def test_running(self, extrapolate_lowloss):
s = hs.signals.EELSSpectrum(np.arange(200))
gaussian = Gaussian()
gaussian.A.value = 50
gaussian.sigma.value = 10
gaussian.centre.value = 20
s_ll = hs.signals.EELSSpectrum(gaussian.function(np.arange(0, 200, 1)))
s_ll.axes_manager[0].offset = -50
s.fourier_ratio_deconvolution(s_ll,
extrapolate_lowloss=extrapolate_lowloss)
def setup_method(self, method):
# Create an empty spectrum
s = hs.signals.EELSSpectrum(np.zeros((3, 2, 1024)))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 0.02
energy_axis.offset = -5
gauss = Gaussian()
gauss.centre.value = 0
gauss.A.value = 5000
gauss.sigma.value = 0.5
gauss2 = Gaussian()
gauss2.sigma.value = 0.5
# Inflexion point 1.5
gauss2.A.value = 5000
gauss2.centre.value = 5
s.data[:] = (gauss.function(energy_axis.axis) +
gauss2.function(energy_axis.axis))
self.signal = s
def setup_method(self, method):
# Create an empty spectrum
s = hs.signals.EELSSpectrum(np.zeros((2, 3, 64)))
energy_axis = s.axes_manager.signal_axes[0]
energy_axis.scale = 0.2
energy_axis.offset = -5
gauss = Gaussian()
gauss.centre.value = 0
gauss.A.value = 5000
gauss.sigma.value = 0.5
s.data = s.data + gauss.function(energy_axis.axis)
np.random.seed(1)
s.add_gaussian_noise(1)
self.signal = s
class SEE(Component):
"""Secondary electron emission component for Photoemission Spectroscopy
Attributes
----------
A : float
Phi : float
B : float
sigma : float
Resolution parameter.
"""
def __init__(self, A=1., Phi=1., B=0., sigma=0):
Component.__init__(self, ('A', 'Phi', 'B', 'sigma'))
self.A.value, self.Phi.value, self.B.value, self.sigma.value = \
A, Phi, B, sigma
self._position = self.Phi
# Boundaries
self.A.bmin = 0.
self.A.bmax = None
self.convolved = True
# Gradients
self.A.grad = self.grad_A
self.Phi.grad = self.grad_Phi
self.B.grad = self.grad_B
self.sigma.grad = self.grad_sigma
# Resolution functions
self.gaussian = Gaussian()
self.gaussian.centre.free, self.gaussian.A.free = False, False
self.gaussian.sigma.free = True
self.gaussian.A.value = 1.
def __repr__(self):
return 'SEE'
def function(self, x):
"""
"""
if self.sigma.value:
self.gaussian.sigma.value = self.sigma.value
self.gaussian.origin.value = (x[-1] + x[0]) / 2
return np.convolve(
self.gaussian.function(x),
np.where(
x > self.Phi.value,
self.A.value * (x - self.Phi.value) /
(x - self.Phi.value + self.B.value)**4, 0), 'same')
else:
return np.where(
x > self.Phi.value,
self.A.value * (x - self.Phi.value) /
(x - self.Phi.value + self.B.value)**4, 0)
def grad_A(self, x):
"""
"""
if self.sigma.value:
self.gaussian.sigma.value = self.sigma.value
self.gaussian.origin.value = (x[-1] + x[0]) / 2
return np.convolve(
self.gaussian.function(x),
np.where(x > self.Phi.value, (x - self.Phi.value) /
(x - self.Phi.value + self.B.value)**4, 0), 'same')
else:
return np.where(x > self.Phi.value, (x - self.Phi.value) /
(x - self.Phi.value + self.B.value)**4, 0)
def grad_sigma(self, x):
"""
"""
self.gaussian.sigma.value = self.sigma.value
self.gaussian.origin.value = (x[-1] + x[0]) / 2
return np.convolve(
self.gaussian.grad_sigma(x),
np.where(
x > self.Phi.value,
self.A.value * (x - self.Phi.value) /
(x - self.Phi.value + self.B.value)**4, 0), 'same')
def grad_Phi(self, x):
"""
"""
if self.sigma.value:
self.gaussian.sigma.value = self.sigma.value
self.gaussian.origin.value = (x[-1] + x[0]) / 2
return np.convolve(
self.gaussian.function(x),
np.where(x > self.Phi.value,
(4 * (x - self.Phi.value) * self.A.value) /
(self.B.value + x - self.Phi.value)**5 -
self.A.value / (self.B.value + x - self.Phi.value)**4,
0), 'same')
else:
return np.where(
x > self.Phi.value, (4 * (x - self.Phi.value) * self.A.value) /
(self.B.value + x - self.Phi.value)**5 - self.A.value /
(self.B.value + x - self.Phi.value)**4, 0)
def grad_B(self, x):
if self.sigma.value:
self.gaussian.sigma.value = self.sigma.value
self.gaussian.origin.value = (x[-1] + x[0]) / 2
return np.convolve(
self.gaussian.function(x),
np.where(
x > self.Phi.value,
-(4 * (x - self.Phi.value) * self.A.value) /
(self.B.value + x - self.Phi.value)**5, 0), 'same')
else:
return np.where(
x > self.Phi.value,
-(4 * (x - self.Phi.value) * self.A.value) /
(self.B.value + x - self.Phi.value)**5, 0)
class Vignetting(Component):
"""
Model the vignetting of the lens with a cos^4 law multiplied by lines on
the edges
"""
def __init__(self):
Component.__init__(self,
['optical_center',
'height',
'period',
'left_slope',
'right_slope',
'left',
'right',
'sigma'])
self.left.value = np.nan
self.right.value = np.nan
self.side_vignetting = False
self.fix_side_vignetting()
self.gaussian = Gaussian()
self.gaussian.centre.free, self.gaussian.A.free = False, False
self.sigma.value = 1.
self.gaussian.A.value = 1.
self.period.value = 1.
self.extension_nch = 100
self._position = self.optical_center
def function(self, x):
sigma = self.sigma.value
x0 = self.optical_center.value
A = self.height.value
period = self.period.value
la = self.left_slope.value
ra = self.right_slope.value
l = self.left.value
r = self.right.value
ex = self.extension_nch
if self.side_vignetting is True:
x = x.tolist()
x = list(range(-ex, 0)) + x + \
list(range(int(x[-1]) + 1, int(x[-1]) + ex + 1))
x = np.array(x)
v1 = A * np.cos((x - x0) / (2 * np.pi * period)) ** 4
v2 = np.where(x < l,
1. - (l - x) * la,
np.where(x < r,
1.,
1. - (x - r) * ra))
self.gaussian.sigma.value = sigma
self.gaussian.origin.value = (x[-1] + x[0]) / 2
result = np.convolve(self.gaussian.function(x), v1 * v2, 'same')
return result[ex:-ex]
else:
return A * np.cos((x - x0) / (2 * np.pi * period)) ** 4
def free_side_vignetting(self):
self.left.free = True
self.right.free = True
self.left_slope.free = True
self.right_slope.free = True
self.sigma.free = True
def fix_side_vignetting(self):
self.left.free = False
self.right.free = False
self.left_slope.free = False
self.right_slope.free = False
self.sigma.free = False
def free_cos_vignetting(self):
self.optical_center.free = True
self.period.free = True
self.height.free = True
def fix_cos_vignetting(self):
self.optical_center.free = False
self.period.free = False
self.height.free = False