Comb Traceability Uncertainty
Combine independent fractional uncertainties in an optical-frequency traceability chain.
Description
Independent fractional uncertainties combine by root sum of squares.
Independent fractional uncertainties combine by root sum of squares. Multiplication by optical frequency expresses the aggregate as an absolute hertz uncertainty.1
Combine independent fractional uncertainties in an optical-frequency traceability chain.
When to use Comb Traceability Uncertainty
Use this tool to combine independent fractional uncertainties in an optical-frequency traceability chain.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Comb Traceability Uncertainty and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter opticalFrequencyHertz, fractionalUncertainties using the field table and calculation rules, then run the tool.
- Read combinedFractionalUncertainty, absoluteUncertaintyHertz. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| opticalFrequencyHertz | Optical frequency (Hz) | number; minimum: 0 | Required |
| fractionalUncertainties | Independent fractional uncertainties | list of number | Required |
Enter nonnegative optical frequency and nonempty nonnegative fractional uncertainties. Return combined fraction and hertz.
combined=sqrt(Σu_i²); absolute=frequency×combined Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| combinedFractionalUncertainty | Combined fractional uncertainty | number; minimum: 0 |
| absoluteUncertaintyHertz | Absolute frequency uncertainty (Hz) | number; minimum: 0 |
{
"input": {
"opticalFrequencyHertz": 1000,
"fractionalUncertainties": [
0.003,
0.004
]
},
"output": {
"combinedFractionalUncertainty": 0.005,
"absoluteUncertaintyHertz": 5
}
}Limitations and assumptions
Common coverage factors and independence must be established externally. No traceability records, correlation or systematic offsets are checked.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Tracker Error Budget: Combine independent laser-tracker error components by root-sum-square. For a complementary task, use Lunar-Ranging Precision: Convert round-trip timing uncertainty into one-way lunar-ranging distance uncertainty.
References
-
Comb Traceability Uncertainty — tool.io
Similar or alternative tools
- Tracker Error Budget
Combine independent laser-tracker error components by root-sum-square.
- Lunar-Ranging Precision
Convert round-trip timing uncertainty into one-way lunar-ranging distance uncertainty.