Source code for typhon.spectroscopy

# -*- coding: utf-8 -*-

"""Functions directly related to spectroscopy.
import numpy as np
from scipy import interpolate

import typhon.constants as constants

__all__ = [

[docs]def linewidth(f, a): """Calculate the full-width at half maximum (FWHM) of an absorption line. Parameters: f (ndarray): Frequency grid. a (ndarray): Line properties (e.g. absorption coefficients or cross-sections). Returns: float: Linewidth. Examples: >>> f = np.linspace(0, np.pi, 100) >>> a = np.sin(f)**2 >>> linewidth(f, a) 1.571048056449009 """ s = interpolate.UnivariateSpline(f, a - np.max(a)/2, s=0) return float(np.diff(s.roots()))
[docs]def doppler_broadening(t, f0, m): """Calculate the doppler broadening half-width half-maximum .. math:: \\gamma_D(T) = \\sqrt{ \\frac{2\\log(2) k_B T}{mc^2} } f_0 Parameters: t (float or ndarray): Temperature [Kelvin] f0 (float or like temperature): Central frequency [Hertz/invcm] m (float or like temperature): Mass [kilogram] Returns hwhm (like temperature): Half-width half-maximum [Hertz/invcm] """ return np.sqrt(2 * constants.boltzmann * t * np.log(2) / (m * constants.speed_of_light**2)) * f0
[docs]def boltzmann_level(elow, t, t0): """Computes the Boltzmann level function .. math:: K_1 = \\exp\\left(\\frac{E_l \\left[T-T_0\\right]}{k_B T T_0}\\right), where :math:`k_B` is the Boltzmann constant. All ndarrays must be of same size, any of the inputs can be ndarray Parameters: elow (float or ndarray): Lower state energy level [J] t (float or ndarray): Temperature [Kelvin] t0 (float or ndarray): Line temperature [Kelvin] Returns K1 (like input): How much Boltzmann statistics feeds the transition .. math:: S(T) = S(T_0)K_1K_2 \\frac{Q(T_0)}{Q(T)} """ return np.exp(elow * (t - t0) / (constants.boltzmann * t * t0))
[docs]def stimulated_emission(f0, t, t0): """Computes the stimulated emission function .. math:: K_2 = \\frac{1 - \\exp\\left( - \\frac{h f_0}{k_B T}\\right)} {1 - \\exp\\left( - \\frac{h f_0}{k_B T_0}\\right)}, with Planck constant :math:`h` and Boltzmann constant :math:`k_B`. Parameters: f0 (float or ndarray): Line frequency [Hz] t (float or ndarray): Temperature [Kelvin] t0 (float or ndarray): Line temperature [Kelvin] Returns K2 (like input): How stimulated the emission is .. math:: S(T) = S(T_0)K_1K_2 \\frac{Q(T_0)}{Q(T)} """ return (1. - np.exp(- constants.planck * f0/(constants.boltzmann * t))) / \ (1. - np.exp(- constants.planck * f0/(constants.boltzmann * t0)))