Phase fitting
This package contains python functions for the fitting of crystalline phase transformation from the attenuation Bragg pattern. The model assumes that the measured linear attenuation coefficient μ, is a linear combination of phases with an a-priori reference linear attenuation coefficients φ.
Currently implemented are the solvers for the 2 phases case (i=1,2) and 3 phases case (i=1,2,3).
IMPORTANT NOTES:
- In the following functions spectrum, lambda_range_norm, lambda_range_edges must all be in the same domain (by default is lambda (wavelenght) but could also be bin index or tof).
- Currently texture is not implemented. For a refined method accuracy, this should be modeled in the reference phase linear attenuation coefficients.
FUNCTION LIST:
PhaseFitting.py:
Module containing the fucntions for the phase fitting.
PhaseRatioLinearCombination:
Fit two phases for a 1d array. Printout example:
INPUTS:
| Parameter | Description |
|---|---|
| lac | 1d array the attenuation -log(I/I0) (1darray) [REQUIRED] |
| spectrum | spectrum range corresponding to lac (1darray) [REQUIRED] |
| phase1lac | lac of the phase 1 (1darray) [REQUIRED] |
| phase2lac | lac of the phase 2 (1darray) [REQUIRED] |
| phase_spectrum | spectrum range corresponding to phase1lac and phase2lac (1darray) [REQUIRED] |
| lambda_range_norm | lambda range where to normalize spectra ([lambda1, lambda2]) [REQUIRED] |
| lambda_range_fit = | lambda range where to do the fitting ([lambda1, lambda2]) [REQUIRED] |
| est_phi | estimate phase 1 weight [Default = 0.5] |
| method | fitting method [Default = ‘least_squares’] |
| bool_SG | set to True to perform Savitzky-Golay filtering [Default = False] |
| SG_w | window size of S-G filter [Default = 5] |
| SG_n | order of S-G filter [Default = 1] |
| bool_print | set to True to print output [Default = False] |
OUTPUTS: dictionary with the following fit in the dimension of the mask
| Parameter | Description |
|---|---|
| ‘phi’ | phase 1 weight |
PhaseRatioLinearCombination2D:
Fit two phases, for a 2D stack of TOF data in the form of 3D array (x,y,lambda). Printout example:
INPUTS:
| Parameter | Description |
|---|---|
| lac_tof | 3darray the attenuation -log(I/I0) (x,y,lambda) [REQUIRED] |
| spectrum | spectrum range corresponding to lac (1darray) [REQUIRED] |
| phase1lac | lac of the phase 1 (1darray) [REQUIRED] |
| phase2lac | lac of the phase 2 (1darray) [REQUIRED] |
| phase_spectrum | spectrum range corresponding to phase1lac and phase2lac (1darray) [REQUIRED] |
| lambda_range_norm | lambda range where to normalize spectra ([lambda1, lambda2]) [REQUIRED] |
| lambda_range_fit | lambda range where to do the fitting ([lambda1, lambda2]) [REQUIRED] |
| 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_phi | estimate phase 1 weight [Default = 0.5] |
| method | fitting method [Default = ‘least_squares’] |
| bool_SG | set to True to perform Savitzky-Golay filtering [Default = False] |
| SG_w | window size of S-G filter [Default = 5] |
| SG_n | order of S-G filter [Default = 1] |
| 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 |
|---|---|
| ‘phase_ratio’ | phase 1 weight |
PhaseRatioLinearCombination3:
Fit three phases.
INPUTS:
| Parameter | Description |
|---|---|
| lac | 1d array the attenuation -log(I/I0) (1darray) [REQUIRED] |
| spectrum | spectrum range corresponding to lac (1darray) [REQUIRED] |
| phase1lac | lac of the phase 1 (1darray) [REQUIRED] |
| phase2lac | lac of the phase 2 (1darray) [REQUIRED] |
| phase3lac | lac of the phase 3 (1darray) [REQUIRED] |
| phase_spectrum | spectrum range corresponding to phase1lac,phase2lac and phase3lac (1darray) [REQUIRED] |
| lambda_range_norm | lambda range where to normalize spectra ([lambda1, lambda2]) [REQUIRED] |
| lambda_range_edges | lambda range where to do the fitting ([lambda1, lambda2]) [REQUIRED] |
| est_f1 | estimate phase 1 weight [Default = 0.333] |
| est_f2 | estimate phase 2 weight [Default = 0.333] |
| est_f3 | estimate phase 3 weight [Default = 0.334] |
| method | fitting method [Default = ‘least_squares’] |
| bool_SG | set to True to perform Savitzky-Golay filtering [Default = False] |
| SG_w | window size of S-G filter [Default = 5] |
| SG_n | order of S-G filter [Default = 1] |
| bool_print | set to True to print output [Default = False] |
OUTPUTS: dictionary with the following fit in the dimension of the mask
| Parameter | Description |
|---|---|
| ‘phi1’ | phase 1 weight |
| ‘phi2’ | phase 2 weight |
| ‘phi3’ | phase 3 weight |
PhaseRatioLinearCombination32D:
Fit three phases, for a 2D stack of TOF data in the form of 3D array (x,y,lambda).
INPUTS:
| Parameter | Description |
|---|---|
| lac_tof | 3darray the attenuation -log(I/I0) (x,y,lambda) [REQUIRED] |
| spectrum | spectrum range corresponding to lac (1darray) [REQUIRED] |
| phase1lac | lac of the phase 1 (1darray) [REQUIRED] |
| phase2lac | lac of the phase 2 (1darray) [REQUIRED] |
| phase3lac | lac of the phase 3 (1darray) [REQUIRED] |
| phase_spectrum | spectrum range corresponding to phase1lac,phase2lac and phase3lac (1darray) [REQUIRED] |
| lambda_range_norm | lambda range where to normalize spectra ([lambda1, lambda2]) [REQUIRED] |
| lambda_range_edges | lambda range where to do the fitting ([lambda1, lambda2]) [REQUIRED] |
| 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_f1 | estimate phase 1 weight [Default = 0.333] |
| est_f2 | estimate phase 2 weight [Default = 0.333] |
| est_f3 | estimate phase 3 weight [Default = 0.334] |
| method | fitting method [Default = ‘least_squares’] |
| bool_SG | set to True to perform Savitzky-Golay filtering [Default = False] |
| SG_w | window size of S-G filter [Default = 5] |
| SG_n | order of S-G filter [Default = 1] |
| 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 |
|---|---|
| ‘phase1_ratio’ | phase 1 weight |
| ‘phase2_ratio’ | phase 2 weight |
| ‘phase3_ratio’ | phase 3 weight |