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

The settings the tape begins from, under the constant set modern-si-2019. Values are the model's own, not the laboratory control's display: a radius of 5e-7 is half a micrometre.
SettingValue
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

  1. 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.

    What the author recorded that a reader should see here.
    QuantityExpectedUnder
    naive expectation4.2944e-13 m2/smodern-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.

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