pyFAI.geometry package

Module contents

This sub-package contains mostly a large Geometry class (defined in core) which is in charge of:

  • calculating the geometry, i.e. the position in the detector space of each pixel of the detector

  • manages caches to store intermediate results

There are several other helper classes which provide conversion to other software

NOTA: The Geometry class is not a “transformation class” which would take a detector and transform it. It is rather a description of the experimental setup.

pyFAI.geometry.core module

This modules contains only one (large) class in charge of:

  • calculating the geometry, i.e. the position in the detector space of each pixel of the detector

  • manages caches to store intermediate results

NOTA: The Geometry class is not a “transformation class” which would take a detector and transform it. It is rather a description of the experimental setup.

class pyFAI.geometry.core.Geometry(dist=1, poni1=0, poni2=0, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None, orientation=0)

Bases: object

This class is the parent-class of azimuthal integrator.

This class contains a detector (using composition) which provides the position of all pixels, or only a limited set of pixel indices. The Geometry class is responsible for translating/rotating those pixel to their position in reference to the sample position. The description of the experimental setup is inspired by the work of P. Boesecke

Detector is assumed to be corrected from “raster orientation” effect. It is not addressed here but rather in the Detector object or at read time. Considering there is no tilt:

  • Detector fast dimension (dim2) is supposed to be horizontal (dimension X of the image)

  • Detector slow dimension (dim1) is supposed to be vertical, upwards (dimension Y of the image)

  • The third dimension is chose such as the referential is orthonormal, so dim3 is along incoming X-ray beam

Demonstration of the equation done using Mathematica:

__init__(dist=1, poni1=0, poni2=0, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None, orientation=0)
Parameters:

  • dist – distance sample - detector plan (orthogonal distance, not along the beam), in meter.

  • poni1 – coordinate of the point of normal incidence along the detector’s first dimension, in meter

  • poni2 – coordinate of the point of normal incidence along the detector’s second dimension, in meter

  • rot1 – first rotation from sample ref to detector’s ref, in radians

  • rot2 – second rotation from sample ref to detector’s ref, in radians

  • rot3 – third rotation from sample ref to detector’s ref, in radians

  • pixel1 (float) – Deprecated. Pixel size of the fist dimension of the detector, in meter. If both pixel1 and pixel2 are not None, detector pixel size is overwritten. Prefer defining the detector pixel size on the provided detector object. Prefer defining the detector pixel size on the provided detector object (detector.pixel1 = 5e-6).

  • pixel2 (float) – Deprecated. Pixel size of the second dimension of the detector, in meter. If both pixel1 and pixel2 are not None, detector pixel size is overwritten. Prefer defining the detector pixel size on the provided detector object (detector.pixel2 = 5e-6).

  • splineFile (str) – Deprecated. File containing the geometric distortion of the detector. If not None, pixel1 and pixel2 are ignored and detector spline is overwritten. Prefer defining the detector spline manually (detector.splineFile = "file.spline").

  • detector (str or pyFAI.Detector) – name of the detector or Detector instance. String description is deprecated. Prefer using the result of the detector factory: pyFAI.detector_factory("eiger4m")

  • wavelength (float) – Wave length used in meter

  • orientation (int) – orientation of the detector, see pyFAI.detectors.orientation.Orientation

array_from_unit(shape=None, typ='center', unit=2th_deg, scale=True)

Generate an array of position in different dimentions (R, Q, 2Theta …)

Parameters:

  • shape (ndarray.shape) – shape of the expected array, leave it to None for safety

  • typ (str) – “center”, “corner” or “delta”

  • unit (pyFAI.units.Unit or 2-tuple of them (valid only for corner coordinates calculation) – can be any valid unit (found in units.AZIMUTHAL_UNITS or units.RADIAL_UNITS)

  • scale – set to False for returning the internal representation (S.I. often) which is faster

Returns:

R, Q or 2Theta array depending on unit

Return type:

ndarray

calc_pos_zyx(d0=None, d1=None, d2=None, param=None, corners=False, use_cython=True, do_parallax=False)

Calculate the position of a set of points in space in the sample’s centers referential.

This is usually used for calculating the pixel position in space.

Nota: dim3 is the same as dim0

Parameters:

  • d0 – altitude on the point compared to the detector (i.e. z), may be None

  • d1 – position on the detector along the slow dimension (i.e. y)

  • d2 – position on the detector along the fastest dimension (i.e. x)

  • corners – return positions on the corners (instead of center)

  • use_cython – set to False to validate using pure numpy

  • do_parallax – position should be corrected for parallax effect

Returns:

3-tuple of nd-array, with dim0=along the beam, dim1=along slowest dimension dim2=along fastest dimension

calc_transmission(t0, shape=None)

Defines the absorption correction for a phosphor screen or a scintillator from t0, the normal transmission of the screen.

\[ \begin{align}\begin{aligned}Icor = \frac{Iobs(1-t0)}{1-exp(ln(t0)/cos(incidence))}\\let_t = \frac{1-exp(ln(t0)/cos(incidence))}{1 - t0}\end{aligned}\end{align} \]

See reference on: J. Appl. Cryst. (2002). 35, 356–359 G. Wu et al. CCD phosphor

Parameters:

  • t0 – value of the normal transmission (from 0 to 1)

  • shape – shape of the array

Returns:

actual

calcfrom1d(tth, I, shape=None, mask=None, dim1_unit=2th_deg, correctSolidAngle=True, dummy=0.0, polarization_factor=None, polarization_axis_offset=0, dark=None, flat=None)

Computes a 2D image from a 1D integrated profile

Parameters:

  • tth – 1D array with radial unit, this array needs to be ordered

  • I – scattering intensity, corresponding intensity

  • shape – shape of the image (if not defined by the detector)

  • dim1_unit – unit for the “tth” array

  • correctSolidAngle –

  • dummy – value for masked pixels

  • polarization_factor – set to true to use previously used value

  • polarization_axis_offset – axis_offset to be send to the polarization method

  • dark – dark current correction

  • flat – flatfield corrction

Returns:

2D image reconstructed

calcfrom2d(I, tth, chi, shape=None, mask=None, dim1_unit=2th_deg, dim2_unit=chi_deg, correctSolidAngle=True, dummy=0.0, polarization_factor=None, polarization_axis_offset=0, dark=None, flat=None)

Computes a 2D image from a cake / 2D integrated image

Parameters:

  • I – scattering intensity, as an image n_tth, n_chi

  • tth – 1D array with radial unit, this array needs to be ordered

  • chi – 1D array with azimuthal unit, this array needs to be ordered

  • shape – shape of the image (if not defined by the detector)

  • dim1_unit – unit for the “tth” array

  • dim2_unit – unit for the “chi” array

  • correctSolidAngle –

  • dummy – value for masked pixels

  • polarization_factor – set to true to use previously used value

  • polarization_axis_offset – axis_offset to be send to the polarization method

  • dark – dark current correction

  • flat – flatfield corrction

Returns:

2D image reconstructed

center_array(shape=None, unit='2th_deg', scale=True)

Generate a 2D array of the given shape with (i,j) (radial angle ) for all elements.

Parameters:

  • shape (2-tuple of integer) – expected shape

  • unit – string like “2th_deg” or an instance of pyFAI.units.Unit

  • scale – set to False for returning the internal representation (S.I. often) which is faster.

Returns:

2d array of given shape

check_chi_disc(azimuth_range)

Check the position of the \(\chi\) discontinuity

Parameters:

range – range of chi for the integration

Returns:

True if there is a problem

chi(d1, d2, path='cython')

Calculate the chi (azimuthal angle) for the centre of a pixel at coordinate d1, d2. Conversion to lab coordinate system is performed in calc_pos_zyx.

Parameters:

  • d1 (float or array of them) – pixel coordinate along the 1st dimention (C convention)

  • d2 (float or array of them) – pixel coordinate along the 2nd dimention (C convention)

  • path – can be “tan” (i.e via numpy) or “cython”

Returns:

chi, the azimuthal angle in rad

chiArray(shape=None)

Generate an array of azimuthal angle chi(i,j) for all elements in the detector.

Azimuthal angles are in radians

Nota: Refers to the pixel centers !

Parameters:

shape – the shape of the chi array

Returns:

the chi array as numpy.ndarray

chi_corner(d1, d2)

Calculate the chi (azimuthal angle) for the corner of a pixel at coordinate d1,d2 which in the lab ref has coordinate:

Parameters:

  • d1 (float or array of them) – pixel coordinate along the 1st dimention (C convention)

  • d2 (float or array of them) – pixel coordinate along the 2nd dimention (C convention)

Returns:

chi, the azimuthal angle in rad

property chia

chi array in cache

cornerArray(shape=None)

Generate a 4D array of the given shape with (i,j) (radial angle 2th, azimuthal angle chi ) for all elements.

Parameters:

shape (2-tuple of integer) – expected shape

Returns:

3d array with shape=(*shape,4,2) the two elements are: * dim3[0]: radial angle 2th * dim3[1]: azimuthal angle chi

cornerQArray(shape=None)

Generate a 3D array of the given shape with (i,j) (azimuthal angle) for all elements.

Parameters:

shape (2-tuple of integer) – expected shape

Returns:

3d array with shape=(*shape,4,2) the two elements are (scattering vector q, azimuthal angle chi)

cornerRArray(shape=None)

Generate a 3D array of the given shape with (i,j) (azimuthal angle) for all elements.

Parameters:

shape (2-tuple of integer) – expected shape

Returns:

3d array with shape=(*shape,4,2) the two elements are (radial distance, azimuthal angle chi)

cornerRd2Array(shape=None)

Generate a 3D array of the given shape with (i,j) (azimuthal angle) for all elements.

Parameters:

shape (2-tuple of integer) – expected shape

Returns:

3d array with shape=(*shape,4,2) the two elements are (reciprocal spacing squared, azimuthal angle chi)

corner_array(shape=None, unit=None, use_cython=True, scale=True)

Generate a 3D array of the given shape with (i,j) (radial angle 2th, azimuthal angle chi ) for all elements.

Parameters:

  • shape (2-tuple of integer) – expected shape

  • unit – string like “2th_deg” or an instance of pyFAI.units.Unit

  • use_cython – set to False to use the slower Python path (for tests)

  • scale – set to False for returning the internal representation (S.I. often) which is faster

Returns:

3d array with shape=(*shape,4,2) the two elements are: - dim3[0]: radial angle 2th, q, r… - dim3[1]: azimuthal angle chi

property correct_SA_spline
cos_incidence(d1, d2, path='cython')

Calculate the cosinus of the incidence angle (alpha) for current pixels (P). The poni being the point of normal incidence, it’s incidence angle is \({\alpha} = 0\) hence \(cos({\alpha}) = 1\).

Works also for non-flat detectors where the normal of the pixel is considered.

Parameters:

  • d1 – 1d or 2d set of points in pixel coord

  • d2 – 1d or 2d set of points in pixel coord

  • path – can be “cython”, “numexpr” or “numpy” (fallback).

Returns:

cosine of the incidence angle

del_chia()
del_dssa()
del_qa()
del_ra()
del_ttha()
delta2Theta(shape=None)

Generate a 2D array of the given shape with the max distance between the center and any corner in 2 theta angle in radians

Parameters:

shape – The shape of the detector array: 2-tuple of integer

Returns:

2D-array containing the max delta angle between a pixel center and any corner in 2theta-angle (rad)

deltaChi(shape=None, use_cython=True)

Generate a 2D array of the given shape with the max distance between the center and any corner in chi-angle (rad)

Parameters:

shape – The shape of the detector array: 2-tuple of integer

Returns:

2D-array containing the max delta angle between a pixel center and any corner in chi-angle (rad)

deltaQ(shape=None)

Generate a 2D array of the given shape with the max distance between the center and any corner in q_vector unit (nm^-1)

Parameters:

shape – The shape of the detector array: 2-tuple of integer

Returns:

array 2D containing the max delta Q between a pixel center and any corner in q_vector unit (nm^-1)

deltaR(shape=None)

Generate a 2D array of the given shape with (i,j) with the max distance between the center and any corner in radius unit (m)

Parameters:

shape – The shape of the detector array: 2-tuple of integer

Returns:

array 2D containing the max delta Q between a pixel center and any corner in distance (m)

deltaRd2(shape=None)

Generate a 2D array of the given shape with the max distance between the center and any corner in unit: reciprocal spacing squarred (1/nm^2)

Parameters:

shape – The shape of the detector array: 2-tuple of integer

Returns:

array 2D containing the max delta (d*)^2 between a pixel center and any corner in reciprocal spacing squarred (1/nm^2)

delta_array(shape=None, unit='2th_deg', scale=False)

Generate a 2D array of the given shape with the delta-radius for all elements.

Parameters:

  • shape (2-tuple of integer) – expected shape

  • unit – string like “2th_deg” or an instance of pyFAI.units.Unit

  • scale – set to False for returning the internal representation (S.I. often) which is faster

Returns:

2D array

diffSolidAngle(d1, d2)

Calculate the solid angle of the current pixels (P) versus the PONI (C)

\[ \begin{align}\begin{aligned}dOmega = \frac{Omega(P)}{Omega(C)} = \frac{A \cdot cos(a)}{SP^2} \cdot \frac{SC^2}{A \cdot cos(0)} = \frac{3}{cos(a)} = \frac{SC^3}{SP^3}\\cos(a) = \frac{SC}{SP}\end{aligned}\end{align} \]
Parameters:

  • d1 – 1d or 2d set of points

  • d2 – 1d or 2d set of points (same size&shape as d1)

Returns:

solid angle correction array

property dist
property dssa

solid angle array in cache

property energy
getCXI()

Export the geometry in the CXI format as defined in https://raw.githubusercontent.com/cxidb/CXI/master/cxi_file_format.pdf

Returns:

dict with the structure of a CXI file to be written into HDF5

getFit2D()

Export geometry setup with the geometry of Fit2D

Returns:

dict with parameters compatible with fit2D geometry

getImageD11()

Export the current geometry in ImageD11 format. Please refer to the documentation in doc/source/geometry_conversion.rst for the orientation and units of those values.

Returns:

an Ordered dict with those parameters: distance 294662.658 #in nm o11 1 o12 0 o21 0 o22 -1 tilt_x 0.00000 tilt_y -0.013173 tilt_z 0.002378 wavelength 0.154 y_center 1016.328171 y_size 48.0815 z_center 984.924425 z_size 46.77648

getPyFAI()

Export geometry setup with the geometry of PyFAI

Deprecated, please use get/set_config which is cleaner! when it comes to detector specification

Returns:

dict with the parameter-set of the PyFAI geometry

getSPD()

get the SPD like parameter set: For geometry description see Peter Boesecke J.Appl.Cryst.(2007).40, s423–s427

Basically the main difference with pyFAI is the order of the axis which are flipped

Returns:

dictionnary with those parameters: SampleDistance: distance from sample to detector at the PONI (orthogonal projection) Center_1, pixel position of the PONI along fastest axis Center_2: pixel position of the PONI along slowest axis Rot_1: rotation around the fastest axis (x) Rot_2: rotation around the slowest axis (y) Rot_3: rotation around the axis ORTHOGONAL to the detector plan PSize_1: pixel size in meter along the fastest dimention PSize_2: pixel size in meter along the slowst dimention splineFile: name of the file containing the spline BSize_1: pixel binning factor along the fastest dimention BSize_2: pixel binning factor along the slowst dimention WaveLength: wavelength used in meter

get_chia()
get_config()

return the configuration as a dictionnary

Returns:

dictionary with the current configuration

get_correct_solid_angle_for_spline()
get_dist()
get_dssa()
get_energy()
get_mask()
get_maskfile()
get_parallax()
get_pixel1()
get_pixel2()
get_poni1()
get_poni2()
get_qa()
get_ra()
get_rot1()
get_rot2()
get_rot3()
get_shape(shape=None)

Guess what is the best shape ….

Parameters:

shape – force this value (2-tuple of int)

Returns:

2-tuple of int

get_spline()
get_splineFile()
get_ttha()
get_wavelength()
guess_npt_rad()

calculate the number of pixels from the beam-center to the corner the further away from it.

Returns:

this distance as a number of pixels.

It is a good guess of the number of bins to be used without oversampling too much the data for azimuthal integration

load(filename)

Load the refined parameters from a file.

Parameters:

filename (string) – name of the file to load

Returns:

itself with updated parameters

make_headers(type_='list')

Create a configuration / header for the integrated data

Parameters:

type – can be “list” or “dict”

Returns:

the header with the proper format

property mask
property maskfile
normalize_azimuth_range(azimuth_range)

Convert the azimuth range from degrees to radians

This method takes care of the position of the discontinuity and adapts the range accordingly!

Parameters:

azimuth_range – 2-tuple of float in degrees

Returns:

2-tuple of float in radians in a range such to avoid the discontinuity

oversampleArray(myarray)
property parallax
property pixel1
property pixel2
polarization(shape=None, factor=None, axis_offset=0, with_checksum=False, path='numexpr')

Calculate the polarization correction accoding to the polarization factor:

  • If the polarization factor is None,

    the correction is not applied (returns 1)

  • If the polarization factor is 0 (circular polarization),

    the correction correspond to (1+(cos2θ)^2)/2

  • If the polarization factor is 1 (linear horizontal polarization),

    there is no correction in the vertical plane and a node at 2th=90, chi=0

  • If the polarization factor is -1 (linear vertical polarization),

    there is no correction in the horizontal plane and a node at 2th=90, chi=90

  • If the polarization is elliptical, the polarization factor varies between -1 and +1.

The axis_offset parameter allows correction for the misalignement of the polarization plane (or ellipse main axis) and the the detector’s X axis.

Parameters:

  • shape – the shape of the array, can be guessed most of the time from the detector definition

  • factor – (Ih-Iv)/(Ih+Iv): varies between 0 (circular/random polarization) and 1 (where division by 0 could occure at 2th=90, chi=0)

  • axis_offset – Angle between the polarization main axis and detector’s X direction (in radians !!!)

  • with_checksum – calculate also the checksum (used with OpenCL integration)

  • path – set to numpy to enforce the use of numpy, else uses numexpr (mutithreaded)

Returns:

2D array with polarization correction (normalization) array or namedtuple if with_checksum

property poni1
property poni2
positionArray(*arg, **kwarg)

Deprecated version of position_array(), left for compatibility see doc of position_array

position_array(shape=None, corners=False, dtype=<class 'numpy.float64'>, use_cython=True, do_parallax=False)

Generate an array for the pixel position given the shape of the detector.

if corners is False, the coordinates of the center of the pixel is returned in an array of shape: (shape[0], shape[1], 3) where the 3 coordinates are: * z: along incident beam, * y: to the top/sky, * x: towards the center of the ring

If is True, the corner of each pixels are then returned. the output shape is then (shape[0], shape[1], 4, 3)

Parameters:

  • shape – shape of the array expected

  • corners – set to true to receive a (…,4,3) array of corner positions

  • dtype – output format requested. Double precision is needed for fitting the geometry

  • use_cython ((bool)) – set to false to test the Python path (slower)

  • do_parallax – correct for parallax effect (if parametrized)

Returns:

3D coodinates as nd-array of size (…,3) or (…,3) (default)

Nota: this value is not cached and actually generated on demand (costly)

qArray(shape=None)

Generate an array of the given shape with q(i,j) for all elements.

qCornerFunct(d1, d2)

Calculate the q_vector for any pixel corner (in nm^-1)

Parameters:

shape – expected shape of the detector

qFunction(d1, d2, param=None, path='cython')

Calculates the q value for the center of a given pixel (or set of pixels) in nm-1

q = 4pi/lambda sin( 2theta / 2 )

Parameters:

  • d1 (scalar or array of scalar) – position(s) in pixel in first dimension (c order)

  • d2 (scalar or array of scalar) – position(s) in pixel in second dimension (c order)

Returns:

q in in nm^(-1)

Return type:

float or array of floats.

property qa

Q array in cache

quaternion(param=None)

Calculate the quaternion associated to the current rotations from rot1, rot2, rot3.

Uses the transformations-library from C. Gohlke

Parameters:

param – use this set of parameters instead of the default one.

Returns:

numpy array with 4 elements [w, x, y, z]

rArray(shape=None)

Generate an array of the given shape with r(i,j) for all elements; The radius r being in meters.

Parameters:

shape – expected shape of the detector

Returns:

2d array of the given shape with radius in m from beam center on detector.

rCornerFunct(d1, d2)

Calculate the radius array for any pixel corner (in m)

rFunction(d1, d2, param=None, path='cython')

Calculates the radius value for the center of a given pixel (or set of pixels) in m

r = distance to the incident beam

Parameters:

  • d1 (scalar or array of scalar) – position(s) in pixel in first dimension (c order)

  • d2 (scalar or array of scalar) – position(s) in pixel in second dimension (c order)

Returns:

r in in m

Return type:

float or array of floats.

property ra

R array in cache

rd2Array(shape=None)

Generate an array of the given shape with (d*(i,j))^2 for all pixels.

d*^2 is the reciprocal spacing squared in inverse nm squared

Parameters:

shape – expected shape of the detector

Returns:

2d array of the given shape with reciprocal spacing squared

read(filename)

Load the refined parameters from a file.

Parameters:

filename (string) – name of the file to load

Returns:

itself with updated parameters

reset(collect_garbage=True)

reset most arrays that are cached: used when a parameter changes.

Parameters:

collect_garbage – set to False to prevent garbage collection, faster

property rot1
property rot2
property rot3
rotation_matrix(param=None)

Compute and return the detector tilts as a single rotation matrix

Corresponds to rotations about axes 1 then 2 then 3 (=> 0 later on) For those using spd (PB = Peter Boesecke), tilts relate to this system (JK = Jerome Kieffer) as follows: JK1 = PB2 (Y) JK2 = PB1 (X) JK3 = PB3 (Z) …slight differences will result from the order FIXME: make backwards and forwards converter helper function

axis1 is vertical and perpendicular to beam axis2 is horizontal and perpendicular to beam axis3 is along the beam, becomes axis0 see: http://pyfai.readthedocs.io/en/latest/geometry.html#detector-position or ../doc/source/img/PONI.png

Parameters:

param (list of float) – list of geometry parameters, defaults to self.param uses elements [3],[4],[5]

Returns:

rotation matrix

Return type:

3x3 float array

save(filename)

Save the geometry parameters.

Parameters:

filename (string) – name of the file where to save the parameters

setCXI(dico)

Set the geometry of the azimuthal integrator from a CXI data structure (as dict)

Parameters:

dico – dictionary with CXI information

setChiDiscAtPi()

Set the position of the discontinuity of the chi axis between -pi and +pi. This is the default behavour

setChiDiscAtZero()

Set the position of the discontinuity of the chi axis between 0 and 2pi. By default it is between pi and -pi

setFit2D(directDist, centerX, centerY, tilt=0.0, tiltPlanRotation=0.0, pixelX=None, pixelY=None, splineFile=None, detector=None, wavelength=None)

Set the Fit2D-like parameter set: For geometry description see HPR 1996 (14) pp-240 https://doi.org/10.1080/08957959608201408

Warning: Fit2D flips automatically images depending on their file-format. By reverse engineering we noticed this behavour for Tiff and Mar345 images (at least). To obtaine correct result you will have to flip images using numpy.flipud.

Parameters:

  • direct – direct distance from sample to detector along the incident beam (in millimeter as in fit2d)

  • tilt – tilt in degrees

  • tiltPlanRotation – Rotation (in degrees) of the tilt plan arround the Z-detector axis * 0deg -> Y does not move, +X goes to Z<0 * 90deg -> X does not move, +Y goes to Z<0 * 180deg -> Y does not move, +X goes to Z>0 * 270deg -> X does not move, +Y goes to Z>0

  • pixelX,pixelY – as in fit2d they ar given in micron, not in meter

  • centerY (centerX,) – pixel position of the beam center

  • splineFile – name of the file containing the spline

  • detector – name of the detector or detector object

setImageD11(param)

Set the geometry from the parameter set which contains distance, o11, o12, o21, o22, tilt_x, tilt_y tilt_z, wavelength, y_center, y_size, z_center and z_size. Please refer to the documentation in doc/source/geometry_conversion.rst for the orientation and units of those values.

Parameters:

param – dict with the values to set.

setOversampling(iOversampling)

set the oversampling factor

setPyFAI(**kwargs)

set the geometry from a pyFAI-like dict

Deprecated, please use get/set_config which is cleaner! when it comes to detector specification

setSPD(SampleDistance, Center_1, Center_2, Rot_1=0, Rot_2=0, Rot_3=0, PSize_1=None, PSize_2=None, splineFile=None, BSize_1=1, BSize_2=1, WaveLength=None)

Set the SPD like parameter set: For geometry description see Peter Boesecke J.Appl.Cryst.(2007).40, s423–s427

Basically the main difference with pyFAI is the order of the axis which are flipped

Parameters:

  • SampleDistance – distance from sample to detector at the PONI (orthogonal projection)

  • Center_1 – pixel position of the PONI along fastest axis

  • Center_2 – pixel position of the PONI along slowest axis

  • Rot_1 – rotation around the fastest axis (x)

  • Rot_2 – rotation around the slowest axis (y)

  • Rot_3 – rotation around the axis ORTHOGONAL to the detector plan

  • PSize_1 – pixel size in meter along the fastest dimention

  • PSize_2 – pixel size in meter along the slowst dimention

  • splineFile – name of the file containing the spline

  • BSize_1 – pixel binning factor along the fastest dimention

  • BSize_2 – pixel binning factor along the slowst dimention

  • WaveLength – wavelength used

set_chia(_)
set_config(config)

Set the config of the geometry and of the underlying detector

Parameters:

config – dictionary with the configuration

Returns:

itself

set_correct_solid_angle_for_spline(value)
set_dist(value)
set_dssa(_)
set_energy(energy)

Set the energy in keV

set_mask(mask)
set_maskfile(maskfile)
set_parallax(value)
set_param(param)

set the geometry from a 6-tuple with dist, poni1, poni2, rot1, rot2, rot3

set_pixel1(pixel1)
set_pixel2(pixel2)
set_poni1(value)
set_poni2(value)
set_qa(_)
set_ra(_)
set_rot1(value)
set_rot2(value)
set_rot3(value)
set_rot_from_quaternion(w, x, y, z)

Quaternions are convieniant ways to represent 3D rotation This method allows to define rot1(left-handed), rot2(left-handed) and rot3 (right handed) as definied in the documentation from a quaternion, expressed in the right handed (x1, x2, x3) basis set.

Uses the transformations-library from C. Gohlke

Parameters:

  • w – Real part of the quaternion (correspond to cos alpha/2)

  • x – Imaginary part of the quaternion, correspond to u1*sin(alpha/2)

  • y – Imaginary part of the quaternion, correspond to u2*sin(alpha/2)

  • z – Imaginary part of the quaternion, correspond to u3*sin(alpha/2)

set_spline(spline)
set_splineFile(splineFile)
set_ttha(_)
set_wavelength(value)

Set the wavelength in meter!

sin_incidence(d1, d2, path='cython')

Calculate the sinus of the incidence angle (alpha) for current pixels (P). The poni being the point of normal incidence, it’s incidence angle is \({\alpha} = 0\) hence \(sin({\alpha}) = 0\).

Works also for non-flat detectors where the normal of the pixel is considered.

Parameters:

  • d1 – 1d or 2d set of points in pixel coord

  • d2 – 1d or 2d set of points in pixel coord

  • path – can be “cython”, “numexpr” or “numpy” (fallback).

Returns:

cosine of the incidence angle

classmethod sload(filename)

A static method combining the constructor and the loader from a file

Parameters:

filename (string) – name of the file to load

Returns:

instance of Geometry of AzimuthalIntegrator set-up with the parameter from the file.

solidAngleArray(shape=None, order=3, absolute=False, with_checksum=False)

Generate an array for the solid angle correction given the shape of the detector.

solid_angle = cos(incidence)^3

Parameters:

  • shape – shape of the array expected

  • order – should be 3, power of the formula just obove

  • absolute – the absolute solid angle is calculated as:

  • with_checksum – returns the array _and_ its checksum as a 2-tuple

SA = pix1*pix2/dist^2 * cos(incidence)^3

property spline
property splineFile
tth(d1, d2, param=None, path='cython')

Calculates the 2theta value for the center of a given pixel (or set of pixels)

Parameters:

  • d1 (scalar or array of scalar) – position(s) in pixel in first dimension (c order)

  • d2 (scalar or array of scalar) – position(s) in pixel in second dimension (c order)

  • path – can be “cos”, “tan” or “cython”

Returns:

2theta in radians

Return type:

float or array of floats.

tth_corner(d1, d2)

Calculates the 2theta value for the corner of a given pixel (or set of pixels)

Parameters:

  • d1 (scalar or array of scalar) – position(s) in pixel in first dimension (c order)

  • d2 (scalar or array of scalar) – position(s) in pixel in second dimension (c order)

Returns:

2theta in radians

Return type:

floar or array of floats.

property ttha

2theta array in cache

twoThetaArray(shape=None)

Generate an array of two-theta(i,j) in radians for each pixel in detector

the 2theta array values are in radians

Parameters:

shape – shape of the detector

Returns:

array of 2theta position in radians

property wavelength
write(filename)

Save the geometry parameters.

Parameters:

filename (string) – name of the file where to save the parameters

class pyFAI.geometry.core.PolarizationArray(array, checksum)

Bases: tuple

array

Alias for field number 0

checksum

Alias for field number 1

class pyFAI.geometry.core.PolarizationDescription(polarization_factor, axis_offset)

Bases: tuple

axis_offset

Alias for field number 1

polarization_factor

Alias for field number 0

pyFAI.geometry.cxi module

This modules contains helper function to convert to/from CXI format described in:

https://raw.githubusercontent.com/cxidb/CXI/master/cxi_file_format.pdf

ToDo

pyFAI.geometry.fit2d module

This modules contains helper function to convert to/from FIT2D geometry

class pyFAI.geometry.fit2d.Fit2dGeometry(directDist: float = None, centerX: float = None, centerY: float = None, tilt: float = 0.0, tiltPlanRotation: float = 0.0, pixelX: float = None, pixelY: float = None, splineFile: str = None, detector: Detector = None, wavelength: float = None)

Bases: NamedTuple

This object represents the geometry as configured in Fit2D

Parameters:

  • directDist – Distance from sample to the detector along the incident beam in mm. The detector may be extrapolated when tilted.

  • centerX – Position of the beam-center on the detector in pixels, along the fastest axis of the image.

  • centerY – Position of the beam-center on the detector in pixels, along the slowest axis of the image.

  • tilt – Angle of tilt of the detector in degrees

  • tiltPlanRotation – Direction of the tilt (unefined when tilt is 0)

  • detector – Detector definition as is pyFAI.

  • wavelength – Wavelength of the beam in Angstrom

centerX: float

Alias for field number 1

centerY: float

Alias for field number 2

detector: Detector

Alias for field number 8

directDist: float

Alias for field number 0

pixelX: float

Alias for field number 5

pixelY: float

Alias for field number 6

splineFile: str

Alias for field number 7

tilt: float

Alias for field number 3

tiltPlanRotation: float

Alias for field number 4

wavelength: float

Alias for field number 9

pyFAI.geometry.fit2d.convert_from_Fit2d(f2d)

Import the geometry from Fit2D

Parameters:

f2d – instance of Fit2dGeometry

Returns:

PoniFile instance

pyFAI.geometry.fit2d.convert_to_Fit2d(poni)

Convert a Geometry|PONI object to the geometry of Fit2D Please see the doc from Fit2dGeometry

Parameters:

poni – azimuthal integrator, geometry or poni

Returns:

same geometry as a Fit2dGeometry named-tuple

pyFAI.geometry.fit2d.degrees(x)
pyFAI.geometry.fit2d.radians(x)