Description
Return variance-corrected harmonic trap stiffness.
Polymer elasticity and optical trapping relate small displacements or equilibrium fluctuations to an effective stiffness. A linear force law and a variance-based estimate depend on different assumptions; a supplied length or noise correction does not establish that a real system is harmonic or in equilibrium.
Return variance-corrected harmonic trap stiffness.
When to use this tool
Use Optical Trap Stiffness Variance Term when evaluating the stated polymer or harmonic-trap term under its supplied assumptions.
How to use the tool and how it works
- Enter thermalEnergy, positionVariance, measurementVariance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read correctedVariance, stiffness. Use the output convention below.
Return variance-corrected harmonic trap stiffness. Require thermalEnergy/measurementVariance >= 0 and positionVariance > measurementVariance; correctedVariance subtracts measurement noise, stiffness = thermalEnergy/correctedVariance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| thermalEnergy | Thermal Energy | Required. Finite number; minimum 0. |
| positionVariance | Equilibrium variance of one trapped position coordinate. | Required. Finite number. |
| measurementVariance | Independent additive localization/noise variance on that same coordinate and squared-length basis. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| correctedVariance | Corrected Variance | Required. Finite number. |
| stiffness | Stiffness | Required. Finite number. |
{
"input": {
"thermalEnergy": 4,
"positionVariance": 10,
"measurementVariance": 2
},
"output": {
"correctedVariance": 8,
"stiffness": 0.5
}
}Limitations and assumptions
- This equipartition model assumes appropriate equilibrium position variance and independent noise; no time-series fitting or calibration is performed.
- 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 the appropriate complete polymer/trap model, calibrated observations and a justified equilibrium/noise analysis for physical parameter inference.
References
Similar or alternative tools
- Optical Trap Offset Force Term
Return trap displacement and force under a supplied sign.
- Trap Force Displacement Residual
Return restoring-force prediction and residual.