spectroscopy4 params
Gaussian Peak Profile
The fundamental symmetric bell-shaped peak model describing thermal Doppler broadening and instrumental slit resolution.
$y = y_0 + A \exp\left( -\frac{(x - \mu)^2}{2\sigma^2} \right)$
Spectroscopy & Optics
Spectral Line Profiles, Peak Deconvolution & Broadening Models
Mathematical models engineered for resolving overlapping vibrational bands, atomic emission lines, Raman spectra, FTIR absorption, and optical transmission peaks with exact instrumental and physical broadening.
Target Disciplines:Raman SpectroscopyFTIRUV-VisPhotoluminescenceLaser PhysicsAstronomy
Common Fitting Challenges in Spectroscopy & Optics
- Deconvolving overlapping spectral bands without over-fitting baseline artifacts
- Separating thermal Doppler broadening (Gaussian) from natural lifetime damping (Lorentzian)
- Estimating robust initial peak centers and half-widths from noisy spectrometer data
AltaiPlot High-Performance Fitting Engine
- Real-time 60 FPS multi-peak deconvolution on high-density spectral channels
- Built-in AsLS and polynomial baseline correction before fitting
- Instant parameter bounds locking for physical FWHM and amplitude constraints
Spectroscopy & Optics Models (5)
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Lorentzian (Cauchy-Lorentz) Profile
The characteristic heavy-tailed peak profile describing natural radiative lifetime broadening and collisional damping.
$y = y_0 + \frac{2A}{\pi} \frac{\gamma}{4(x - \mu)^2 + \gamma^2}$
spectroscopy5 params
Pseudo-Voigt Profile
A linear combination of Gaussian and Lorentzian functions providing high-speed approximation of Voigt profile line shapes.
$y = y_0 + A \left[ \eta \frac{2}{\pi \gamma} \frac{1}{1 + 4\left(\frac{x - \mu}{\gamma}\right)^2} + (1 - \eta) \frac{2\sqrt{\ln 2}}{\sqrt{\pi} \gamma} \exp\left( -4\ln 2 \left(\frac{x - \mu}{\gamma}\right)^2 \right) \right]$
spectroscopy5 params
True Voigt Profile (Faddeeva Convolution)
The exact physical convolution of Gaussian Doppler broadening and Lorentzian lifetime broadening.
$V(x; \sigma, \gamma) = \int_{-\infty}^{\infty} G(x'; \sigma) L(x - x'; \gamma) \, dx' = \frac{\text{Re}[w(z)]}{\sigma \sqrt{2\pi}}$
spectroscopy5 params
Pearson VII Profile
A versatile continuous peak model bridging pure Gaussian and Lorentzian shapes via a variable exponential exponent (m).
$y = y_0 + A \left[ 1 + 4\left( 2^{1/m} - 1 \right) \left( \frac{x - \mu}{\gamma} \right)^2 \right]^{-m}$