xrayutilities.analysis package

Submodules

xrayutilities.analysis.line_cuts module

xrayutilities.analysis.line_cuts.get_arbitrary_line(qpos, intensity, point, vec, npoints, intrange)

extracts a line scan from reciprocal space map data along an arbitrary line defined by the point ‘point’ and propergation vector ‘vec’. Integration of the data is performed in a cylindrical volume along the line. This function works for 2D and 3D input data!

Parameters:

qposlist of array-like objects

arrays of x, y (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

pointtuple, list or array-like

point on the extraction line (2 or 3 coordinates)

vectuple, list or array-like

propergation vector of the extraction line (2 or 3 coordinates)

npointsint

number of points in the output data

intrangefloat

radius of the cylindrical integration volume around the extraction line

Returns:

qpos, qintndarray

line scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> qcut, qint, mask = get_arbitrary_line([qx, qy, qz], inten,     ... (1.1, 2.2, 0.0),     ... (1, 1, 1), 200, 0.1)  

xrayutilities.analysis.line_cuts.get_omega_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts an omega scan from reciprocal space map data with integration along either the 2theta, or radial (omega-2theta) direction. The coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

This function works for 2D and 3D input data in the same way!

Parameters:

qposlist of array-like objects

arrays of y, z (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

cutpostuple or list

y/z-position or x/y/z-position at which the line scan should be extracted. this must be have two entries for 2D data (z-position) and a three for 3D data

npointsint

number of points in the output data

intrangefloat

integration range in along intdir in degree. data will be integrated from -intrange .. +intrange

intdir{‘2theta’, ‘radial’}, optional

integration direction: ‘2theta’: scattering angle (default), or ‘radial’: omega-2theta direction.

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

Although applicable for any set of data, the extraction only makes sense when the data are aligned into the y/z-plane.

Returns:

om, omintndarray

omega scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> omcut, omcut_int, mask = get_omega_scan([qy, qz], inten, [2.0, 5.0],     ... 250, intrange=0.1)  

xrayutilities.analysis.line_cuts.get_qx_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts a qx scan from 3D reciprocal space map data with integration along either, the perpendicular plane in q-space, omega (sample rocking angle) or 2theta direction. For the integration in angular space (omega, or 2theta) the coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

Parameters:

qposlist of array-like objects

arrays of x, y, z (list with three components) momentum transfers

intensityarray-like

3D array of reciprocal space intensity with shape equal to the qpos entries

cutpostuple/list

y/z-position at which the line scan should be extracted. this must be and a tuple/list with the qy, qz cut position

npointsint

number of points in the output data

intrangefloat

integration range in along intdir, either in 1/AA (q) or degree (‘omega’, or ‘2theta’). data will be integrated from -intrange .. +intrange

intdir{‘q’, ‘omega’, ‘2theta’}, optional

integration direction: ‘q’: perpendicular Q-plane (default), ‘omega’: sample rocking angle, or ‘2theta’: scattering angle.

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

The angular integration directions although applicable for any set of data only makes sense when the data are aligned into the y/z-plane.

Returns:

qx, qxintndarray

qx scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> qxcut, qxcut_int, mask = get_qx_scan([qx, qy, qz], inten, [0, 2.0], \
... 250, intrange=0.01)  

xrayutilities.analysis.line_cuts.get_qy_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts a qy scan from reciprocal space map data with integration along either, the perpendicular plane in q-space, omega (sample rocking angle) or 2theta direction. For the integration in angular space (omega, or 2theta) the coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

This function works for 2D and 3D input data in the same way!

Parameters:

qposlist of array-like objects

arrays of y, z (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

cutposfloat or tuple/list

x/z-position at which the line scan should be extracted. this must be a float for 2D data (z-position) and a tuple with two values for 3D data

npointsint

number of points in the output data

intrangefloat

integration range in along intdir, either in 1/AA (q) or degree (‘omega’, or ‘2theta’). data will be integrated from -intrange .. +intrange

intdir{‘q’, ‘omega’, ‘2theta’}, optional

integration direction: ‘q’: perpendicular Q-plane (default), ‘omega’: sample rocking angle, or ‘2theta’: scattering angle.

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

For 3D data the angular integration directions although applicable for any set of data only makes sense when the data are aligned into the y/z-plane.

Returns:

qy, qyintndarray

qy scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> qycut, qycut_int, mask = get_qy_scan([qy, qz], inten, 5.0, 250, \
... intrange=0.02, intdir='2theta')  

xrayutilities.analysis.line_cuts.get_qz_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts a qz scan from reciprocal space map data with integration along either, the perpendicular plane in q-space, omega (sample rocking angle) or 2theta direction. For the integration in angular space (omega, or 2theta) the coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

This function works for 2D and 3D input data in the same way!

Parameters:

qposlist of array-like objects

arrays of y, z (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

cutposfloat or tuple/list

x/y-position at which the line scan should be extracted. this must be a float for 2D data and a tuple with two values for 3D data

npointsint

number of points in the output data

intrangefloat

integration range in along intdir, either in 1/AA (q) or degree (‘omega’, or ‘2theta’). data will be integrated from -intrange/2 .. +intrange/2

intdir{‘q’, ‘omega’, ‘2theta’}, optional

integration direction: ‘q’: perpendicular Q-plane (default), ‘omega’: sample rocking angle, or ‘2theta’: scattering angle.

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

For 3D data the angular integration directions although applicable for any set of data only makes sense when the data are aligned into the y/z-plane.

Returns:

qz, qzintndarray

qz scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> qzcut, qzcut_int, mask = get_qz_scan([qy, qz], inten, 3.0, 200,\
... intrange=0.3)  

xrayutilities.analysis.line_cuts.get_radial_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts a radial scan from reciprocal space map data with integration along either the omega or 2theta direction. The coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

This function works for 2D and 3D input data in the same way!

Parameters:

qposlist of array-like objects

arrays of y, z (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

cutpostuple or list

y/z-position or x/y/z-position at which the line scan should be extracted. this must be have two entries for 2D data (z-position) and a three for 3D data

npointsint

number of points in the output data

intrangefloat

integration range in along intdir in degree. data will be integrated from -intrange .. +intrange

intdir{‘omega’, ‘2theta’}, optional

integration direction: ‘omega’: sample rocking angle (default), ‘2theta’: scattering angle

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

Although applicable for any set of data, the extraction only makes sense when the data are aligned into the y/z-plane.

Returns:

tt, omttintndarray

omega-2theta scan coordinates (2theta values) and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> ttcut, omtt_int, mask = get_radial_scan([qy, qz], inten, [2.0, 5.0],     ... 250, intrange=0.1)  

xrayutilities.analysis.line_cuts.get_ttheta_scan(qpos, intensity, cutpos, npoints, intrange, **kwargs)

extracts a 2theta scan from reciprocal space map data with integration along either the omega or radial direction. The coplanar diffraction geometry with qy and qz as diffraction plane is assumed. This is consistent with the coplanar geometry implemented in the HXRD-experiment class.

This function works for 2D and 3D input data in the same way!

Parameters:

qposlist of array-like objects

arrays of y, z (list with two components) or x, y, z (list with three components) momentum transfers

intensityarray-like

2D or 3D array of reciprocal space intensity with shape equal to the qpos entries

cutpostuple or list

y/z-position or x/y/z-position at which the line scan should be extracted. this must be have two entries for 2D data (z-position) and a three for 3D data

npointsint

number of points in the output data

intrangefloat

integration range in along intdir in degree. data will be integrated from -intrange .. +intrange

intdir{‘omega’, ‘radial’}, optional

integration direction: ‘omega’: sample rocking angle (default), ‘radial’: omega-2theta direction

wlfloat or str, optional

wavelength used to determine angular integration positions

Note:

Although applicable for any set of data, the extraction only makes sense when the data are aligned into the y/z-plane.

Returns:

tt, ttintndarray

2theta scan coordinates and intensities

used_maskndarray

mask of used data, shape is the same as the input intensity: True for points which contributed, False for all others

Examples

>>> ttcut, tt_int, mask = get_ttheta_scan([qy, qz], inten, [2.0, 5.0],     ... 250, intrange=0.1)  

xrayutilities.analysis.misc module

miscellaneous functions helpful in the analysis and experiment

xrayutilities.analysis.misc.coplanar_intensity(mat, exp, hkl, thickness, thMono, sample_width=10, beam_width=1)

Calculates the expected intensity of a Bragg peak from an epitaxial thin film measured in coplanar geometry (integration over omega and 2theta in angular space!)

Parameters:

matCrystal

Crystal instance for structure factor calculation

expExperiment

Experimental(HXRD) class for the angle calculation

hkllist, tuple or array-like

Miller indices of the peak to calculate

thicknessfloat

film thickness in nm

thMonofloat

Bragg angle of the monochromator (deg)

sample_widthfloat, optional

width of the sample along the beam

beam_widthfloat, optional

width of the beam in the same units as the sample size

Returns:

float

intensity of the peak

xrayutilities.analysis.misc.getangles(peak, sur, inp)

calculates the chi and phi angles for a given peak

Parameters:

peaklist or array-like

hkl for the peak of interest

surlist or array-like

hkl of the surface

inplist or array-like

inplane reference peak or direction

Returns:

list

[chi, phi] for the given peak on surface sur with inplane direction inp as reference

Examples

To get the angles for the -224 peak on a 111 surface type

>>> [chi, phi] = getangles([-2, 2, 4], [1, 1, 1], [2, 2, 4])

xrayutilities.analysis.misc.getunitvector(chi, phi, ndir=(0, 0, 1), idir=(1, 0, 0))

return unit vector determined by spherical angles and definition of the polar axis and inplane reference direction (phi=0)

Parameters:

chi, phifloat

spherical angles (polar and azimuthal) in degree

ndirtuple, list or array-like

polar/z-axis (determines chi=0)

idirtuple, list or array-like

azimuthal axis (determines phi=0)

xrayutilities.analysis.sample_align module

functions to help with experimental alignment during experiments, especially for experiments with linear and area detectors

xrayutilities.analysis.sample_align.area_detector_calib(angle1, angle2, ccdimages, detaxis, r_i, plot=True, cut_off=0.7, start=(None, None, 1, 0, 0, 0, 0), fix=(False, False, True, False, False, False, False), fig=None, wl=None, plotlog=False, nwindow=50, debug=False)

function to calibrate the detector parameters of an area detector it determines the detector tilt possible rotations and offsets in the detector arm angles

Parameters:

angle1array-like

outer detector arm angle

angle2array-like

inner detector arm angle

ccdimagesarray-like

images of the ccd taken at the angles given above

detaxislist of str

detector arm rotation axis; default: [‘z+’, ‘y-‘]

r_istr

primary beam direction [xyz][+-]; default ‘x+’

plotbool, optional

flag to determine if results and intermediate results should be plotted; default: True

cut_offfloat, optional

cut off intensity to decide if image is used for the determination or not; default: 0.7 = 70%

starttuple, optional

sequence of start values of the fit for parameters, which can not be estimated automatically or might want to be fixed. These are: pwidth1, pwidth2, distance, tiltazimuth, tilt, detector_rotation, outerangle_offset. By default (None, None, 1, 0, 0, 0, 0) is used.

fixtuple of bool

fix parameters of start (default: (False, False, True, False, False, False, False)) It is strongly recommended to either fix the distance or the pwidth1, 2 values.

figFigure, optional

matplotlib figure used for plotting the error default: None (creates own figure)

wlfloat or str

wavelength of the experiment in angstrom (default: config.WAVELENGTH) value does not really matter here but does affect the scaling of the error

plotlogbool

flag to specify if the created error plot should be on log-scale

nwindowint

window size for determination of the center of mass position after the center of mass of every full image is determined, the center of mass is determined again using a window of size nwindow in order to reduce the effect of hot pixels.

debugbool

flag to specify that you want to see verbose output and saving of images to show if the CEN determination works

xrayutilities.analysis.sample_align.area_detector_calib_hkl(sampleang, angle1, angle2, ccdimages, hkls, experiment, material, detaxis, r_i, plot=True, cut_off=0.7, start=(None, None, 1, 0, 0, 0, 0, 0, 0, 'config'), fix=(False, False, True, False, False, False, False, False, False, False), fig=None, plotlog=False, nwindow=50, debug=False)

function to calibrate the detector parameters of an area detector it determines the detector tilt possible rotations and offsets in the detector arm angles

in this variant not only scans through the primary beam but also scans at a set of symmetric reflections can be used for the detector parameter determination. for this not only the detector parameters but in addition the sample orientation and wavelength need to be fit. Both images from the primary beam hkl = (0, 0, 0) and from a symmetric reflection hkl = (h, k, l) need to be given for a successful run.

Parameters:

sampleangarray-like

sample rocking angle (needed to align the reflections (same rotation direction as inner detector rotation)) other sample angle are not allowed to be changed during the scans

angle1array-like

outer detector arm angle

angle2array-like

inner detector arm angle

ccdimagesarray-like

images of the ccd taken at the angles given above

hklslist or array-like

hkl values for every image

experimentExperiment

Experiment class object needed to get the UB matrix for the hkl peak treatment

materialCrystal

material used as reference crystal

detaxislist of str

detector arm rotation axis; default: [‘z+’, ‘y-‘]

r_istr

primary beam direction [xyz][+-]; default ‘x+’

plotbool, optional

flag to determine if results and intermediate results should be plotted; default: True

cut_offfloat, optional

cut off intensity to decide if image is used for the determination or not; default: 0.7 = 70%

starttuple, optional

sequence of start values of the fit for parameters, which can not be estimated automatically or might want to be fixed. These are: pwidth1, pwidth2, distance, tiltazimuth, tilt, detector_rotation, outerangle_offset, sampletilt, sampletiltazimuth, wavelength. By default (None, None, 1, 0, 0, 0, 0, 0, 0, ‘config’).

fixtuple of bool

fix parameters of start (default: (False, False, True, False, False, False, False, False, False, False)) It is strongly recommended to either fix the distance or the pwidth1, 2 values.

figFigure, optional

matplotlib figure used for plotting the error default: None (creates own figure)

plotlogbool

flag to specify if the created error plot should be on log-scale

nwindowint

window size for determination of the center of mass position after the center of mass of every full image is determined, the center of mass is determined again using a window of size nwindow in order to reduce the effect of hot pixels.

debugbool

flag to specify that you want to see verbose output and saving of images to show if the CEN determination works

xrayutilities.analysis.sample_align.fit_bragg_peak(om, tt, psd, omalign, ttalign, exphxrd, frange=(0.03, 0.03), peaktype='Gauss', plot=True)

helper function to determine the Bragg peak position in a reciprocal space map used to obtain the position needed for correction of the data. the determination is done by fitting a two dimensional Gaussian (xrayutilities.math.Gauss2d) or Lorentzian (xrayutilities.math.Lorentz2d)

PLEASE ALWAYS CHECK THE RESULT CAREFULLY!

Parameters:

om, ttarray-like

angular coordinates of the measurement either with size of psd or of psd.shape[0]

psdarray-like

intensity values needed for fitting

omalignfloat

aligned omega value, used as first guess in the fit

ttalignfloat

aligned two theta values used as first guess in the fit these values are also used to set the range for the fit: the peak should be within +/-frangeAA^{-1} of those values

exphxrdExperiment

experiment class used for the conversion between angular and reciprocal space.

frangetuple of float, optional

data range used for the fit in both directions (see above for details default:(0.03, 0.03) unit: AA^{-1})

peaktype{‘Gauss’, ‘Lorentz’}

peak type to fit

plotbool, optional

if True (default) function will plot the result of the fit in comparison with the measurement.

Returns:

omfit, ttfitfloat

fitted angular values

paramslist

fit parameters (of the Gaussian/Lorentzian)

covariancendarray

covariance matrix of the fit parameters

xrayutilities.analysis.sample_align.linear_detector_calib(angle, mca_spectra, **keyargs)

function to calibrate the detector distance/channel per degrees for a straight linear detector mounted on a detector arm

Parameters:

anglearray-like

array of angles in degree of measured detector spectra

mca_spectraarray-like

corresponding detector spectra (shape: (len(angle), Nchannels)

r_istr, optional

primary beam direction as vector [xyz][+-]; default: ‘y+’

detaxisstr, optional

detector arm rotation axis [xyz][+-]; default: ‘x+’

Returns:

pixelwidthfloat

width of the pixel at one meter distance, pixelwidth is negative in case the hit channel number decreases upon an increase of the detector angle

center_channelfloat

central channel of the detector

detector_tiltfloat, optional

if usetilt=True the fitted tilt of the detector is also returned

Note

L/pixelwidth*pi/180 ~= channel/degree, with the sample detector distance L

The function also prints out how a linear detector can be initialized using

the results obtained from this calibration. Carefully check the results

Other Parameters:

plotbool

flag to specify if a visualization of the fit should be done

usetiltbool

whether to use model considering a detector tilt, i.e. deviation angle of the pixel direction from orthogonal to the primary beam (default: True)

See also

psd_chdeg

low level function with more configurable options

xrayutilities.analysis.sample_align.miscut_calc(phi, aomega, zeros=None, omega0=None, plot=True)

function to calculate the miscut direction and miscut angle of a sample by fitting a sinusoidal function to the variation of the aligned omega values of more than two reflections. The function can also be used to fit reflectivity alignment values in various azimuths.

Parameters:

philist, tuple or array-like

azimuths in which the reflection was aligned (deg)

aomegalist, tuple or array-like

aligned omega values (deg)

zeroslist, tuple or array-like, optional

angles at which surface is parallel to the beam (deg). For the analysis the angles (aomega - zeros) are used.

omega0float, optional

if specified the nominal value of the reflection is not included as fit parameter, but is fixed to the specified value. This value is MANDATORY if ONLY TWO AZIMUTHs are given.

plotbool, optional

flag to specify if a visualization of the fit is wanted. default: True

Returns:

omega0float

the omega value of the reflection should be close to the nominal one

phi0float

the azimuth in which the primary beam looks upstairs

miscutfloat

amplitude of the sinusoidal variation == miscut angle

xrayutilities.analysis.sample_align.psd_chdeg(angles, channels, stdev=None, usetilt=True, plot=True, datap='xk', modelline='--r', modeltilt='-b', fignum=None, mlabel='fit', mtiltlabel='fit w/tilt', dlabel='data', figtitle=True)

function to determine the channels per degree using a linear fit of the function nchannel = center_ch+chdeg*tan(angles) or the equivalent including a detector tilt

Parameters:

anglesarray-like

detector angles for which the position of the beam was measured

channelsarray-like

detector channels where the beam was found

stdevarray-like, optional

standard deviation of the beam position

plotbool, optional

flag to specify if a visualization of the fit should be done

usetiltbool, optional

whether to use model considering a detector tilt, i.e. deviation angle of the pixel direction from orthogonal to the primary beam (default: True)

Returns:

pixelwidthfloat

the width of one detector channel @ 1m distance, which is negative in case the hit channel number decreases upon an increase of the detector angle.

centerchfloat

center channel of the detector

tiltfloat

tilt of the detector from perpendicular to the beam (will be zero in case of usetilt=False)

Note

L/pixelwidth*pi/180 = channel/degree for large detector distance with the sample detector disctance L

Other Parameters:

datapstr, optional

plot format of data points

modellinestr, optional

plot format of modelline

modeltiltstr, optional

plot format of modeltilt

fignumint or str, optional

figure number to use for the plot

mlabelstr

label of the model w/o tilt to be used in the plot

mtiltlabelstr

label of the model with tilt to be used in the plot

dlabelstr

label of the data line to be used in the plot

figtitlebool

flag to tell if the figure title should show the fit parameters

xrayutilities.analysis.sample_align.psd_refl_align(primarybeam, angles, channels, plot=True)

function which calculates the angle at which the sample is parallel to the beam from various angles and detector channels from the reflected beam. The function can be used during the half beam alignment with a linear detector.

Parameters:

primarybeamint

primary beam channel number

angleslist or array-like

incidence angles

channelslist or array-like

corresponding detector channels

plotbool, optional

flag to specify if a visualization of the fit is wanted default : True

Returns:

float

angle at which the sample is parallel to the beam

Examples

>>> zeroangle = psd_refl_align(500, [0, 0.1, 0.2, 0.3],
... [550, 600, 640, 700])
XU.analysis.psd_refl_align: sample is parallel to beam at goniometer angle -0.0986 (R^2=0.9942)

Module contents

xrayutilities.analysis is a package for assisting with the analysis of x-ray diffraction data, mainly reciprocal space maps

Routines for obtaining line cuts from gridded reciprocal space maps are offered, with the ability to integrate the intensity perpendicular to the line cut direction.