= Section compression
{title2=$c=1-L_s/L_b$}
<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 (mechanics)> 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.<Ultramicrotomy Techniques for Materials Sectioning by Leica Microsystems>[How to prepare high-quality sections of polymers: wedge-angle tradeoff]{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 fraction
$$
c=1-\frac{L_s}{L_b}.
$$
The corresponding <engineering strain> is $\varepsilon=(L_s-L_b)/L_b=-c$. 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 $10\,\mathrm{\mu m}$ feature recovered as $8\,\mathrm{\mu m}$ 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 thickness
$$
t_s=\frac{70}{0.8}=87.5\,\mathrm{nm}.
$$
Neither transverse constancy nor <volume conservation> is automatic. Material loss, cracking, relaxation and nonuniform <deformation (mechanics)> 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.
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