 Section-thickness anisotropy

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 isIt 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.^[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 $p^2\Delta z=800\mathrm{n}{\mathrm{m}}^3$. A displacement of three pixels laterally and two section intervals axially has physical lengthTreating all three index coordinates as though they had spacing $p$ would instead give $p\sqrt{3^2+2^2}\simeq 14.42\mathrm{nm}$, 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 $200\Delta z=10\mu \mathrm{m}$ of thickness while the first and last centers are only $199\Delta z=9.95\mu \mathrm{m}$ apart. For variable or missing sections, retain the actual section coordinates rather than assuming a single constant $\Delta z$.