SpectraUtils

SpectraUtils

Utilities for constructing and evaluating spectroscopy line models. The package provides line-shape definitions, convenience helpers for bundling parameters into reusable Line objects, and utilities for estimating linewidths from physical conditions.

DopplerFree(depth, envelop, dip)

Callable representation of a Doppler-free spectral profile. The resulting shape multiplies a broad envelope envelop(x) by a saturation dip, returning envelop(x) * (1 - depth * dip(x)) when evaluated. The envelop and dip arguments can be any callable line-shape models (for example, Gaussian or Lorentzian).

Gaussian(sigma)

Callable representation of a Gaussian profile with standard deviation sigma. Call shape(x) to evaluate the profile at offset x.

Line(amplitude, position, shape)

Bundle a spectral line definition with an amplitude, position, and callable shape. Each field may be either a numeric value or a function that consumes a parameter set when the line is evaluated. Call the resulting object as line(x, p) to evaluate the profile at a scalar position and as line(xs, p) to broadcast over a vector of positions.

Abstract supertype for supported line-shape models.

Lorentzian(hwhm)

Callable representation of a Lorentzian profile with half-width at half-maximum hwhm. Invoke the object as shape(x) to evaluate the profile at offset x.

Smith(cross_relaxation, sigma, gamma)

Cross-relaxation–broadened line shape following Smith et al. (Phys. Rev. Lett. 26, 740). The profile smoothly blends a normalized Lorentzian–Gaussian product with a Gaussian term according to the dimensionless cross-relaxation factor cross_relaxation ∈ [0, 1]:

(1 - c) * e^{-(γ/2σ)^2}/erfc(γ/2σ) * (γ/π)/(x^2 + γ^2) * e^{-x^2/4σ^2}
  + c * Gaussian(x, σ)

The parameters are the Gaussian standard deviation sigma, the Lorentzian half-width at half-maximum gamma, and the mixing factor cross_relaxation. The analytic prefactor ensures the profile integrates to one for any parameter values.

Voigt(sigma, gamma)

Callable representation of the full Voigt profile with standard deviation sigma and Lorentzian half-width gamma. Evaluate using shape(x) to compute the line shape at offset x.

VoigtApprx(sigma, gamma)

Pseudo-Voigt approximation that blends Gaussian and Lorentzian profiles with standard deviation sigma and half-width at half-maximum gamma. Evaluate instances as shape(x) to compute the approximated Voigt profile at offset x.

gamma_hard_sphere(p, T; μ, cs)

Compute the Lorentzian half-width at half-maximum (in cm⁻¹) under the hard-sphere collisional model. The calculation uses the pressure p (Pa), temperature T (K), reduced mass μ (kg), and average relative speed cs (m/s).

Evaluate the Gaussian profile with standard deviation σ.

Evaluate the Lorentzian profile with half-width at half-maximum γ.

sigma_doppler(f0, T; m)

Return the Doppler Gaussian standard deviation for a transition at frequency f0 and temperature T (in kelvin). The molecular mass m is supplied as a keyword argument and should be expressed in kilograms.

Evaluate the full Voigt profile for standard deviation σ and γ.