AFM · Metrology
More measurements. The same uncertainty floor.
Separate independent read noise from shared calibration error before trusting a smaller error bar.
Standard uncertainty
Values & comparison details
Difference = comparison − reference. Rounded for display; original data retained.
- 8 reference readings
- 0.30678799182888106 nm
- 128 reference readings
- 0.30237279060069183 nm
Same shared-error model. Uncertainty of one profile mean; synthetic study.
Open full figure THE QUESTION
Can repeated reference readings remove uncertainty in the mean absolute height of one AFM profile?
THE APPROACH
A fixed synthetic measurement model is evaluated with eight reference positions and 1, 4 or 16 readings per position. The same 512 trial estimates are assessed using a shared-error covariance model and an intentionally incorrect independence assumption.
WHAT THE COMPARISON SHOWS
Three things to take away.
- 01
Increasing the total from 8 to 128 readings lowers the correctly propagated standard uncertainty only from 0.3068 to 0.3024 nm. The fixed model has a 0.3021 nm limiting floor.
- 02
Treating the shared calibration error as independent suggests 0.0463 nm at 128 readings. Repetition has not created that information.
- 03
Across the same 512 synthetic trials, the nominal 95% intervals cover the true mean in 94.53% of trials with the shared-error model and 23.24% with the incorrect model.
Evidence, assumptions & the next question
What was numerically checked
Independent augmented-QR and algebraic controls, uncertainty reconstruction, paired synthetic trials and replay checks support the bounded numerical comparison.
How far the result goes
Synthetic measurement model. The quantity is uncertainty in one profile’s mean absolute height, not pixel RMSE or the uncertainty of a Monte Carlo grand mean. This is not an AFM instrument calibration.
What a physical study would need next
A real application needs reference calibration, drift and covariance information, native readings and a clearly defined measurand.
SA-MET-VARIABILITY-UQ-068 · AFM reference-zero uncertainty · 2026-09-30
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