Tonometry

Goldmann applanation rests on the Imbert-Fick relationship: the pressure inside a sphere equals the force needed to flatten a portion of its wall divided by the area flattened. The relationship holds cleanly only for an infinitely thin, perfectly flexible, dry membrane. A cornea is thick, rigid and wet, so two real-world forces intrude — the cornea's own rigidity, which resists flattening and pushes the reading up, and the surface tension of the tear film, which grips the prism and pulls it in, pushing the reading down. Goldmann chose an applanation diameter of 3.06 mm because at that size the two errors approximately cancel. What is left is the calibration every technician uses: the drum reads grams of force, and grams × 10 = mmHg, so 0.1 g equals 1 mmHg and a drum setting of 1.6 is 16 mmHg.

Read that paragraph as a list of assumptions, because every assumption is a source of error later. The cancellation assumes a cornea of roughly average thickness (Goldmann's calibration sits near 520 μm), average rigidity, a normal tear film, and a surface that flattens as a circle. Thick, thin, edematous, scarred, surgically flattened and strongly astigmatic corneas each break one of those assumptions in a predictable direction.