foofit

X-ray reflectivity (XRR) fitting library using the Parratt recursion formalism and the refraction-corrected master formula.

Installation

Requires git to be installed.

pip install git+https://github.com/hgstei/foofit.git

Quick start

from foofit import *

# use the bundled example dataset (polystyrene on silicon)
si_ps_xrr = example_data

params = Parameters()
params.add('numbLayers', value=1, vary=False)
params.add('wavelength', value=1.0, vary=False)
params.add('I0', value=1, vary=False)
params.add('bkg', value=0, vary=False)
params.add('pre_rho', value=0, vary=False)
params.add('pre_beta', value=0, vary=False)
params.add('layer0_dd', value=220, min=150, max=300, vary=True)
params.add('layer0_rho', value=0.25, min=0.1, max=0.4, vary=True)
params.add('layer0_sig', value=5, min=0.5, max=15, vary=True)
params.add('layer0_beta', value=0, vary=False)
params.add('sub_rho', value=0.71, vary=False)
params.add('sub_sig', value=4, min=0.5, max=10, vary=True)
params.add('sub_beta', value=0, vary=False)

# single fit
performFit(si_ps_xrr, params, fitFunc=xrr_parratt_fit,
           method='powell', qmin=0.0, qmax=0.4, plot=2,
           outputName='my_sample', weight=2)

# Monte Carlo error analysis (parallelized)
params2 = loadParams('my_sample_<timestamp>_fit.fitParams', lowLim=0.3, highLim=0.3)
performFit_mc(si_ps_xrr, params2, fitFunc=xrr_parratt_fit,
              method='powell', qmin=0.0, qmax=0.4,
              outputName='my_sample', weight=2, NN=250)

# corner plot of MC parameter distributions
analyze_mc('my_sample_<timestamp>_fit_mc.fitParams')

See example.ipynb for a full worked example and foofit_manual.pdf for the full manual.

Interactive plots in Jupyter

Uncomment the appropriate line at the top of your notebook:

# %matplotlib widget
# (JupyterLab — requires: pip install ipympl)
# %matplotlib notebook
# (classic Jupyter Notebook)

Note: do not add comments on the same line as a %matplotlib magic command — IPython does not treat # as a comment in magic arguments.

Parameters convention

Parameter	Description
numbLayers	number of layers between ambient and substrate (int, fixed)
wavelength	X-ray wavelength in Å (fixed)
I0, bkg	intensity scale factor and background
pre_rho, pre_beta	ambient medium optical constants
layer{n}_dd	layer thickness in Å
layer{n}_rho	layer electron density in e/ų
layer{n}_sig	layer roughness in Å
layer{n}_beta	layer absorption constant
sub_rho, sub_sig, sub_beta	substrate parameters

Layer index n starts at 0 (topmost layer, closest to ambient).

Functions

Function	Description
xrr_parratt_calc(params, qq, doConv=0)	Parratt recursion reflectivity
xrr_master_refractionCorrected_calc(params, qq, doConv=0)	Refraction-corrected master formula
xrr_parratt_fit / xrr_master_refractionCorrected_fit	Residual functions for lmfit
xrr_eDens(params, zz)	Electron density profile
xrr_eDens_zeroRoughness(params, zz)	Electron density profile (sharp interfaces)
xrr_beta(params, zz)	Absorption profile
xrr_beta_zeroRoughness(params, zz)	Absorption profile (sharp interfaces)
performFit(...)	Single fit with plotting and file output
performFit_mc(...)	Monte Carlo error analysis (parallelized with joblib)
loadParams(filename, lowLim, highLim)	Load saved .fitParams file into lmfit Parameters
analyze_mc(file, bins)	Corner plot of MC parameter distributions
example_data	Path to the bundled si_ps.xrr example dataset

Physical constants

Classical electron radius and critical-q prefactor are computed from astropy constants at import time:

r_e_AA   # classical electron radius in Å  (from astropy sigma_T)
qc_factor  # 4 * sqrt(r_e_AA * pi)