Full Spectrum Fitting

Table of contents

  1. Introduction
  2. How to use
  3. Behavior
  4. Method
  5. References

Introduction

Full Spectrum Fitting represents a spectrum as a sum of peak-shaped components. It can estimate component centers, amplitudes, and widths across the spectrum using Gaussian, Lorentzian, or Pseudovoigt curves. Baseline removal before fitting is recommended.

How to use

  1. Upload data, complete any preprocessing, and open Analytics Page.
  2. Select Full Spectrum Fitting from Select analytics plot.
  3. Choose Discrete to set the number of components, or Prominence-Based to select components by peak-prominence rank.
  4. Choose the Average, All, or one individual spectrum, then choose a Peak Shape.
  5. For Discrete, set the number of peaks, cofit range multiplier, and runtime control. For Prominence-Based, set the peak ranking threshold.
  6. Click Run Fit and review the fitted spectrum, residual, component parameters, and component curves. When fitting All, select which result to view.

Behavior

The Discrete algorithm repeatedly locates a prominent peak in the remaining residual and fits it with nearby components, up to the requested number of peaks. The Prominence-Based algorithm derives a prominence threshold from the ranked peaks in the initial spectrum and continues fitting peaks that meet that threshold in the residual. Its ranking value gives an approximate, not exact, component count.

For each fitted spectrum, SpectraGuru displays the original signal, individual components, their summed fit, and a residual plot. A component-parameter table lists fitted centers, amplitudes, full widths at half maximum (FWHM), and the Pseudovoigt mixing fraction when applicable. The residual plot reports root mean squared error (RMSE).

Method

The fitted signal is the sum of component curves:

\[\hat{I}(x)=\sum_{k=1}^{K} A_k S(x;\mu_k,w_k,\eta_k)\]

Here $A_k$ is amplitude, $\mu_k$ is center, $w_k$ is FWHM, and $\eta_k$ is used only for Pseudovoigt components. A Gaussian component has shape $G(x)=\exp[-4\ln(2)((x-\mu)/w)^2]$; a Lorentzian component has shape $L(x)=1/[1+4((x-\mu)/w)^2]$. The Pseudovoigt shape is $(1-\eta)G(x)+\eta L(x)$, with $0\leq\eta\leq1$. Fitting uses local nonlinear least squares, and $\mathrm{RMSE}=\sqrt{\operatorname{mean}[(I-\hat{I})^2]}$.

Parameter Tunable or fixed Implementation
Algorithm version Tunable Discrete or Prominence-Based
Peak shape Tunable Gaussian, Lorentzian, or Pseudovoigt
Number of peaks Tunable Discrete only; default 20, range 1–40
Peak ranking threshold Tunable Prominence-Based only; default 15, range 1–30
Cofit range multiplier Tunable Discrete only; default 0.7, range 0.4–1.0
Runtime control Tunable Discrete only; Quick, Standard, Slow, or Thorough limits nearby components cofit together
Peak detection and fitting Fixed SciPy find_peaks and curve_fit

References

  1. SciPy Developers. scipy.signal.find_peaks.
  2. SciPy Developers. scipy.optimize.curve_fit.