Tracker Error Budget

Combine independent laser-tracker error components by root-sum-square.

Description

Independent error components combine by root sum of squares.

Independent error components combine by root sum of squares. The result assumes components can be represented on the same measurement basis.^[1]

Combine independent laser-tracker error components by root-sum-square.

When to use Tracker Error Budget

Use this tool to combine independent laser-tracker error components by root-sum-square.

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 Tracker Error Budget 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 independentErrors using the field table and calculation rules, then run the tool.
Read rssError, largestComponent. 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
independentErrors	Independent one-sigma errors (length)	list of number	Required

Enter a nonempty finite component list, allowing signs. Return RSS and largest absolute component in the shared input units.

RSS=sqrt(Σerror_i²); largest=max|error_i|

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
rssError	Root-sum-square error (length)	number; minimum: 0
largestComponent	Largest absolute component (length)	number; minimum: 0

json

{
  "input": {
    "independentErrors": [
      1,
      2,
      2
    ]
  },
  "output": {
    "rssError": 3,
    "largestComponent": 2
  }
}

Limitations and assumptions

Correlation and systematic bias are not modeled. The tool does not verify independence.

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 Jitter-Rejection Budget: Calculate fast-steering-mirror jitter rejection and margin against a caller requirement. For a complementary task, use Comb Traceability Uncertainty: Combine independent fractional uncertainties in an optical-frequency traceability chain.

References

Tracker Error Budget — tool.io

Similar or alternative tools

Jitter-Rejection Budget
Calculate fast-steering-mirror jitter rejection and margin against a caller requirement.
Comb Traceability Uncertainty
Combine independent fractional uncertainties in an optical-frequency traceability chain.