= Section-thickness anisotropy
{title2=$\Delta z/p$}
<Section-thickness anisotropy> describes unequal spatial sampling along and across a serial-section <image stack>. For uniform section thickness $\Delta z$ and square lateral <pixel pitch> $p$, a useful dimensionless ratio is
$$
r=\frac{\Delta z}{p}.
$$
It compares assigned sampling scales, rather than automatically specifying an achieved <spatial resolution>. Section collection followed by image alignment and stacking produces a physical cutting coordinate that must be calibrated separately from lateral image dimensions.<Serial Section TEM by JEOL>[Definition and Figure1(a)–(e)]{ref}
For an original example, let $p=4\,\mathrm{nm}$ and $\Delta z=50\,\mathrm{nm}$. Then $r=12.5$ and a rectangular <voxel> has volume $p^2\Delta z=800\,\mathrm{nm^3}$. A displacement of three pixels laterally and two section intervals axially has physical length
$$
d=\sqrt{(3p)^2+(2\Delta z)^2}=\sqrt{12^2+100^2}\,\mathrm{nm}\simeq100.72\,\mathrm{nm}.
$$
Treating all three index coordinates as though they had spacing $p$ would instead give $p\sqrt{3^2+2^2}\simeq14.42\,\mathrm{nm}$, a serious geometrical error.
<Image resampling> to $4\,\mathrm{nm}$ cubic <voxels> can regularize display coordinates, but the inserted axial samples are <interpolation>, not new independent observations. Likewise, 200 uniform sections represent $200\Delta z=10\,\mathrm{\mu m}$ of thickness while the first and last centers are only $199\Delta z=9.95\,\mathrm{\mu m}$ apart. For variable or missing sections, retain the actual section coordinates rather than assuming a single constant $\Delta z$.
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