Description
Subtract localization noise from measured mean-square displacement.
Diffusive and thermal scales depend on dimensionality, geometry, drag and compatible energy/time units. A local displacement correction or ideal spherical diffusivity is distinct from fitting a stochastic trajectory or establishing that a measured system satisfies the model.
Subtract localization noise from measured mean-square displacement.
When to use this tool
Use Trajectory Localization Variance Factor when checking the stated diffusion, drift, work or thermal-energy convention.
How to use the tool and how it works
- Enter measuredMsd, localizationVariance, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read noiseContribution, correctedMsd. Use the output convention below.
Subtract localization noise from measured mean-square displacement. Require nonnegative measuredMsd/localizationVariance and whole dimensions 1..3; noiseContribution = 2*dimensions*localizationVariance, correctedMsd = measuredMsd-noise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| measuredMsd | Measured Msd | Required. Finite number; minimum 0. |
| localizationVariance | Per-coordinate position-error variance, in the squared displacement unit. | Required. Finite number; minimum 0. |
| dimensions | Dimensions | Required. Safe integer; minimum 1; maximum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| noiseContribution | Noise Contribution | Required. Finite number. |
| correctedMsd | Measured MSD minus the independent two-endpoint localization contribution; may be negative. | Required. Finite number. |
{
"input": {
"measuredMsd": 10,
"localizationVariance": 1,
"dimensions": 2
},
"output": {
"noiseContribution": 4,
"correctedMsd": 6
}
}Limitations and assumptions
- Variance is per coordinate with independent endpoint errors; a negative corrected MSD is retained rather than interpreted as physical diffusion.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use calibrated trajectories and an appropriate geometry/noise/transport model for fitted diffusion parameters, uncertainty or molecular mechanisms.
References
Similar or alternative tools
- Rotational Diffusion Viscosity Radius Term
Return spherical rotational diffusivity and second-rank correlation time.
- Diffusion Time Scale Ratio
Return a ratio of diffusive time scales.