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Lateral position jitter is the fluctuating in-plane displacement of successive acquired images relative to a chosen reference. In serial block-face scanning electron microscopy, it can displace corresponding features between block faces even when the cutting increment is perfectly regular. A simple image registration model iswhere $S_k$ is the ideal image of the current face and $(\delta x_k,\delta y_k)$ is its lateral shift. The specimen itself changes between faces, so not every apparent shift is instrumental motion.

A primary apparatus study estimated inter-image displacement from cross-correlation peaks in several subregions. Its Figure4 central cluster had standard deviations of $10.9\mathrm{nm}$ and $11.8\mathrm{nm}$ along the two axes; outliers and changing specimen patterns required interpretation.^[ref]

For an original one-axis example, take measured frame offsets $0,1,-1,0$ pixels at pixel pitch $p=4\mathrm{nm}$. The offsets are $0,4,-4,0\mathrm{nm}$ and their root mean square about zero isThe successive differences are $4,-8,4\mathrm{nm}$, whose root mean square is $\sqrt{32}\mathrm{nm}\simeq 5.66\mathrm{nm}$. These are different statistics. For independent equal-variance frame offsets, the theoretical difference variance is $2{\sigma }^2$; correlation or drift changes that relation. Specify the reference, detrending and normalization when reporting jitter. Image registration can estimate a correction but does not prove that all residual motion or specimen deformation has been removed.

Serial block-face scanning electron microscopy acquires a three-dimensional dataset by repeatedly imaging an exposed specimen face in a scanning electron microscope and removing a thin layer with an ultramicrotome. The removed layer is not the imaged object: each image records the newly exposed block face. This differs from collecting and imaging thin sections in serial-section electron microscopy.^[ref]

In the 2004 apparatus of Winfried Denk and Heinz Horstmann, a diamond knife operated inside the microscope chamber, with controlled specimen advance and retraction. A backscattered electron signal supplied image contrast. Keeping the cutting and imaging operations in the chamber enabled automated image stack acquisition.^[ref]

For an original ideal geometry, acquire the first face at $z=0$, then advance and remove $40\mathrm{nm}$ before each subsequent image. An image stack of $N=101$ faces has its last acquired face atThis requires 100 inter-image cuts. If a data format assigns each face a $40\mathrm{nm}$-deep voxel, its nominal represented thickness is instead $N\Delta z=4.04\mu \mathrm{m}$. State which extent is intended. At lateral pixel pitch $5\mathrm{nm}$, the sampling ratio $\Delta z/p$ is 8.

The resulting image stack needs image registration and a calibrated cutting coordinate. Lateral position jitter, cutting artifacts and the depth range contributing to the electron signal limit the useful reconstruction. Finite voxel spacing is not itself a measurement of spatial resolution. Destructive cutting also means that later imaging cannot recover an exposed face that has already been removed.

Serial-section electron microscopy reconstructs a volume from an ordered image stack of thin physical slices. In the transmission electron microscopy implementation, an ultramicrotome cuts successive slices, which are collected on a support and imaged through the specimen. Image registration aligns corresponding features; image segmentation identifies structures to follow between slices. JEOL's glossary describes sections of 40–100 nm and illustrates the separate registration and segmentation stages.^[ref]

The motivation is geometrical: one isolated slice cannot show whether a feature continues, divides, or ends outside that slice. An ordered image stack provides observations along the third coordinate, although finite section-thickness anisotropy and missing material limit what can be inferred. A change between neighboring images may come from specimen structure, a slice deformation, or imperfect image registration.

For a chosen numerical example, suppose each of $N=200$ consecutive sections has uniform thickness $\Delta z=50\mathrm{nm}$, with lateral pixel pitch $p=4\mathrm{nm}$. Ignoring lost material and thickness variation, the sections coverThe voxel sampling is 12.5 times coarser along the cutting direction. These are chosen dimensions, not measurements from either cited experiment. The first and last section centers are only $(N-1)\Delta z$ apart: center-to-center extent differs from total represented thickness. Neither spacing is automatically the achieved spatial resolution.

Image resampling onto a cubic grid can make an image stack easier to display, but interpolation supplies no additional independent observations. Likewise, smooth image registration cannot resolve missing-section ambiguity in volume reconstruction: a small connecting feature could lie wholly inside lost material. Checking a reconstructed connection therefore needs evidence in the acquired slices, not just a visually smooth rendered surface.

A historically important automation change illustrates the distinction between section and surface imaging. In 2004, Winfried Denk and Heinz Horstmann placed an ultramicrotome with a diamond knife inside a scanning electron microscope. Their serial block-face scanning electron microscopy imaged the exposed block surface between cuts instead of collecting the removed sections. They reported stacks several hundred layers deep, 50–70 nm sectioning, and typically less than 10 nm lateral position jitter. These observations tested an apparatus for acquiring closely aligned serial images; they did not remove the finite spacing between observations.^[ref]

A mechanical detail makes the measurement chain concrete. Their specimen-advance lever reduced the motorized micrometer's motion by 0.11. Thus its stated position measurement uncertainty of 50 nm contributed $0.11\times 50=5.5\mathrm{nm}$ after that reduction; other sources of section-thickness error still required assessment.^[ref]