def __init__(self, *args, **kwargs):

"""

Modified hypespy EELS signal. Input can be array or EELSSpectrum type.

In the last case, additional *args and **kwargs are discarded.

"""

if len(args) > 0 and isinstance(args[0], hs.signals.EELSSpectrum):

# Pretend it is a hs signal, copy axes and metadata

sdict = args[0]._to_dictionary()

hs.signals.EELSSpectrum.__init__(self, **sdict)

else:

hs.signals.EELSSpectrum.__init__(self, *args, **kwargs)

def remove_negative_intensity(self, inplace=False):

'''

By definition, electron energy-loss spectral intensity is positive but,

sometimes, our spectral treatments overlook this important fact.

Parameters

----------

inplace : bool

Performs the operation in-place.

Returns

-------

spc : EELSSpectrum

Negative intensity is set to 0.

'''

if inplace:

spc = self

else:

spc = self.deepcopy()

spc.data[spc.data < 0.] = 0

return spc

def remove_intensity(self, left_value=None, right_value=None, inplace=False):

'''

Remove all intensity in a range.

Parameters

----------

threshold : {int, float}

Integer index or energy-loss units.

inplace : bool

Performs the operation in-place.

Returns

-------

spc : EELSSpectrum

Spectral intensity in this range is set to 0.

'''

self._check_signal_dimension_equals_one()

try:

signal_range_from_roi = hs.hyperspy.misc.utils.signal_range_from_roi

left_value, right_value = signal_range_from_roi(left_value)

except TypeError:

# It was not a ROI, we carry on

pass

eax = self.axes_manager.signal_axes[0]

i1, i2 = eax._get_index(left_value), eax._get_index(right_value)

if inplace:

spc = self

else:

spc = self.deepcopy()

spc.data[(slice(None),)*eax.index_in_array+(slice(i1, i2),Ellipsis)]=0.

return spc

def get_effective_collection_angle(self):

"""

Calculates the effective collection angle for the whole energy axis.

The beam energy, convergence and collection angles need to be set in the

metadata.

Returns

-------

bstar : Signal1D

Contains the effective collection energy for each energy-loss in

mrad. It is a signal with the same length as the signal dimension.

References

----------

The calculation is done following Egerton (3rd edition) page 276.

"""

try:

e0 = self.metadata.Acquisition_instrument.TEM.beam_energy

except BaseException:

raise AttributeError("Please define the beam energy."

"You can do this e.g. by using the "

"set_microscope_parameters method")

try:

alpha = self.metadata.Acquisition_instrument.TEM.convergence_angle

except BaseException:

raise AttributeError("Please define the convergence semi-angle. "

"You can do this e.g. by using the "

"set_microscope_parameters method")

try:

beta = self.metadata.Acquisition_instrument.TEM.Detector.\

EELS.collection_angle

except BaseException:

raise AttributeError("Please define the collection semi-angle. "

"You can do this e.g. by using the "

"set_microscope_parameters method")

energy = self.axes_manager.signal_axes[0].axis

tgt = e0 * (1.+e0/1022.) / (1.+e0/511.)

thetae = (energy+1e-6) / tgt

# A2,B2,T2 ARE SQUARES OF ANGLES IN RADIANS**2

a2 = alpha * alpha * 1e-6 + 1e-10

b2 = beta * beta * 1e-6

t2 = thetae * thetae * 1e-6

eta1 = np.sqrt((a2+b2+t2)**2 - 4.*a2*b2) - a2 - b2 - t2

eta2 = 2.*b2 * np.log(0.5/t2*(np.sqrt((a2+t2-b2)**2 + 4.*b2*t2) \

+ a2 + t2 - b2))

eta3 = 2.*a2 * np.log(0.5/t2*(np.sqrt((b2+t2-a2)**2 + 4.*a2*t2) \

+ b2 + t2 - a2))

eta = (eta1+eta2+eta3) / a2 / np.log(4./t2)

f1 = (eta1+eta2+eta3) / 2. / a2 / np.log(1.+b2/t2)

f2 = f1

if (alpha/beta > 1.):

f2 = f1 * a2/b2

bstar = thetae * np.sqrt(np.exp(f2*np.log(1.+b2/t2))-1.)

bstar = self._get_signal_signal(bstar)

bstar.set_signal_type('Signal1D')

return bstar

def model_zero_loss_peak_mirror(self, hanning=True):

'''

Model the zero-loss peak as a mirror using the negative energy-losses.

This model only makes sense if the ZLP is symmetric around zero.

Parameters

----------

hanning : bool

Optionally apply a Hanning taper to the border, so that they intensity

decays smoothily to 0.

Returns

-------

zlp : EELSSignal

Mirrored ZLP model.

'''

zlp = self.deepcopy()

eax = zlp.axes_manager.signal_axes[0]

if eax.high_index*0.5 > eax.value2index(0.):

eaxshift = - eax.scale*0.5

elif eax.high_index*0.5 < eax.value2index(0.):

eaxshift = eax.scale*0.5

else:

eaxshift = 0

eax.offset = eax.offset + eaxshift

plz = zlp.deepcopy().isig[0.::-1]

xae = plz.axes_manager.signal_axes[0]

xae.scale *= -1

xae.offset *= -1

plz.get_dimensions_from_data()

Ea = xae.low_value

Eb = xae.high_value

Ec = eax.high_value

i1 = eax.value2index(Ea)

if Eb<Ec:

i2 = eax.value2index(Eb)

i3 = -1

elif Eb>Ec:

i2 = eax.high_index

i3 = i2-xae.high_index-1

else:

i2 = eax.high_index

i3 = -1

zlp.data[(slice(None),)*eax.index_in_array+(slice(i1, i2), Ellipsis)]= \

plz.data[(slice(None),)*xae.index_in_array+(slice(0, i3), Ellipsis)]

zlp.data[(slice(None),)*eax.index_in_array + \

(slice(i2, None), Ellipsis)] = 0.

eax = zlp.axes_manager.signal_axes[0]

eax.offset = eax.offset-eaxshift

if hanning:

zlp_h = zlp.isig[:Eb-eaxshift]

zlp_h.hanning_taper('both')

return zlp

def model_zero_loss_peak_tail(self, signal_range, show_progressbar=None,

*args, **kwargs):

'''

Model the zero-loss peak tail using a (power-law) model fit. The fit

window is set using the signal_range tuple in axis units (not indices).

Spectral intensity at energies above the signal_range is substituted by

the model tail. The fit is performed using `remove_background`,

*args and **kwargs are passed to this method.

Parameters

----------

signal_range : tuple

Initial and final position of the fit window. Given in axis units. The

components can be single or multidimensional. If multidimensional, an

array or a signal with the same dimensions as the navigation dimension

should be used.

Returns

-------

zlp : EELSSignal

Modeled tail ZLP model.

Examples

--------

>>> s = hs.load('some_eels.h5')

>>> zlp = s.model_zero_loss_peak_tail((0.5, 1.),

... fast=False,

... show_progressbar=False)

'''

self._check_signal_dimension_equals_one()

if not isinstance(signal_range, tuple):

raise AttributeError('signal_range not recognized:'

'must be a tuple!')

if len(signal_range) != 2:

raise AttributeError('signal_range not recognized,'

'must be len = 2')

axis = self.axes_manager.signal_axes[0]

if isinstance(signal_range[0], Number) and (

isinstance(signal_range[1], Number)):

zlp = self - self.remove_background(signal_range,

show_progressbar=show_progressbar,

*args, **kwargs)

I2 = axis.value2index(signal_range[1])

ids = (slice(None),)*axis.index_in_array + (slice(None, I2), Ellipsis)

zlp.data[ids] = self.data[ids]

return zlp

if isinstance(signal_range[0], (np.ndarray, hs.signals.BaseSignal)) or (

isinstance(signal_range[1], (np.ndarray, hs.signals.BaseSignal))):

signal_range_ini = self._check_adapt_map_input(signal_range[0])

signal_range_fin = self._check_adapt_map_input(signal_range[1])

for name in ['signal_range_ini', 'signal_range_fin']:

parameter = eval(name)

if isinstance(parameter, ValueError):

parameter.args = (parameter.args[0]+name,)

raise parameter

zlp = self.deepcopy()

for si in progressbar(self, disable=not show_progressbar):

indices = self.axes_manager.indices

E1 = signal_range_ini.inav[indices].data[0]

E2 = signal_range_fin.inav[indices].data[0]

ri = si.remove_background((E1, E2), show_progressbar=False,

*args, **kwargs)

I2 = axis.value2index(E2)

ids = (*indices, slice(I2, None), Ellipsis)

zlp.data[ids] = si.data[I2:] - ri.data[I2:]

return zlp

def power_law_extrapolation_until(self, window_size=20, total_size=1024,

hanning=True, *args, **kwargs):

'''

Usefullity mathod. Extends the spectrum using `power_law_extrapolation`

until the resulting spectrum has the given total number of pixels.

Parameters

----------

window_size : {int, float}

Window size. Alternatively, this parameter can be a float specifying

the size in energy-loss units.

total_size : {int, float}

Total number of pixels. Alternatively, this parameter can be a float

specifying the size in energy-loss units.

Returns

-------

spc : EELSSpectrum

The extended spectrum.

'''

eax = self.axes_manager.signal_axes[0]

if type(total_size) is float:

offset = self.axes_manager[-1].offset - self.axes_manager[-1].scale

total_size = int(round((total_size-offset)/eax.scale))

if type(window_size) is float:

window_size = int(round(window_size/eax.scale))

extrapolation_size = total_size-eax.size

if extrapolation_size < 0:

raise AttributeError("total_size is less than spectral axis size")

spc = self.power_law_extrapolation(window_size,

extrapolation_size,

*args,

**kwargs)

if hanning:

spc.hanning_taper('both')

return spc

def relativistic_kramers_kronig(self,

zlp=None,

n=None,

t=None,

delta=0.9,

fsmooth=None,

iterations=20,

chi2_target=1e-4,

average=False,

full_output=True,

show_progressbar=None,

*args,

**kwargs):

r"""Calculate the complex dielectric function from a single scattering

distribution (SSD) using the Kramers-Kronig relations and a relativistic

correction for thin slab geometry.

The input SSD should be and EELSSpectrum instance, containing only

inelastic scattering information (elastic and plural scattering

deconvolved). The dielectric information is obtained by normalization of

the inelastic scattering using the elastic scattering intensity and

either refractive index or thickness information.

A full complex dielectric function (CDF) is obtained by Kramers-Kronig

transform, solved using FFT as in `kramers_kronig_analysis`. This inital

guess for the CDF is improved in an iterative loop, devised to

approximately subtract the relativistic contribution supposing an

unoxidized planar surface.

The loop runs until a chi-square target has been achieved or for a

maximum number of iterations. This behavior can be modified using the

parameters below. This method does not account for instrumental and

finite-size effects.

Note: either refractive index or thickness (`n` or `t`) are required.

If both are None or if both are provided an exception is raised. Many

input types are accepted for zlp, n and t parameters, which are parsed

using `self._check_adapt_map_input`, see the documentation therein for

more information.

Parameters

----------

zlp: {None, number, ndarray, Signal}

ZLP intensity. It is optional (can be None) if t is given,

full_output is False and no iterations are run. In any other case,

the ZLP is required either to perform the normalization step,

to calculate the thickness and/or to calculate the relativistic

correction.

n: {None, number, ndarray, Signal}

The medium refractive index. Used for normalization of the

SSD to obtain the energy loss function. If given the thickness

is estimated and returned. It is only required when `t` is None.

t: {None, number, ndarray, Signal}

The sample thickness in nm. Used for normalization of the

SSD to obtain the energy loss function. It is only required when

`n` is None.

delta : {None, float}

Optionally apply a fractional limit to the relativistic correction

in order to improve stability. Can be None, if no limit is desired.

A value of around 0.9 ensures the correction is never larger than

the original EELS signal, producing a negative spectral region.

fsmooth : {None, float}

Optionally apply a gaussian filter to the relativistic correction

in order to eliminate high-frequency noise. The cut-off is set in

the energy-loss scale, e.g. fsmooth = 1.5 (eV).

iterations: {None, int}

Number of the iterations for the internal loop to remove the

relativistic contribution. If None, the loop runs until a chi-square

target has been achieved (see below).

chi2_target : float

The average chi-square test score is measured in each iteration, and

the reconstruction loop terminates when the target score is reached.

See `_chi2_score` for more information.

average : bool

If True, use the average of the obtained dielectric functions over

the navigation dimensions to calculate the relativistic correction.

False by default, should only be used when analyzing spectra from a

homogenous sample, as only one dielectric function is retrieved.

This switch has no effect if only one spectrum is being analyzed.

full_output : bool

If True, return a dictionary that contains the estimated

thickness if `t` is None and the estimated relativistic correction

if `iterations` > 1.

Returns

-------

eps: DielectricFunction instance

The complex dielectric function results,

.. math::

\epsilon = \epsilon_1 + i*\epsilon_2,

contained in an DielectricFunction instance.

output: Dictionary (optional)

A dictionary of optional outputs with the following keys:

``thickness``

The estimated thickness in nm calculated by normalization of

the corrected spectrum (only when `t` is None).

``relativistic correction``

The estimated relativistic correction at the final iteration.

Raises

------

ValueError

If both `n` and `t` are undefined (None).

AttributeError

If the beam_energy or the collection semi-angle are not defined in

metadata.

See also

--------

get_relativistic_spectrum, _check_adapt_map_input

"""

# prepare data arrays

if iterations == 1:

# In this case s.data is not modified so there is no need to make

# a deep copy.

s = self.isig[0.:]

else:

s = self.isig[0.:].deepcopy()

sorig = self.isig[0.:]

# Avoid singularity at 0

if s.axes_manager.signal_axes[0].axis[0] == 0:

s = s.isig[1:]

sorig = self.isig[1:]

axis = s.axes_manager.signal_axes[0]

eaxis = axis.axis.copy()

# Constants and units, electron mass, beam energy and collection angle

me = constants.value(

'electron mass energy equivalent in MeV') * 1e3 # keV

try:

e0 = s.metadata.Acquisition_instrument.TEM.beam_energy

except BaseException:

raise AttributeError("Please define the beam energy."

"You can do this e.g. by using the "

"set_microscope_parameters method")

try:

beta = s.metadata.Acquisition_instrument.TEM.Detector.\

EELS.collection_angle

except BaseException:

raise AttributeError("Please define the collection semi-angle. "

"You can do this e.g. by using the "

"set_microscope_parameters method")

# Mapped parameters, zlp, n and t

if isinstance(zlp, hs.signals.Signal1D):

if (zlp.axes_manager.signal_dimension == 1) and (

zlp.axes_manager.navigation_shape ==

self.axes_manager.navigation_shape):

zlp = zlp.integrate1D(axis.index_in_axes_manager)

elif zlp is None and (full_output or iterations > 1):

raise AttributeError("Please define the zlp parameter when "

"full output or iterations > 1 are selected.")

zlp = self._check_adapt_map_input(zlp)

n = self._check_adapt_map_input(n)

t = self._check_adapt_map_input(t)

for name in ['zlp', 'n', 't']:

parameter = eval(name)

if isinstance(parameter, ValueError):

parameter.args = (parameter.args[0]+name,)

raise parameter

# select refractive or thickness loop

if n is None and t is None:

raise ValueError('Thickness and refractive index undefined.'

'Please provide one of them.')

elif n is not None and t is not None:

raise ValueError('Thickness and refractive index both defined.'

'Please provide only one of them.')

elif n is not None:

refractive_loop = True

if (zlp is not None) and (full_output is True or iterations > 1):

t = self._get_navigation_signal().T

elif t is not None:

refractive_loop = False

if zlp is None:

raise ValueError('Zero-loss intensity is needed for thickness '

'normalization. Provide also parameter zlp')

# Slicer to get the signal data from 0 to axis.size

slicer = s.axes_manager._get_data_slice(

[(axis.index_in_array, slice(None, axis.size)), ])

# Kinetic definitions

ke = e0 * (1 + e0 / 2. / me) / (1 + e0 / me) ** 2

tgt = e0 * (2 * me + e0) / (me + e0)

rk0 = 2590 * (1 + e0 / me) * np.sqrt(2 * ke / me)

# prepare the output dielectric function

eps = s._deepcopy_with_new_data(np.zeros_like(s.data, np.complex128))

eps.set_signal_type("DielectricFunction")

eps.metadata.General.title = (self.metadata.General.title +

'KKA dielectric function')

if eps.tmp_parameters.has_item('filename'):

eps.tmp_parameters.filename = (

self.tmp_parameters.filename +

'_CDF_after_Kramers_Kronig_transform')

from dielectric import ModifiedCDF

eps = ModifiedCDF(eps)

eps_corr = eps.deepcopy()

# progressbar support

if show_progressbar is None:

show_progressbar = preferences.General.show_progressbar

pbar = progressbar(total = iterations,

desc = '1.00e+30',

disable=not show_progressbar)

# initialize iteration control

io = 0

chi2 = chi2_target*1e3

while (io < iterations) and (chi2 > chi2_target):

# Calculation of the ELF by normalization of the SSD

Im = s.data / (np.log(1 + (beta * tgt / eaxis) ** 2)) / axis.scale

if refractive_loop:

# normalize using the refractive index.

K = (Im / eaxis).sum(axis=axis.index_in_array) * axis.scale

K = (K / (np.pi / 2) / (1 - 1. / n.data ** 2))

# Calculate the thickness only if possible and required

if full_output or iterations > 1:

te = (332.5 * K * ke / zlp.data)

t.data = te.squeeze()

else:

# normalize using the thickness

K = t.data * zlp.data / (332.5 * ke)

Im = Im / K[..., None] if len(self) != 1 else Im / K

# Kramers-Kronig transform

esize = 2 * axis.size

q = -2 * np.fft.fft(Im, esize, axis.index_in_array).imag / esize

q[slicer] *= -1

q = np.fft.fft(q, axis=axis.index_in_array)

Re = q[slicer].real + 1

epsabs = (Re ** 2 + Im ** 2)

eps.data = Re / epsabs + 1j* Im / epsabs

del Im, Re, q, epsabs

if average and (eps.axes_manager.navigation_dimension > 0):

eps_corr.data[:] = eps.data.mean(

eps.axes_manager.navigation_indices_in_array,

keepdims=True)

else:

eps_corr.data = eps.data.copy()

if full_output or iterations > 1:

# Relativistic correction

# Calculates relativistic correction from the Kroeger equation

# The difference with the relativistic DCS is subtracted

scorr = eps_corr.get_relativistic_spectrum(zlp=zlp, t=t,

output='diff',

*args, **kwargs)

# Limit the fractional correction

if delta is not None:

fcorr = np.clip(scorr.data / sorig.data, -delta, delta)

scorr.data = fcorr * sorig.data

# smooth

if fsmooth is not None:

scorr.gaussian_filter(fsmooth)

# Apply correction

s.data = sorig.data - scorr.data

s.data[s.data < 0.] = 0.

if io > 0:

#chi2 = ((scorr.data-smemory)**2/smemory**2).sum()

chi2 = smemory._chi2_score(scorr)

chi2str = '{:0.2e}'.format(chi2)

pbar.set_description(chi2str)

smemory = scorr.deepcopy()

io += 1

pbar.update(1)

pbar.close()

if full_output:

output = {}

tstr = self.metadata.General.title

if refractive_loop:

t.metadata.General.title = tstr + ', r-KKA thickness'

output['thickness'] = t

scorr.metadata.General.title = tstr + ', r-KKA correction'

output['relativistic correction'] = scorr

return eps, output

else:

return eps

def _chi2_score(self, sig, p=0.5):

"""

Calculate the mean chi-2 score removing outliers in a pedestrian way.

Parameters

----------

sig : signal

Must be of equal dimensions to self or this won't work.

p : float

Remove outliers coefficient: percentage of the data left out above and

below.

Returns

-------

chi2 : float

Average of the chi-square test score.

"""

chi2 = (sig.data - self.data)**2 / self.data**2

chi2 = np.nan_to_num(chi2)

a_min, a_max = np.percentile(chi2, p), np.percentile(chi2, 100-p)