A teaching tape for BM-08, Measurement bias with localization noise, drift, and exposure models
Camera noise and exposure bias
Open BM-08 with these settings
Where it starts
| Setting | Value |
|---|---|
| Diffusivity (D) | 4.2944e-13 |
| Fluid flow drift velocity (flowDrift) | 0 |
| Number of increments (M) | 100 |
| Measured coordinates (d) | 2 |
| Frame spacing (dt) | 1 |
| Exposure time (exposure) | 0.5 |
| Localization error (sigma) | 2e-7 |
| Stage drift velocity (stageDrift) | 0 |
| Stationary clicks (clicks) | 30 |
| Nominal coverage (coverage) | 0.95 |
| Hypothetical experiments (coverageTrials) | 0 |
What it changes, and what to expect
Set Localization error (sigma) to 2e-7 changes how it is watched, not what happens
Noisy, exposure-blurred camera observations
Camera noise adds 2*sigma^2 variance and negative lag-1 covariance, and the two do not cancel: at these settings the exposure blur takes 7.157e-14 m2/s off the estimate while the localization noise puts 4e-14 back, so the naive estimator reads 3.9787e-13 where the true D is 4.2944e-13, 7.3 per cent low. Reading the naive number as D is the mistake this instrument exists to show.
What the author recorded that a reader should see here. Quantity Expected Under naive expectation 3.97867 × 10⁻¹³ m²/s modern-si-2019
These are the values the tape's author recorded, not a result this page computed. Nothing here runs the instrument. Open BM-08 with these settings: the link puts them in its form, and it calculates when you apply them. Compare what it gives you with what is recorded here. The settings travel in the link and the laboratory reads them as it loads, so without JavaScript it opens at its worked example instead.
What these numbers were recorded under
| Identity | Recorded as |
|---|---|
| Model | inference-bm08-host version 1 |
| Seed | 1905 |
| Random-stream semantics | version 1 |