def get_elliptical_distortion(
self,
mask_radius,
scale=100,
amplitude=1000,
spread=2,
direct_beam_amplitude=500,
asymmetry=1,
rotation=0,
center=None,
):
"""Determine elliptical distortion of the diffraction pattern.
Parameters
----------
mask_radius : int
The radius in pixels for a mask over the direct beam disc
(the direct beam disc within given radius will be excluded
from the fit)
scale : float
An initial guess for the diffraction calibration
in 1/Angstrom units
amplitude : float
An initial guess for the amplitude of the polycrystalline rings
in arbitrary units
spread : float
An initial guess for the spread within each ring (Gaussian width)
direct_beam_amplitude : float
An initial guess for the background intensity from the direct
beam disc in arbitrary units
asymmetry : float
An initial guess for any elliptical asymmetry in the
pattern (for a perfectly circular pattern asymmetry=1)
rotation : float
An initial guess for the rotation of the (elliptical) pattern
in radians.
center : None or list
The center of the diffraction pattern.
Returns
-------
fit_params : np.array()
Array of fitting parameters. [scale, amplitude, spread,
direct_beam_amplitude, asymmetry,
rotation].
affine_matrix : np.array()
Array defining the affine transformation that corrects for lens
distortions in the diffraction pattern.
See Also
--------
pyxem.utils.calibration_utils.call_ring_pattern
"""
# Check that necessary calibration data is provided
if self.diffraction_pattern is None:
raise ValueError(
"This method requires a calibration diffraction pattern"
" to be provided. Please set self.diffraction_pattern equal"
" to some Signal2D."
)
standard_dp = self.diffraction_pattern
image_size = standard_dp.data.shape[0]
if center is None:
center = [(image_size -1)/2, (image_size -1)/2]
# Set diffraction pattern variable
x, y = np.mgrid[0:image_size, 0:image_size]
radius_map = calc_radius_with_distortion(x, y, center[0], center[1], 1, 0)
mask = radius_map < mask_radius
ref = standard_dp.data[~mask]
fullx,fully = [x,y]
pts = np.array([fully[~mask], fullx[~mask]]).ravel()
# Set initial parameters for fitting
x0 = [scale, amplitude, spread, direct_beam_amplitude, asymmetry, rotation]
# Fit ring pattern to experimental data
xf, cov = curve_fit(call_ring_pattern(center[0], center[1]), pts, ref, p0=x0)
# Set ring fitting parameters to attribute
self.ring_params = xf
# Calculate affine transform parameters from fit parameters
scaling = np.array([[1, 0], [0, xf[4] ** -0.5]])
rotation = np.array([[cos(xf[5]), -sin(xf[5])], [sin(xf[5]), cos(xf[5])]])
correction = np.linalg.inv(np.dot(rotation.T, np.dot(scaling, rotation)))
affine = np.array(
[
[correction[0, 0], correction[0, 1], 0.00],
[correction[1, 0], correction[1, 1], 0.00],
[0.00, 0.00, 1.00],
]
)
# Set affine matrix to attribute
self.affine_matrix = affine
return affine
def get_elliptical_distortion(self,
mask_radius,
scale=100,
amplitude=1000,
spread=2,
direct_beam_amplitude=500,
asymmetry=1,
rotation=0):
"""Determine elliptical distortion of the diffraction pattern.
Parameters
----------
mask_radius : int
The radius in pixels for a mask over the direct beam disc
(the direct beam disc within given radius will be excluded
from the fit)
scale : float
An initial guess for the diffraction calibration
in 1/Angstrom units
amplitude : float
An initial guess for the amplitude of the polycrystalline rings
in arbitrary units
spread : float
An initial guess for the spread within each ring (Gaussian width)
direct_beam_amplitude : float
An initial guess for the background intensity from the direct
beam disc in arbitrary units
asymmetry : float
An initial guess for any elliptical asymmetry in the
pattern (for a perfectly circular pattern asymmetry=1)
rotation : float
An initial guess for the rotation of the (elliptical) pattern
in radians.
Returns
-------
fit_params : np.array()
Array of fitting parameters. [scale, amplitude, spread,
direct_beam_amplitude, asymmetry,
rotation].
affine_matrix : np.array()
Array defining the affine transformation that corrects for lens
distortions in the diffraction pattern.
See Also
--------
pyxem.utils.calibration_utils.call_ring_pattern
"""
# Check that necessary calibration data is provided
if self.calibration_data.au_x_grating_dp is None:
raise ValueError(
"This method requires an Au X-grating diffraction "
"pattern to be provided. Please update the "
"CalibrationDataLibrary.")
# Set diffraction pattern variable
standard_dp = self.calibration_data.au_x_grating_dp
# Define grid values and center indices for ring pattern evaluation
image_size = standard_dp.data.shape[0]
xi = np.linspace(0, image_size - 1, image_size)
yi = np.linspace(0, image_size - 1, image_size)
x, y = np.meshgrid(xi, yi)
xcenter = (image_size - 1) / 2
ycenter = (image_size - 1) / 2
# Calculate eliptical parameters
mask = calc_radius_with_distortion(x, y, (image_size - 1) / 2,
(image_size - 1) / 2, 1, 0)
# Mask direct beam
mask[mask > mask_radius] = 0
standard_dp.data[mask > 0] *= 0
# Manipulate measured data for fitting
ref = standard_dp.data[standard_dp.data > 0]
ref = ref.ravel()
# Define points for fitting
pts = np.array(
[x[standard_dp.data > 0].ravel(),
y[standard_dp.data > 0].ravel()]).ravel()
# Set initial parameters for fitting
x0 = [
scale, amplitude, spread, direct_beam_amplitude, asymmetry,
rotation
]
# Fit ring pattern to experimental data
xf, cov = curve_fit(call_ring_pattern(xcenter, ycenter),
pts,
ref,
p0=x0)
# Set ring fitting parameters to attribute
self.ring_params = xf
# Calculate affine transform parameters from fit parameters
scaling = np.array([[1, 0], [0, xf[4]**-0.5]])
rotation = np.array([[cos(xf[5]), -sin(xf[5])],
[sin(xf[5]), cos(xf[5])]])
correction = np.linalg.inv(
np.dot(rotation.T, np.dot(scaling, rotation)))
affine = np.array([[correction[0, 0], correction[0, 1], 0.00],
[correction[1, 0], correction[1, 1], 0.00],
[0.00, 0.00, 1.00]])
# Set affine matrix to attribute
self.affine_matrix = affine
return affine