FBG Peak Interpolation
Interpolate an FBG spectral peak from three equally spaced power samples.
Description
Three-point parabolic interpolation estimates a spectral extremum between equally spaced samples.
Three-point parabolic interpolation estimates a spectral extremum between equally spaced samples. The offset is measured in sample spacings from the center.1
Interpolate an FBG spectral peak from three equally spaced power samples.
When to use FBG Peak Interpolation
Use this tool to interpolate an FBG spectral peak from three equally spaced power samples.
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 FBG Peak Interpolation 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 leftWavelengthNanometers, centerWavelengthNanometers, rightWavelengthNanometers, leftPower, centerPower, rightPower using the field table and calculation rules, then run the tool.
- Read interpolatedPeakNanometers, subsampleOffset. 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 |
|---|---|---|---|
| leftWavelengthNanometers | Left sample wavelength (nm) | number | Required |
| centerWavelengthNanometers | Center sample wavelength (nm) | number | Required |
| rightWavelengthNanometers | Right sample wavelength (nm) | number | Required |
| leftPower | Left sample power | number | Required |
| centerPower | Center sample power | number | Required |
| rightPower | Right sample power | number | Required |
Enter finite wavelengths/powers with positive left spacing and left/right spacing equal within 1e−9 relative tolerance. Reject zero curvature denominator. Return interpolated wavelength and offset.
offset=0.5(leftPower−rightPower)/(leftPower−2centerPower+rightPower) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| interpolatedPeakNanometers | Interpolated peak wavelength (nm) | number |
| subsampleOffset | Peak offset in sample intervals | number |
{
"input": {
"leftWavelengthNanometers": 1549,
"centerWavelengthNanometers": 1550,
"rightWavelengthNanometers": 1551,
"leftPower": 1,
"centerPower": 4,
"rightPower": 3
},
"output": {
"interpolatedPeakNanometers": 1550.25,
"subsampleOffset": 0.25
}
}Limitations and assumptions
Downward curvature, center maximum and offset inside the sample interval are not required, so a fitted minimum or distant extremum can be returned.
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 Fizeau Frequency Precision: Estimate Fizeau wavemeter precision from scan span, FFT size, and interpolation precision. For a complementary task, use Parabolic Pulse Fit: Fit intensity as a linear function of squared time and report parabolic-fit R squared.
References
-
FBG Peak Interpolation — tool.io
Similar or alternative tools
- Fizeau Frequency Precision
Estimate Fizeau wavemeter precision from scan span, FFT size, and interpolation precision.
- Parabolic Pulse Fit
Fit intensity as a linear function of squared time and report parabolic-fit R squared.