CarsFit

Least-square fit of experimental CARS spectra.

class carspy.cars_fit.CarsFit(spec_cars, nu_spec, ref_fac=100.0, bg_cars=None, spec_stokes=None, bg_stokes=None, fit_mode=None, **kwargs)[source]

Fitting experimental CARS spectrum.

Note

It can also be used to fit the laser linewidth or slit function.

Input measured CARS spectrum and its background.

Parameters
spec_cars1d array of floats

Measured CARS spectrum.

nu_spec1d array of floats

Spectral range (axis) of the supplied CARS spectrum in [\(\mathrm{cm}^{-1}\)]. This can either be absolute values or Raman shifted ones.

ref_facfloat

Refining factor based on the supplied spectral domain, by default 100. This factor is used in the fitting procedure to synthesize spectra with much higher spectral resolution to be compared (after downsampling) with the supplied (expt.) CARS spectrum. Higher value will result in more accurate spectra at the cost of CPU time.

bg_cars1d array of floats

Background noise for the measured CARS spectrum.

spec_stokes1d array of floats

Measured broadband Stokes profile (usually with Ar), by default None. If not supplied, it is assumed that spec_cars is already corrected by the Stokes profile.

bg_stokes1d array of floats

Background noise for the measured Stokes profile.

fit_modedict, optional

A dictionary containing the control parameters used to perform the CARS fit. By default:

power_factor0

0 (fit I) or 1 (fit sqrt(I)).

downsample‘local_mean’

Choose between ‘local_mean’ (highly efficient custom algorithm) and ‘interp’ (interpolation with numpy.interp).

slit‘sVoigt’

Choose between (asymmetric) ‘sVoigt’ and ‘sGaussian’ as the slit impulse response function, see the documentations for carspy.convol_fcn.asym_Voigt and carspy.convol_fcn.asym_Gaussian. ‘sGaussian’ will be deprecated in future updates.

pump_ls‘Gaussian’

‘Gaussian’ or ‘Lorentzian’ laser lineshape.

chi_rs‘G-matrix’

Choose between ‘isolated’ and ‘G-matrix’ for the consideration of pressure effects.

convol‘Kataoka’

‘Kataoka’/’K’ (double convolution) or ‘Yuratich’/’Y’ (single convolution).

doppler_effectTrue

Whether or not to consider Doppler effect on the Raman lineshape.

chem_eqFalse

Whether or not to assume chemical equilibrium during the fit.

fit‘custom’

Type of build-in fitting setups: ‘T_x’ or ‘custom’.

  • ‘T_x’: fitting variables related to the experimental setup (e.g., spectrometer) are inheritted from an existing fit and fixed. Only temperature and species concentrations are by default allowed to vary.

  • ‘custom’: all fitting variables need to be provided before a fit can process.

See carspy.cars_fit.CarsFit.ls_fit for details.

Other Parameters
**kwargs:

This method also allows the keyword arguments found for initializing carspy.cars_synth.CarsSpectrum.

cars_expt_synth(nu_expt, x_mol, temperature, del_Tv, nu_shift, nu_stretch, pump_lw, param1, param2, param3, param4, param5, param6)[source]

Synthesize a CARS spectrum based on the experimental spectral domain.

Parameters
nu_expt1d array of floats

The spectral axis determined in the experiment. This is used as the independent variable during the fit.

x_molfloat

Mole fraction of probed molecule.

temperaturefloat

Temperature in the probe volume in [K].

nu_shiftfloat

Shift applied to correctly center the spectrum in [\(\mathrm{cm}^{-1}\)].

nu_strechfloat

Strech applied to nu to compensate for incorrect dispersion calibration.

pump_lwfloat

Pump laser linewdith in [\(\mathrm{cm}^{-1}\)].

del_Tvfloat

The amount vibrational temperature exceeds the rotational temperature.

param1, param2, param3, param4, param5, param6float

Fitting parameters for the slit function

ls_fit(**kwargs)[source]

Fitting the experimental CARS spectrum.

Attention

The least-quare fit module lmfit is necessary for this method. Please be aware that certain Python versions may not be supported by lmfit. For displaying the fit results matplotlib will be needed as well.

Parameters
add_paramsnested tuple, optional

List of parameters controlling the fitting process. This option can be used to modify these initial parameters:

(('temperature', 2000, True, 250, 3000),
 ('del_Tv', 0, False),
 ('x_mol', 0.6, x_mol_var, 0.2, 1.5),
 ('nu_shift', fit_params['nu_shift'], False),
 ('nu_stretch', fit_params['nu_stretch'], False),
 ('pump_lw', fit_params['pump_lw'], False),
 ('param1', fit_params['param1'], False),
 ('param2', fit_params['param2'], False),
 ('param3', fit_params['param3'], False),
 ('param4', fit_params['param4'], False),
 ('param5', fit_params['param5'], False),
 ('param6', fit_params['param6'], False))

Each element of the nested tuple has the following element in order:

variable_namestr

All the arguments of carspy.cars_fit.CarsFit.cars_expt_synth are admissible variables except for the independent variable nu_expt.

initial_guessfloat

Initial guess or fixed value set for this variable.

variablebool

Determine if the variable is fixed (False) or not (True) during the fit.

lower_boundfloat

Lower boundary for the fitting variable. If not provided, negative infinity will be assumed.

upper_boundfloat

Upper boundary for the fitting variable. If not provide, positive infinity will be assumed.

For more details refer to the documentation of lmfit.Model.

path_fitstr

Path to the .pkl file of fitting result created by carspy.cars_fit.CarsFit.save_fit. This allows importing the fitting result of an existing spectrum, such that the inferred values of certain parameters (such as those related to the spectrometer) could be re-used in the next fit. A standard use case for this would be the fitting result of a room-temperature spectrum. This is needed if the fit in fit_mode of carspy.cars_fit.CarsFit is set to T_x.

show_fitbool, optional

If True, the fitting results will be reported and plotted. This is done via built-in functions in lmfit.

Other Parameters
**kwargs:

Keyword arguments of the Model.fit() method from the module lmfit.

preprocess(w_Stokes=0, nu_Stokes=0, crop=None, bg_subtract=False, bg_offset=0, bg_loc=None)[source]

Prepare the raw data for the fitting.

Parameters
w_Stokesfloat, optional

Center wavelength of the Stokes (e.g., dye laser) beam in [nm], by default 0.

nu_shiftfloat, optional

Center wavenumber of the Stokes beam in [\(\mathrm{cm}^{-1}\)], by default 0. In essence, w_Stokes and nu_Stokes are equivalent.

croplist, optional

Two indices to crop the spectrum with, by default None. Needs to be adjusted based on the experimental setup.

bg_subtractbool, optional

If True, an extra offset specified by bg_offset or determined within bg_loc is subtracted from the spectrum. This is not recommended as there shouldn’t be any physical background left if backgrounds are subtracted properly from the experimental spectrum beforehand. This might help if S/N is bad. By default it is set to False.

bg_offsetfloat, optional

Value used as background to subtract, be default 0. This is ignored if bg_log is provided.

bg_loclist, optional

Two indices to select the part of spectrum as background, only used if bg_subtract is True.

save_fit(dir_save, file_name)[source]

Save the fitting results in a pickle file.

Parameters
dir_savepath

A valid local directory.

file_namestr

File name of the pickle file to be saved.

carspy.cars_fit.bg_removal(spec, bg=None)[source]

Subtract background from spectrum and normalize it by its peak.

Parameters
spec1d array

Spectrum.

bgNone, 1d array, optional

Background noise.

carspy.cars_fit.slit_fit(*args, **kwargs)[source]

fitting the experimental slit function with a chosen lineshape

Attention

It is recommended to always look for initial parameters by using the eval_only option to roughly match the shape of the experimental slit function. The built-in initial parameters may not work for all the cases.

Parameters
nu1d array of floats

Spectral positions in [\(\mathrm{cm}^{-1}\)].

spec1d array of floats

Experimentally obtained slit function, usually an isolated atomic line from a calibration lamp.

init_paramsdict, optional

Initial fitting parameters for the lineshape. Refer to carspy.convol_fcn.asym_Voigt and carspy.convol_fcn.asym_Gaussian for the required arguments.

lineshapestr, optional

Type of the lineshape, by default ‘sGaussian’. Choose between ‘sGaussian’ and ‘sVoigt’.

eval_onlybool, optional

If true, returns the evaluation with given initial parameters.

save_fitbool, optional

If true, fit results will be saved in a pickle file.

dir_savestr, optional

If save_fit is true, a string to the desired directory for saving.

file_namestr, optional

If save_fit is true, specify the file name without file extension.

Returns
1d array

If eval_only is true, the evaluation result is returned.

Other Parameters
**kwargs:

Keyword arguments of the Model.fit() method from the module lmfit.

CarsSpectrum Lineshapes