Vernier FSR
Calculate the approximate compound-cavity Vernier free spectral range.
Description
The Vernier effect produces a larger compound repetition spacing from two close unequal free spectral ranges.
The Vernier effect produces a larger compound repetition spacing from two close unequal free spectral ranges. Their difference controls the enhancement.1
Calculate the approximate compound-cavity Vernier free spectral range.
When to use Vernier FSR
Use this tool to calculate the approximate compound-cavity Vernier free spectral range.
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 Vernier FSR 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 firstFsrHertz, secondFsrHertz using the field table and calculation rules, then run the tool.
- Read fsrDifferenceHertz, vernierFsrHertz. 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 |
|---|---|---|---|
| firstFsrHertz | First-cavity FSR (Hz) | number; minimum: 0 | Required |
| secondFsrHertz | Second-cavity FSR (Hz) | number; minimum: 0 | Required |
Enter positive unequal FSRs in Hz. Return absolute difference and approximate compound FSR.
VernierFSR=FSR1×FSR2/|FSR1−FSR2| Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fsrDifferenceHertz | FSR difference (Hz) | number; minimum: 0 |
| vernierFsrHertz | Vernier free spectral range (Hz) | number; minimum: 0 |
{
"input": {
"firstFsrHertz": 100,
"secondFsrHertz": 110
},
"output": {
"fsrDifferenceHertz": 10,
"vernierFsrHertz": 1100
}
}Limitations and assumptions
No cavity resonance phases, dispersion or mode alignment is solved. Equal FSRs are rejected.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Mode-Sorter Crosstalk: Calculate diagonal mode-sorting efficiency and off-diagonal crosstalk. For a complementary task, use Fabry-Pérot Linewidth: Calculate Fabry–Pérot free spectral range and linewidth from cavity length, index, and finesse.
References
-
Vernier FSR — tool.io
Similar or alternative tools
- Mode-Sorter Crosstalk
Calculate diagonal mode-sorting efficiency and off-diagonal crosstalk.
- Fabry-Pérot Linewidth
Calculate Fabry–Pérot free spectral range and linewidth from cavity length, index, and finesse.