 Section compression

Section compression is shortening of a cut section relative to the corresponding specimen-block dimension, usually measured parallel to the cutting direction in ultramicrotomy. It is a physical deformation introduced during preparation, so an accurately calibrated microscope can still measure a distorted specimen. Manufacturer guidance for polymer sectioning connects reduced compression with smaller knife wedge angles, while noting the resulting greater sensitivity of the cutting edge.^[ref]

Let $L_b$ be a reference length in the block and $L_s$ its recovered section length along the same direction. Define a positive compression fractionThe corresponding engineering strain is $\epsilon =(L_s-L_b)/L_b=-c$. State this sign convention: a reported positive percentage compression and a negative longitudinal strain can describe the same shortening.

For an original geometrical model, a $10\mu \mathrm{m}$ feature recovered as $8\mu \mathrm{m}$ has $c=0.20$. If transverse dimensions are unchanged and the shortening is uniform, an originally circular feature becomes an ellipse with axis ratio $0.8$. Its area becomes $80\%$ of the original, not $64\%$: only one direction was shortened. Under the additional assumption of volume conservation, a nominal $70\mathrm{nm}$ layer would have thicknessNeither transverse constancy nor volume conservation is automatic. Material loss, cracking, relaxation and nonuniform deformation can invalidate the model; section length alone cannot establish recovered thickness.

A useful materials check compares recognizable features in the block face and collected section, recording cutting direction, knife wedge angle, knife clearance angle and specimen conditions. Repeating the comparison at several positions tests whether one compression fraction is adequate. Under the simple model above, expanding the shortened coordinate by $1/0.8=1.25$ would reverse the geometrical shortening, but this is a model-based correction rather than an extra observation. Image registration can align features without proving that it has recovered their original shapes.