Choose a Peak Model

OpticalSpectroscopy.jl supports three peak models from CurveFitModels.jl. This guide explains when to use each one.

Available Models

Model	Parameters	Line shape
`lorentzian`	`[A, x₀, Γ, offset]`	Natural line shape (homogeneous broadening)
`gaussian`	`[A, x₀, σ, offset]`	Doppler / inhomogeneous broadening
`pseudo_voigt`	`[A, x₀, σ, η]`	Weighted mix of Gaussian and Lorentzian

All models use the signature fn(p, x) (parameters first) and are ForwardDiff-compatible.

When to Use Each

Start with some example data:

using OpticalSpectroscopy
using CurveFitModels

x = collect(range(2000, 2150, length=500))
y = lorentzian([0.45, 2062.0, 24.0, 0.01], x) .+ 0.003 .* randn(length(x))

Lorentzian (default)

Best for peaks broadened by a single mechanism with a well-defined lifetime:

Solution-phase FTIR (collisional broadening)
Isolated Raman peaks in crystals (phonon lifetime)
Fluorescence emission from single emitters

result = fit_peaks(x, y, (2000, 2150))  # lorentzian is the default

The width parameter Γ is the full width at half maximum (FWHM).

Gaussian

Best for peaks broadened by a distribution of environments:

Gas-phase spectra (Doppler broadening)
Amorphous or disordered materials
XRD peaks at moderate resolution

result = fit_peaks(x, y, (2000, 2150); model=gaussian)

The width parameter σ is the standard deviation. FWHM = 2√(2 ln 2) × σ ≈ 2.355 σ.

Pseudo-Voigt

Best when both homogeneous and inhomogeneous broadening contribute:

Solution-phase spectra with concentration-dependent broadening
Solid-state spectra with mixed broadening
When neither Lorentzian nor Gaussian fits well

result = fit_peaks(x, y, (2000, 2150); model=pseudo_voigt)

The mixing parameter η (0 to 1) gives the Lorentzian fraction. η = 0 is pure Gaussian, η = 1 is pure Lorentzian.

Comparing Models

Fit the same data with multiple models and compare:

r_lor = fit_peaks(x, y, (2000, 2150))
r_gau = fit_peaks(x, y, (2000, 2150); model=gaussian)
r_voi = fit_peaks(x, y, (2000, 2150); model=pseudo_voigt)

println("Lorentzian: R² = ", round(r_lor.r_squared, digits=5))
println("Gaussian:   R² = ", round(r_gau.r_squared, digits=5))
println("Voigt:      R² = ", round(r_voi.r_squared, digits=5))

Check residuals visually — the model with the smallest systematic patterns in the residuals is the best choice, not necessarily the one with the highest R².

Note

Pseudo-Voigt has one more parameter than Lorentzian or Gaussian. A modest improvement in R² may not be statistically meaningful. See Fitting Statistics for model comparison criteria (AIC, BIC, F-test).