def test_div(self):
c, dc = EP.EPdiv(1.1, 0.5, 1.1, 0.5)
assert_array_almost_equal(1, c)
assert_array_almost_equal(0.642824346533225, dc)
c, dc = EP.EPdiv(0, 0.5, 1.1, 0.5)
assert_equal(0, c)
assert_array_almost_equal(0.45454545454545453, dc)
def reflectivity(self):
"""
The reflectivity of the sampled system
"""
rerr = np.sqrt(self.reflected_beam)
bmon_reflect_err = np.sqrt(self.bmon_reflect)
ierr = np.sqrt(self.direct_beam)
bmon_direct_err = np.sqrt(self.bmon_direct)
dx = np.sqrt(
(self.dlambda) ** 2 + self.dtheta ** 2 + (0.68 * self.rebin) ** 2
)
dx *= self.q
# divide reflectivity signal by bmon
ref, rerr = ErrorProp.EPdiv(
self.reflected_beam, rerr, self.bmon_reflect, bmon_reflect_err
)
# divide direct signal by bmon
direct, ierr = ErrorProp.EPdiv(
self.direct_beam, ierr, self.bmon_direct, bmon_direct_err
)
# now calculate reflectivity
ref, rerr = ErrorProp.EPdiv(ref, rerr, direct, ierr)
# filter points with zero counts because error is incorrect
mask = rerr != 0
dataset = ReflectDataset(
data=(self.q[mask], ref[mask], rerr[mask], dx[mask])
)
# apply some counting statistics on top of dataset otherwise there will
# be no variation at e.g. critical edge.
# return dataset.synthesise()
return dataset
def reflectivity(self):
"""
The reflectivity of the sampled system
"""
rerr = np.sqrt(self.reflected_beam)
ierr = np.sqrt(self.direct_beam)
dx = np.sqrt((self.dlambda)**2 + self.dtheta**2 + self.rebin**2)
ref, rerr = ErrorProp.EPdiv(self.reflected_beam, rerr,
self.direct_beam, ierr)
dataset = ReflectDataset(data=(self.q, ref, rerr, dx * self.q))
# apply some counting statistics on top of dataset otherwise there will
# be no variation at e.g. critical edge.
return dataset.synthesise()
def _reduce_single_angle(self, scale=1):
"""
Reduce a single angle.
"""
n_spectra = self.reflected_beam.n_spectra
n_tpixels = np.size(self.reflected_beam.m_topandtail, 1)
n_ypixels = np.size(self.reflected_beam.m_topandtail, 2)
# calculate omega and two_theta depending on the mode.
mode = self.reflected_beam.mode
# we'll need the wavelengths to calculate Q.
wavelengths = self.reflected_beam.m_lambda
m_twotheta = np.zeros((n_spectra, n_tpixels, n_ypixels))
detector_z_difference = (self.reflected_beam.detector_z -
self.direct_beam.detector_z)
beampos_z_difference = (self.reflected_beam.m_beampos -
self.direct_beam.m_beampos)
Y_PIXEL_SPACING = self.reflected_beam.cat.y_pixels_per_mm[0]
total_z_deflection = (detector_z_difference +
beampos_z_difference * Y_PIXEL_SPACING)
if mode in ['FOC', 'POL', 'POLANAL', 'MT']:
# omega_nom.shape = (N, )
omega_nom = np.degrees(
np.arctan(total_z_deflection / self.reflected_beam.detector_y)
/ 2.)
'''
Wavelength specific angle of incidence correction
This involves:
1) working out the trajectory of the neutrons through the
collimation system.
2) where those neutrons intersect the sample.
3) working out the elevation of the neutrons when they hit the
sample.
4) correcting the angle of incidence.
'''
speeds = general.wavelength_velocity(wavelengths)
collimation_distance = self.reflected_beam.cat.collimation_distance
s2_sample_distance = (self.reflected_beam.cat.sample_distance -
self.reflected_beam.cat.slit2_distance)
# work out the trajectories of the neutrons for them to pass
# through the collimation system.
trajectories = find_trajectory(collimation_distance / 1000., 0,
speeds)
# work out where the beam hits the sample
res = parabola_line_intersection_point(s2_sample_distance / 1000,
0, trajectories, speeds,
omega_nom[:, np.newaxis])
intersect_x, intersect_y, x_prime, elevation = res
# correct the angle of incidence with a wavelength dependent
# elevation.
omega_corrected = omega_nom[:, np.newaxis] - elevation
m_twotheta += np.arange(n_ypixels * 1.)[np.newaxis, np.newaxis, :]
m_twotheta -= self.direct_beam.m_beampos[:, np.newaxis, np.newaxis]
m_twotheta *= Y_PIXEL_SPACING
m_twotheta += detector_z_difference
m_twotheta /= (self.reflected_beam.detector_y[:, np.newaxis,
np.newaxis])
m_twotheta = np.arctan(m_twotheta)
m_twotheta = np.degrees(m_twotheta)
# you may be reflecting upside down, reverse the sign.
upside_down = np.sign(omega_corrected[:, 0])
m_twotheta *= upside_down[:, np.newaxis, np.newaxis]
omega_corrected *= upside_down[:, np.newaxis]
elif mode in ['SB', 'DB']:
# the angle of incidence is half the two theta of the reflected
# beam
omega = np.arctan(
total_z_deflection / self.reflected_beam.detector_y) / 2.
# work out two theta for each of the detector pixels
m_twotheta += np.arange(n_ypixels * 1.)[np.newaxis, np.newaxis, :]
m_twotheta -= self.direct_beam.m_beampos[:, np.newaxis, np.newaxis]
m_twotheta += detector_z_difference
m_twotheta -= (
self.reflected_beam.detector_y[:, np.newaxis, np.newaxis] *
np.tan(omega[:, np.newaxis, np.newaxis]))
m_twotheta /= (self.reflected_beam.detector_y[:, np.newaxis,
np.newaxis])
m_twotheta = np.arctan(m_twotheta)
m_twotheta += omega[:, np.newaxis, np.newaxis]
# still in radians at this point
# add an extra dimension, because omega_corrected needs to be the
# angle of incidence for each wavelength. I.e. should be
# broadcastable to (N, T)
omega_corrected = np.degrees(omega)[:, np.newaxis]
m_twotheta = np.degrees(m_twotheta)
'''
--Specular Reflectivity--
Use the (constant wavelength) spectra that have already been integrated
over 2theta (in processnexus) to calculate the specular reflectivity.
Beware: this is because m_topandtail has already been divided through
by monitor counts and error propagated (at the end of processnexus).
Thus, the 2theta pixels are correlated to some degree. If we use the 2D
plot to calculate reflectivity
(sum {Iref_{2theta, lambda}}/I_direct_{lambda}) then the error bars in
the reflectivity turn out much larger than they should be.
'''
ydata, ydata_sd = EP.EPdiv(self.reflected_beam.m_spec,
self.reflected_beam.m_spec_sd,
self.direct_beam.m_spec,
self.direct_beam.m_spec_sd)
# calculate the 1D Qz values.
xdata = general.q(omega_corrected, wavelengths)
xdata_sd = (self.reflected_beam.m_lambda_fwhm /
self.reflected_beam.m_lambda)**2
xdata_sd += (self.reflected_beam.domega[:, np.newaxis] /
omega_corrected)**2
xdata_sd = np.sqrt(xdata_sd) * xdata
'''
---Offspecular reflectivity---
normalise the counts in the reflected beam by the direct beam
spectrum this gives a reflectivity. Also propagate the errors,
leaving the fractional variance (dr/r)^2.
--Note-- that adjacent y-pixels (same wavelength) are correlated in
this treatment, so you can't just sum over them.
i.e. (c_0 / d) + ... + c_n / d) != (c_0 + ... + c_n) / d
'''
m_ref, m_ref_sd = EP.EPdiv(
self.reflected_beam.m_topandtail,
self.reflected_beam.m_topandtail_sd,
self.direct_beam.m_spec[:, :, np.newaxis],
self.direct_beam.m_spec_sd[:, :, np.newaxis])
# you may have had divide by zero's.
m_ref = np.where(np.isinf(m_ref), 0, m_ref)
m_ref_sd = np.where(np.isinf(m_ref_sd), 0, m_ref_sd)
# calculate the Q values for the detector pixels. Each pixel has
# different 2theta and different wavelength, ASSUME that they have the
# same angle of incidence
qx, qy, qz = general.q2(omega_corrected[:, :, np.newaxis], m_twotheta,
0, wavelengths[:, :, np.newaxis])
reduction = {}
reduction['x'] = self.x = xdata
reduction['x_err'] = self.x_err = xdata_sd
reduction['y'] = self.y = ydata / scale
reduction['y_err'] = self.y_err = ydata_sd / scale
reduction['omega'] = omega_corrected
reduction['m_twotheta'] = m_twotheta
reduction['m_ref'] = self.m_ref = m_ref
reduction['m_ref_err'] = self.m_ref_err = m_ref_sd
reduction['qz'] = self.m_qz = qz
reduction['qx'] = self.m_qx = qx
reduction['nspectra'] = self.n_spectra = n_spectra
reduction['start_time'] = self.reflected_beam.start_time
reduction['datafile_number'] = self.datafile_number = (
self.reflected_beam.datafile_number)
fnames = []
datasets = []
datafilename = self.reflected_beam.datafilename
datafilename = os.path.basename(datafilename.split('.nx.hdf')[0])
for i in range(n_spectra):
data_tup = self.data(scanpoint=i)
datasets.append(ReflectDataset(data_tup))
if self.save:
for i, dataset in enumerate(datasets):
fname = '{0}_{1}.dat'.format(datafilename, i)
fnames.append(fname)
with open(fname, 'wb') as f:
dataset.save(f)
fname = '{0}_{1}.xml'.format(datafilename, i)
with open(fname, 'wb') as f:
dataset.save_xml(f, start_time=reduction['start_time'][i])
reduction['fname'] = fnames
return datasets, deepcopy(reduction)
def _reduce_single_angle(self, scale=1):
"""
Reduce a single angle.
"""
n_spectra = self.reflected_beam.n_spectra
n_tpixels = np.size(self.reflected_beam.m_topandtail, 1)
n_xpixels = np.size(self.reflected_beam.m_topandtail, 2)
# we'll need the wavelengths to calculate Q.
wavelengths = self.reflected_beam.m_lambda
m_twotheta = np.zeros((n_spectra, n_tpixels, n_xpixels))
detrot_difference = (self.reflected_beam.detector_z -
self.direct_beam.detector_z)
# difference in pixels between reflected position and direct beam
# at the two different detrots.
QZ_PIXEL_SPACING = self.reflected_beam.cat.qz_pixel_size[0]
dy = self.reflected_beam.detector_y
# convert that pixel difference to angle (in small angle approximation)
# higher `som` leads to lower m_beampos. i.e. higher two theta
# is at lower pixel values
beampos_2theta_diff = -(self.reflected_beam.m_beampos -
self.direct_beam.m_beampos)
beampos_2theta_diff *= QZ_PIXEL_SPACING / dy[0]
beampos_2theta_diff = np.degrees(beampos_2theta_diff)
total_2theta_deflection = detrot_difference + beampos_2theta_diff
# omega_nom.shape = (N, )
omega_nom = total_2theta_deflection / 2.0
omega_corrected = omega_nom[:, np.newaxis]
m_twotheta += np.arange(n_xpixels * 1.0)[np.newaxis, np.newaxis, :]
m_twotheta -= self.direct_beam.m_beampos[:, np.newaxis, np.newaxis]
# minus sign in following line because higher two theta is at lower
# pixel values
m_twotheta *= -QZ_PIXEL_SPACING / dy[:, np.newaxis, np.newaxis]
m_twotheta = np.degrees(m_twotheta)
m_twotheta += detrot_difference
# you may be reflecting upside down, reverse the sign.
upside_down = np.sign(omega_corrected[:, 0])
m_twotheta *= upside_down[:, np.newaxis, np.newaxis]
omega_corrected *= upside_down[:, np.newaxis]
"""
--Specular Reflectivity--
Use the (constant wavelength) spectra that have already been integrated
over 2theta (in processnexus) to calculate the specular reflectivity.
Beware: this is because m_topandtail has already been divided through
by monitor counts and error propagated (at the end of processnexus).
Thus, the 2theta pixels are correlated to some degree. If we use the 2D
plot to calculate reflectivity
(sum {Iref_{2theta, lambda}}/I_direct_{lambda}) then the error bars in
the reflectivity turn out much larger than they should be.
"""
ydata, ydata_sd = EP.EPdiv(
self.reflected_beam.m_spec,
self.reflected_beam.m_spec_sd,
self.direct_beam.m_spec,
self.direct_beam.m_spec_sd,
)
# calculate the 1D Qz values.
xdata = general.q(omega_corrected, wavelengths)
xdata_sd = (self.reflected_beam.m_lambda_fwhm /
self.reflected_beam.m_lambda)**2
xdata_sd += (self.reflected_beam.domega[:, np.newaxis] /
omega_corrected)**2
xdata_sd = np.sqrt(xdata_sd) * xdata
"""
---Offspecular reflectivity---
normalise the counts in the reflected beam by the direct beam
spectrum this gives a reflectivity. Also propagate the errors,
leaving the fractional variance (dr/r)^2.
--Note-- that adjacent y-pixels (same wavelength) are correlated in
this treatment, so you can't just sum over them.
i.e. (c_0 / d) + ... + c_n / d) != (c_0 + ... + c_n) / d
"""
m_ref, m_ref_sd = EP.EPdiv(
self.reflected_beam.m_topandtail,
self.reflected_beam.m_topandtail_sd,
self.direct_beam.m_spec[:, :, np.newaxis],
self.direct_beam.m_spec_sd[:, :, np.newaxis],
)
# you may have had divide by zero's.
m_ref = np.where(np.isinf(m_ref), 0, m_ref)
m_ref_sd = np.where(np.isinf(m_ref_sd), 0, m_ref_sd)
# calculate the Q values for the detector pixels. Each pixel has
# different 2theta and different wavelength, ASSUME that they have the
# same angle of incidence
qx, qy, qz = general.q2(
omega_corrected[:, :, np.newaxis],
m_twotheta,
0,
wavelengths[:, :, np.newaxis],
)
reduction = {}
reduction["x"] = self.x = xdata
reduction["x_err"] = self.x_err = xdata_sd
reduction["y"] = self.y = ydata / scale
reduction["y_err"] = self.y_err = ydata_sd / scale
reduction["omega"] = omega_corrected
reduction["m_twotheta"] = m_twotheta
reduction["m_ref"] = self.m_ref = m_ref
reduction["m_ref_err"] = self.m_ref_err = m_ref_sd
reduction["qz"] = self.m_qz = qz
reduction["qx"] = self.m_qx = qx
reduction["nspectra"] = self.n_spectra = n_spectra
reduction["start_time"] = self.reflected_beam.start_time
reduction[
"datafile_number"] = self.datafile_number = self.reflected_beam.datafile_number
fnames = []
datasets = []
datafilename = self.reflected_beam.datafilename
datafilename = os.path.basename(datafilename.split(".nx.hdf")[0])
for i in range(n_spectra):
data_tup = self.data(scanpoint=i)
datasets.append(ReflectDataset(data_tup))
if self.save:
for i, dataset in enumerate(datasets):
fname = "{0}_{1}.dat".format(datafilename, i)
fnames.append(fname)
with open(fname, "wb") as f:
dataset.save(f)
fname = "{0}_{1}.xml".format(datafilename, i)
with open(fname, "wb") as f:
dataset.save_xml(f, start_time=reduction["start_time"][i])
reduction["fname"] = fnames
return datasets, deepcopy(reduction)
