Package `slstools`

Python package slstools contains several helper functions and classes for reading in data from the SCM SLS setup, Miescat program, generating models for the scattering of spheres of given diameter and polydispersity and fitting those models to the experimental data. The scattering calculations are based on miepython.

Author: Roy Hoitink L.D.Hoitink@uu.nl

Classes

class Experiment (filename, normalise=True, K_unit='m', remove_data_after_pole=True, **kwargs)

Helper class for data generated by the SCM SLS setup.

For example usage, see Fit class.

Attributes

filepath : pathlib.Path: Path object of the file containing the SLS data
data : numpy.ndarray: Numpy array containing all raw data from the file.
theta : numpy.ndarray: Numpy array containing the scattering angles in degrees.
intensity_uncor : numpy.ndarray: Numpy array containing scattering intensities, not corrected for scattering volume (perpendicular polarisation).
intensity : numpy.ndarray: Numpy array containing scattering intensities, corrected for scattering volume (perpendicular polarisation).
K : numpy.ndarray: Numpy array containing the scattering angles (in units of K_unit).
K_unit : str: (inverse) unit of K, one of [nm, µm, m].
temperature : numpy.ndarray: Numpy array containing temperatures that were measured by the setup.

Initialisation of the class, assigns the data as class variables.

Parameters

filename : str: Path to file
normalise : bool, optional: Whether or not to normalise the intensity data to 1. The default is True.
K_unit : str, optional: Inverse units of K, one of [nm, µm, m]. E.g. if nm is given a K_unit, K will be given in units of. The default is m.

Methods

def correct_for_reflection(self, n_m=1.333, n_glass=1.49)

Correct the intensity for reflection

Stores the corrected intensity as intensity atrribute of the class, to allow for easier fitting. The old intensities are now stored in the intensity_reflection_uncor attribute.

Due to reflections, we need to correct the measured intensity for reflection at the glass-air interface of the toluene vessel as follows:

$I_{cor}(\theta) = I_m(\theta)-R*I_m(\pi - \theta)$

with

$I_m(\theta)$ the measured intensity at a certain angle $\theta$
$R = \left( \frac{n_{glass} - n_{air}}{n_{glass}+ n_{air}} \right)^2 +\left( \frac{n_{glass} - n_{solvent}}{n_{glass}+ n_{solvent}} \right)^2$
$n_{air} = 1.00$ , $n_{glass}=$ n_glass , $n_{solvent}=$ n_m

Parameters

n_m : float, optional: Refractive index of the medium, by default 1.333 (water).
n_glass : float, optional: Refractive index of the glass, by default 1.49.

def recalculate_K(self, n_m=1.333, wavelength=632.8)

Recalculate the K attribute of the instance, using the new medium refractive index and laser wavelength

Parameters

n_m : float or complex, optional: Refractive index of the medium, by default 1.333.
wavelength : float, optional: Vacuum wavelength of the laser in nm, by default 632.8.

class Fit (experiment, model, fit_theta_bounds=(45.0, 110.0), model_kwargs={})

Class for performing fitting a model to experimental data.

Example usage

from slstools import Experiment, Model, Fit
experiment = Experiment("Sample01.sls", K_unit="nm")
model = Model(d=1000, pd=5, n_p=1.4345, n_m=1.333)

fit = Fit(experiment, model, model_kwargs=dict(K_unit="nm"))

optimal_model = fit.fit()
fit.save() # save parameters in same directory as the experiment

Initialize fitting a given Model to given Experiment

Parameters

experiment : str or Experiment: The experiment that is used for fitting, if a str is given this will be passed as filename to the Experiment class.
model : Model: Intial model that will be used for the fit, make sure to choose a sensible starting diameter and polydispersity as it helps to speed up the fitting. Also use the correct refractive indices for the particle and medium.
fit_theta_bounds : tuple, optional: Range of theta (scattering angle) that will be used for fitting data, by default (45.,110.).
model_kwargs : dict, optional: Extra keyword arguments to pass onto the final model, by default {}.

Methods

def fit(self, debug=False)

Function to perform the actual fitting of the model to the experiment

Parameters

debug : bool, optional: Whether or not to output intermediate fitting parameters, by default False.

Returns

Model The Model with parameters that best fit the experiment Note: the intensities should be multiplied with self.optimal_params[0] to be accurate to the experiment's intensities.

def save(self, filename=None, overwrite=True, extra_info={}, save_theta=False)

Saves a dictionary, to a pickle file, containing a model_parameters part which can directly be plugged into the Model class and a fit_info part which gives info on what file was fitted to, the theta range and the prefactor used for plotting model and experiment together.

Parameters

filename : str, optional: Filename to save the data as dictionary in pkl format, by default None, which results in saving it as [experiment_filename]_fit.pkl
overwrite : bool, optional: Whether or not to overwrite the file if it already exists, by default True
extra_info : dict, optional: Extra data in dictionary form to store in the fit_info, by default {}
overwrite : bool, optional: Whether or not to save the list of angles (theta), by default False

Returns

bool Whether or not it succeeded in saving the file

class Miescat (filename, K_unit='m', **kwargs)

Helper class for data generated by the miescat program.

Attributes

data : numpy.ndarray: Numpy array containing all raw data from the file.
theta : numpy.ndarray: Numpy array containing the scattering angles in degrees.
K : numpy.ndarray: Numpy array containing the scattering angles (in units of K_unit).
K_unit : str: (inverse) unit of K, one of [nm, µm, m].
intensity : numpy.ndarray: Numpy array containing (normalised) scattering intensities (perpendicular polarised)
intensity_par : numpy.ndarray: Numpy array containing (normalised) scattering intensities (parallel polarised)

Initialisation of the class, assigns the data to objects attributes

Parameters

filename : str: Path to the file that contains the miescat data.
K_unit : str, optional: (inverse) unit of K, one of [nm, µm, m], by default "m".

class Model (n_p, d=1000.0, pd=0.0, n_m=1.333, wavelength=632.8, theta=None, K_unit='m', normalise=True)

Helper class to create a model for scattering spheres of given diameter (and polydispersity).

Example usage

import matplotlib.pyplot as plt
from slstools import Model

# intialise class with spheres of 1200 nm in diameter
# with a polydispersity of 5%
model = Model(d=1200.,pd=5.,n_p=1.4345)
plt.plot(model.K, model.intensity)
plt.xlabel(r"K ($%s^{-1}$)" % model.K_unit)
plt.ylabel("Normalised intensity")
plt.yscale("log")
plt.show()

Attributes

K : numpy.ndarray: Numpy array containing the scattering angles in units of K_unit.
intensity : numpy.ndarray: Numpy array containing scattering intensities for each angle (perpendicular polarisation).

Initialisation of the class, assigns data to class attributes and calculates model from given parameters.

Parameters

n_p : float|complex: (complex) refractive index of the particle.
d : float, optional: Diameter of the particle in nm, by default 1000.0.
pd : float, optional: Polydispersity of the system in % (e.g. 5 for 5% p.d.), by default 0.0.
n_m : float, optional: Refractive index of the medium, by default 1.333 (water).
wavelength : float, optional: Vacuum wavelength of the laser in nm, by default 632.8 (HeNe laser).
theta : numpy.ndarray, optional: List of angles to calculate intensities for, by default np.linspace(0.0, 180.0, 361)
K_unit : str, optional: (inverse) unit of scattering angle K, by default m.
normalise : bool, optional: Whether or not to normalise the intensities to 1.0, by default True.