. Lamella lift-out, a comparison of gallium and xenon ions, ion damage, milling time and calibration to real materials are not modeled. The SEM current is fixed at 50 pA, and each image has 48 by 48 pixels at a 25 nm face pitch, a 1200 nm field and 960 nm total depth. 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 of contrast 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

FIB-SEM: From Slices to Volume

BackgroundA FIB-SEM mills away a thin layer with an ion beam, images the new face with backscattered electrons, and repeats. You adjust the section spacing, dwell, drift and curtaining, then align and threshold the recorded counts into a calibrated 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 25 nm.

Start with the essentials

Focus question: When can clear slices produce a wrong volume?
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
Predict what the cuts miss
Compare the coarse-depth preset with the Resolve the volume preset. 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.
02
Reprocess the same data
Load the Drifting stack preset, then turn on Register counted fiducials. 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.
03
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.
04
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

Predict what the cuts miss

Reprocess the same data

Look at a missing layer

Reach the target