Lineshapes

Functions used in the convolution of CARS spectrum.

  • Laser lineshape

  • Impulse spectral response function (ISRF) for the spectrometer slit

carspy.convol_fcn.asym_Gaussian(w, w0, sigma, k, a_sigma, a_k, offset, power_factor=1.0)[source]

Asymmetric super-Gaussian following [BLL+17].

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the asymmetric Gaussian function in wavenumber cm^(-1).

sigmafloat

FWHM of the Gaussian function in wavenumber cm^(-1).

kfloat

Controls the skewing of the asymmetry.

a_sigma, a_kfloat

Tuning factors for sigma and k.

offsetfloat

Background offset (from experimental spectrum).

power_factorfloat

Power factor on the output (e.g. can be used during slit fitting).

Returns
1d array of floats

Intensities of the peak-normalized asymmetric super-Gaussian over w.

carspy.convol_fcn.asym_Voigt(w, w0, sigma, k, a_sigma, a_k, sigma_L_l, sigma_L_h, offset, power_factor=1.0)[source]

Asymmetric super-Voigt.

Note

This is based on the super-Gaussian from [BLL+17], with additional convolution with two Lorentzian profiles to better capture slow-decaying wings in some experimental slit function

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the asymmetric Gaussian function in wavenumber cm^(-1).

sigmafloat

FWHM of the Gaussian function in wavenumber cm^(-1).

kfloat

Controls the skewing of the asymmetry.

a_sigma, a_kfloat

Tuning factors for sigma and k.

sigma_L_lfloat

FWHM of the Lorentzian function in wavenumber cm^(-1) for the lower half.

sigma_L_hfloat

FWHM of the Lorentzian function in wavenumber cm^(-1) for the higher half.

offsetfloat

Background offset.

power_factorfloat

Power factor on the output (e.g. can be used during slit fitting).

Returns
1d array of floats

Intensities of the peak-normalized asymmetric super-Gaussian over w.

carspy.convol_fcn.asym_Voigt_deprecated(w, w0, sigma_V_l, sigma_V_h, sigma_L_l, sigma_L_h, offset)[source]

Asymmetric Voigt profile following NRC.

Deprecated

This profile cannot capture certain slit functions with broadened Gaussian profile.

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the asymmetric Gaussian function in wavenumber cm^(-1).

sigma_V_lfloat

FWHM of the Voigt function in wavenumber cm^(-1) for the lower half.

sigma_V_hfloat

FWHM of the Voigt function in wavenumber cm^(-1) for the higher half.

sigma_L_lfloat

FWHM of the Lorentzian function in wavenumber cm^(-1) for the lower half.

sigma_L_hfloat

FWHM of the Lorentzian function in wavenumber cm^(-1) for the higher half.

offsetfloat

Background offset.

Returns
1d array of floats

Intensities of the peak-normalized asymmetric super-Gaussian over w.

carspy.convol_fcn.gaussian_line(w, w0, sigma)[source]

Generate a normalized Gaussian lineshape (integral equals to 1).

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the Gaussian lineshape in wavenumber cm^(-1).

sigmafloat

FWHM of the Gaussian lineshape wavenumber cm^(-1).

Returns
1d array of floats

Intensities of the normalized Gaussian lineshape over w.

carspy.convol_fcn.lorentz_line(w, w0, sigma)[source]

Generate a normalized Lorentzian lineshape (integral equals to 1).

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the Lorentzian lineshape in wavenumber cm^(-1).

sigmafloat

FWHM of the Lorentzian lineshape wavenumber cm^(-1).

Returns
1d array of floats

Intensities of the normalized Lorentzian lineshape over w.

carspy.convol_fcn.slit_ISRF(w, w0, param_1, param_2, param_3, param_4, param_5, param_6, offset, mode='sGaussian')[source]

Impulse spectral response function (ISRF) as the slit function.

Parameters
wsorted 1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the asymmetric Gaussian function in wavenumber cm^(-1).

param_1, param_2, param_3, param_4float

Parameters needed for the asymmetric ISRF depending on the mode.

  • ‘sGaussian’:
    sigmafloat

    FWHM of the Gaussian function in wavenumber cm^(-1).

    kfloat

    Controls the skewing of the asymmetry.

    a_sigma, a_kfloat

    Tuning factors for sigma and k.

  • ‘Voigt’:
    sigma_V_lfloat

    FWHM of the Voigt function in wavenumber cm^(-1) for the lower half.

    sigma_L_lfloat

    FWHM of the Lorentzian function in wavenumber cm^(-1) for the lower half.

    sigma_V_hfloat

    FWHM of the Voigt function in wavenumber cm^(-1) for the higher half.

    sigma_L_hfloat

    FWHM of the Lorentzian function in wavenumber cm^(-1) for the higher half.

offsetfloat

Background offset.

mode‘sGaussian’, str, optional

Two options for the ISRF:

  • Asymmetric super Gaussian: ‘sGaussian’.

  • Asymmetric Voigt: ‘Voigt’.

Returns
1d array of floats

Intensities of the peak-normalized asymmetric ISRF.

carspy.convol_fcn.voigt_line(w, w0, sigma_V, sigma_L)[source]

Generate an approximated Voigt lineshape following [Whi68].

Parameters
w1d array of floats

Spectral positions in wavenumber cm^(-1).

w0float

Center of the Lorentzian lineshape in wavenumber cm^(-1).

sigma_Vfloat

FWHM of the Voigt lineshape wavenumber cm^(-1).

sigma_Lfloat

FWHM of the Lorentzian lineshape wavenumber cm^(-1).

Returns
1d array

Intensities of the Voigt lineshape over w.

CarsFit Utilities