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Single Bragg edge fitting

This package contains python functions for the fitting of a single Bragg edge pattern. Currently implemented are:

• Advanced Bragg Edge Fitting: 7 parameters fit as in Santisteban et al., 2001 and Ramadhan et al., 2019 {a_0,b_0,a_{hkl},b_{hkl},λ_{hkl},σ,τ}

• Gaussian Bragg Edge Fitting: This methods takes the attenuation or transmission derivative and fits the edge to a Gaussian, returning centroid, height, and width of the Gaussian fit. The height is converted to the bragg edge slope and the bragg edge height is calculated as the integral of the gaussian fit.

IMPORTANT NOTES:

• In the following functions spectrum and spectrum_range, and eventually initial guesses and boundary conditions must all be in the same domain (by default is lambda (wavelenght) but could be bin index or tof).
• (!) For noisy data the fitting may be challenging. Try playing with initial guesses and boundary conditions to help the fitting module. Especially, try different inputs of initial guesses of the edge width and height.
• For increased efficiency of the image fitting it is highly reccomended to run first the fitting in debugging mode by setting the debug_idx on a desired pixel location, and use the obtained values as initial guesses.
• Boundary conditions may be useful in the cases of double edges / texture to impose the fitting of a specific Bragg edge.
• The advance Bragg edge fitting method works best setting the spectral range inclue a single Bragg edge.

Known bugs

• Fitting may fail in case of dataset containing inf’s and NaN’s values. If that is the case try increasing moving average or other image processing to cleanup data.

FUNCTION LIST:

EdgeFitting.py:

Module containing the fucntions for the Bragg edge fitting.

AdvancedBraggEdgeFitting

Advanced Bragg Edge Fitting (7 iterations) for a 1d array. Printout example:

INPUTS:

Parameter	Description
signal	1darray of the signal containing the Bragg edge (1darray) [REQUIRED]
spectrum	spectrum range corresponding to signal (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
est_pos	estimated bragg edge position (in spectrum_range dimension) [Default = 0]
est_sigma	expected Gaussian broadening [Default = 1]
est_alpha	expected decay constant, a moderator property [Default = 1]
pos_BC	boundary conditions for the Bragg edge position fit ([lambda1, lambda2]) [Default = 0]
sigma_BC	boundary conditions for the Gaussian broadening ([sigma1, sigma2]) [Default = 0]
alpha_BC	boundary conditions for the decay constant ([alpha1, alpha2]) [Default = 0]
est_w	expected edge width [Default = 0]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
bool_linear	flag to activate linear spectrum assumptions at the sides of the edge (otherwise exponential) [Default = False]
bool_print	flag to activate printing of figures [Default = False]

OUTPUTS: dictionary with the following fit in the dimension of the mask

Parameter	Description
‘t0’	fitted bragg edge position
‘sigma’	fitted Gaussian broadening
‘alpha’	fitted decay constant (moderator property)
‘a1, a2, a5, a6’	parameters for spectrum besides the edge: a1 and a2 before, a5 and a6 after the edge
‘final_result’	fitting result after 7th iteration
‘fitted_data’	final fitted spectrum
‘pos_extrema’	extrema of the Bragg edges
‘height’	fitted height of the Bragg edge

AdvancedBraggEdgeFitting2D

Advanced Bragg Edge Fitting (7 iterations) for a 2D stack of TOF data in the form of 3D array (x,y,lambda).

INPUTS:

Parameter	Description
Ttof	3darray of the image TOF stack containing the Bragg edge (x,y,lambda) [REQUIRED]
spectrum	spectrum range corresponding to Ttof third dimension (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
calibration_matrix	calibration matrix with the coefficients to convert from spectrum to lambda size (x,y,[X0,k]). Will convert to lambda using formula Y = X0 + kX where X is spectrum for each pixel (x,y) [Default = np.ndarray([0])]
mask	mask of where to perform the fit (x,y) [Default = np.ndarray([0])]
auto_mask	if True and mask is not given will automatically mask the region based on the mask_thresh thresholds [Default = True]
mask_thresh	low and high threshold for the automatic mask ([thresh_low, thresh_high]) [Default = np.ndarray([0])]
est_pos	estimated bragg edge position (in spectrum_range dimension) [Default = 0]
est_sigma	expected Gaussian broadening [Default = 1]
est_alpha	expected decay constant, a moderator property [Default = 1]
pos_BC	boundary conditions for the Bragg edge position fit ([lambda1, lambda2]) [Default = 0]
sigma_BC	boundary conditions for the Gaussian broadening ([sigma1, sigma2]) [Default = 0]
alpha_BC	boundary conditions for the decay constant ([alpha1, alpha2]) [Default = 0]
est_w	expected edge width [Default = 0]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
bool_linear	flag to activate linear spectrum assumptions at the sides of the edge (otherwise exponential) [Default = False]
bool_save	set to True to save output [Default = False]
bool_print	set to True to print output [Default = False]
debug_idx	pixel coordinates where to test the single pixel fitting ([pixel_x, pixel_y]) [Default = []]

OUTPUTS: dictionary with the following fit in the dimension of the mask

Parameter	Description
‘edge_position’	edge position
‘edge_height’	edge height
‘edge_width’	edge width
‘median_image’	median Transmission image in the selected lambda range

AdvancedDirectBraggEdgeFitting

Advanced Bragg Edge Fitting (direct fit of all parameters) for a 1d array. Printout example:

INPUTS:

Parameter	Description
signal	1darray of the signal containing the Bragg edge (1darray) [REQUIRED]
spectrum	spectrum range corresponding to signal (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
est_pos	estimated bragg edge position (in spectrum_range dimension) [Default = 0]
est_sigma	expected Gaussian broadening [Default = 1]
est_alpha	expected decay constant, a moderator property [Default = 1]
pos_BC	boundary conditions for the Bragg edge position fit ([lambda1, lambda2]) [Default = 0]
sigma_BC	boundary conditions for the Gaussian broadening ([sigma1, sigma2]) [Default = 0]
alpha_BC	boundary conditions for the decay constant ([alpha1, alpha2]) [Default = 0]
est_w	expected edge width [Default = 0]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
bool_linear	flag to activate linear spectrum assumptions at the sides of the edge (otherwise exponential) [Default = False]
bool_print	flag to activate printing of figures [Default = False]

OUTPUTS: dictionary with the following fit in the dimension of the mask

Parameter	Description
‘t0’	fitted bragg edge position
‘sigma’	fitted Gaussian broadening
‘alpha’	fitted decay constant (moderator property)
‘a1, a2, a5, a6’	parameters for spectrum besides the edge: a1 and a2 before, a5 and a6 after the edge
‘final_result’	fitting result after 7th iteration
‘fitted_data’	final fitted spectrum
‘pos_extrema’	extrema of the Bragg edges
‘height’	fitted height of the Bragg edge

AdvancedDirectBraggEdgeFitting2D

Advanced Bragg Edge Fitting (direct fit of all parameters) for a 2D stack of TOF data in the form of 3D array (x,y,lambda).

INPUTS:

Parameter	Description
Ttof	3darray of the image TOF stack containing the Bragg edge (x,y,lambda) [REQUIRED]
spectrum	spectrum range corresponding to Ttof third dimension (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
calibration_matrix	calibration matrix with the coefficients to convert from spectrum to lambda size (x,y,[X0,k]). Will convert to lambda using formula Y = X0 + kX where X is spectrum for each pixel (x,y) [Default = np.ndarray([0])]
mask	mask of where to perform the fit (x,y) [Default = np.ndarray([0])]
auto_mask	if True and mask is not given will automatically mask the region based on the mask_thresh thresholds [Default = True]
mask_thresh	low and high threshold for the automatic mask ([thresh_low, thresh_high]) [Default = np.ndarray([0])]
est_pos	estimated bragg edge position (in spectrum_range dimension) [Default = 0]
est_sigma	expected Gaussian broadening [Default = 1]
est_alpha	expected decay constant, a moderator property [Default = 1]
pos_BC	boundary conditions for the Bragg edge position fit ([lambda1, lambda2]) [Default = 0]
sigma_BC	boundary conditions for the Gaussian broadening ([sigma1, sigma2]) [Default = 0]
alpha_BC	boundary conditions for the decay constant ([alpha1, alpha2]) [Default = 0]
est_w	expected edge width [Default = 0]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
bool_linear	flag to activate linear spectrum assumptions at the sides of the edge (otherwise exponential) [Default = False]
bool_save	set to True to save output [Default = False]
bool_print	set to True to print output [Default = False]
debug_idx	pixel coordinates where to test the single pixel fitting ([pixel_x, pixel_y]) [Default = []]

OUTPUTS: dictionary with the following fit in the dimension of the mask

Parameter	Description
‘edge_position’	edge position
‘edge_height’	edge height
‘edge_width’	edge width
‘median_image’	median Transmission image in the selected lambda range

GaussianBraggEdgeFitting

Gaussian Bragg Edge Fitting for a 1d array. Printout example:

INPUTS:

Parameter	Description
signal	1darray of the spectrum containing the Bragg edge (1darray) [REQUIRED]
spectrum	spectrum range corresponding to signal (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
est_pos	estimated Bragg edge position [Default = 0]
est_wid	estimated Bragg edge width [Default = 0]
est_h	estimated Bragg edge height [Default = 0]
pos_BC	boundary conditions for the Bragg edge position fit ([lambda1, lambda2]) [Default = 0]
wid_BC	boundary conditions for the Bragg edge width fit ([lambda1, lambda2]) [Default = 0]
h_BC	boundary conditions for the Bragg edge height fit ([lambda1, lambda2]) [Default = 0]
bool_log	set to True to perform log norm and convert to attenuation [Default = True]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
interp_factor	if set, this is the factor by which the number of bins are multiplied by interpolation [Default = 0]
bool_print	flag to activate printing of figures [Default = False]

OUTPUTS: dictionary with the following fits

Parameter	Description
‘edge_position’	edge position
‘edge_height’	edge height
‘edge_width’	edge width
‘edge_slope’	edge slope
‘median_image’	median Transmission image in the selected lambda range

GaussianBraggEdgeFitting2D:

Gaussian Bragg Edge Fitting for a 2D stack of TOF data in the form of 3D array (x,y,lambda).

INPUTS:

Parameter	Description
Ttof	3darray of the image TOF stack containing the Bragg edge (x,y,lambda) [REQUIRED]
spectrum	spectrum range corresponding to signal (1darray) [REQUIRED]
spectrum_range	range corresponding to lambda where to perform the fitting ([lambda1, lambda2]) [Default = []]
calibration_matrix	calibration matrix with the coefficients to convert from spectrum to lambda size (x,y,[X0,k]). Will convert to lambda using formula Y = X0 + kX where X is spectrum for each pixel (x,y) [Default = np.ndarray([0])]
mask	mask of where to perform the fit (x,y) [Default = np.ndarray([0])]
auto_mask	if True and mask is not given will automatically mask the region based on the mask_thresh thresholds [Default = True]
mask_thresh	low and high threshold for the automatic mask ([thresh_low, thresh_high]) [Default = np.ndarray([0])]
est_pos	estimated bragg edge position [Default = 0]
est_wid	estimated bragg edge width [Default = 0]
est_h	estimated bragg edge height [Default = 0]
pos_BC	boundary conditions for the bragg edge position fit ([lambda1, lambda2]) [Default = 0]
wid_BC	boundary conditions for the bragg edge width fit ([lambda1, lambda2]) [Default = 0]
h_BC	boundary conditions for the bragg edge height fit ([lambda1, lambda2]) [Default = 0]
bool_log	set to True to perform log norm and convert to attenuation [Default = True]
bool_smooth	set to True to perform Savitzky-Golay filtering of the transmission derivative [Default = False]
smooth_w	window size of S-G filter [Default = 5]
smooth_n	order of S-G filter [Default = 1]
interp_factor	if set, this is the factor by which the number of bins are multiplied by interpolation [Default = 0]
bool_save	set to True to save output [Default = False]
bool_print	set to True to print output [Default = False]
debug_idx	pixel coordinates where to test the single pixel fitting ([pixel_x, pixel_y]) [Default = []]

OUTPUTS: dictionary with the following fits

Parameter	Description
‘edge_position’	edge position
‘edge_height’	edge height
‘edge_width’	edge width
‘edge_slope’	edge slope
‘median_image’	median Transmission image in the selected lambda range