Fit Overlapping Peaks

When two or more peaks overlap, fitting them individually gives wrong widths and areas. Fit them simultaneously instead.

Problem

A spectral region contains multiple peaks that are not fully resolved.

Solution

Construct an example with two overlapping Lorentzians:

using OpticalSpectroscopy
using CurveFitModels
using CairoMakie

x = collect(range(1900, 2200, length=800))
y = lorentzian([0.35, 2040.0, 18.0, 0.0], x) .+
    lorentzian([0.50, 2070.0, 22.0, 0.0], x) .+
    0.01 .+ 0.004 .* randn(length(x))

Specify the Number of Peaks

Use n_peaks to tell fit_peaks how many peaks to fit:

result = fit_peaks(x, y, (1900, 2200); n_peaks=2)

The fitter detects peaks automatically for initial guesses and keeps the n_peaks most prominent ones. If auto-detection finds fewer peaks than requested, synthetic guesses fill the gaps.

Inspect the Decomposition

Each peak is accessible by index:

result[1][:center].value    # first peak position
result[2][:center].value    # second peak position

predict_peak(result, 1)     # curve for peak 1
predict_peak(result, 2)     # curve for peak 2
predict_baseline(result)    # baseline only

Visualize Individual Peaks

Overlay individual peak curves using predict_peak and predict_baseline:

using CairoMakie

fig = Figure(size=(700, 500))
ax = Axis(fig[1, 1], xlabel="Wavenumber (cm⁻¹)", ylabel="Intensity")
scatter!(ax, x, y, label="Data", markersize=5)
lines!(ax, x, predict(result, x), label="Composite fit", linewidth=2)
lines!(ax, x, predict_peak(result, 1, x), linestyle=:dash, label="Peak 1")
lines!(ax, x, predict_peak(result, 2, x), linestyle=:dash, label="Peak 2")
lines!(ax, x, predict_baseline(result, x), linestyle=:dot, label="Baseline")
axislegend(ax)
fig

Control the Baseline

The polynomial baseline order defaults to 1 (linear). For a constant baseline or higher-order polynomial:

result = fit_peaks(x, y, (1900, 2200); n_peaks=2, baseline_order=0)  # constant
result = fit_peaks(x, y, (1900, 2200); n_peaks=2, baseline_order=2)  # quadratic

Tips

Start with n_peaks=1 and increase only if residuals show systematic patterns
If the fit doesn't converge well, try providing manual initial guesses (see Provide Manual Initial Guesses)
Use report(result) to see all peak parameters and fit quality at a glance