Lorentzian Peak
The Lorentzian, or Cauchy, line shape on a constant baseline, with its center and full width at half maximum. Use it for spectral lines, magnetic resonance and other peaks whose wings fall off more slowly than a Gaussian’s.
Fit the example dataStart with your own data
Example: a simulated optical cavity transmission peak, 41 points with y uncertainties, opened as a new copy you can edit.
Parameters
- Peak height above the baseline.
- Peak center.
- Full width at half maximum, in the units of x. Reported as positive unless a requested limit requires the negative equivalent.
- Constant baseline.
Tips
- The wings fall off as 1/(x − x₀)², so include points well out on both sides to determine the baseline C.
- The area under the peak, above the baseline, is πAΓ/2.
- When the line shape is uncertain, also fit Gaussian, which has narrower wings, and compare the AIC of both fits in Previous.
- Near a sharp resonance, the squared amplitude of a driven oscillator has this shape, with Γ = 2β.