pyFAI package¶

`pyFAI` Package¶

pyFAI.__init__.AzimuthalIntegrator(*args, **kwargs)¶

pyFAI.__init__.benchmarks(*arg, **kwarg)¶

Run the integrated benchmarks.

See the documentation of pyFAI.benchmark.run_benchmark

pyFAI.__init__.detector_factory(name, config=None)¶

Create a new detector.

Parameters

name (str) – name of a detector
config (dict) – configuration of the detector supporting dict or JSON representation.

Returns

an instance of the right detector, set-up if possible

Return type

pyFAI.detectors.Detector

pyFAI.__init__.load(filename)¶

Load an azimuthal integrator from a filename description.

Parameters: filename (str) – name of the file to load
Returns: instance of Gerometry of AzimuthalIntegrator set-up with the parameter from the file.

pyFAI.__init__.tests(deprecation=False)¶

Runs the test suite of the installed version

Parameters: deprecation – enable/disables deprecation warning in the tests

pyFAI.__init__.use_opencl = True¶

Global configuration which allow to disable OpenCL programatically. It must be set before requesting any OpenCL modules.

import pyFAI
pyFAI.use_opencl = False

`average` Module¶

Utilities, mainly for image treatment

exception pyFAI.average.AlgorithmCreationError¶

Bases: RuntimeError

Exception returned if creation of an ImageReductionFilter is not possible

class pyFAI.average.Average¶

Bases: object

Process images to generate an average using different algorithms.

__init__()¶: Constructor

add_algorithm(algorithm)¶

Defines another algorithm which will be computed on the source.

Parameters: algorithm (ImageReductionFilter) – An averaging algorithm.

get_counter_frames()¶

Returns the number of frames used for the process.

Return type: int

get_fabio_images()¶

Returns source images as fabio images.

Return type: list(fabio.fabioimage.FabioImage)

get_image_reduction(algorithm)¶

Returns the result of an algorithm. The process must be already done.

Parameters: algorithm (ImageReductionFilter) – An averaging algorithm
Return type: numpy.ndarray

process()¶: Process source images to all defined averaging algorithms defined using defined parameters. To access to the results you have to define a writer (AverageWriter). To follow the process forward you have to define an observer (AverageObserver).

set_correct_flat_from_dark(correct_flat_from_dark)¶

Defines if the dark must be applied on the flat.

Parameters: correct_flat_from_dark (bool) – If true, the dark is applied.

set_dark(dark_list)¶

Defines images used as dark.

Parameters: dark_list (list) – List of dark used

set_flat(flat_list)¶

Defines images used as flat.

Parameters: flat_list (list) – List of dark used

set_images(image_list)¶

Defines the set set of source images to used to process an average.

Parameters: image_list (list) – List of filename, numpy arrays, fabio images used as source for the computation.

set_monitor_name(monitor_name)¶

Defines the monitor name used to correct images before processing the average. This monitor must be part of the file header, else the image is skipped.

Parameters: monitor_name (str) – Name of the monitor available on the header file

set_observer(observer)¶

Set an observer to the average process.

Parameters: observer (AverageObserver) – An observer

set_pixel_filter(threshold, minimum, maximum)¶

Defines the filter applied on each pixels of the images before processing the average.

Parameters

threshold – what is the upper limit? all pixel > max*(1-threshold) are discareded.
minimum – minimum valid value or True
maximum – maximum valid value

set_writer(writer)¶

Defines the object write which will be used to store the result.

Parameters: writer (AverageWriter) – The writer to use.

class pyFAI.average.AverageDarkFilter(filter_name, cut_off, quantiles)¶

Bases: pyFAI.average.ImageStackFilter

Filter based on the algorithm of average_dark

TODO: Must be split according to each filter_name, and removed

__init__(filter_name, cut_off, quantiles)¶: Initialize self. See help(type(self)) for accurate signature.

get_parameters()¶: Return a dictionary containing filter parameters

property name¶

class pyFAI.average.AverageObserver¶

Bases: object

algorithm_finished(algorithm)¶: Called when an algorithm is finished

algorithm_started(algorithm)¶: Called when an algorithm is started

frame_processed(algorithm, frame_index, frames_count)¶: Called after providing a frame to an algorithm

image_loaded(fabio_image, image_index, images_count)¶: Called when an input image is loaded

process_finished()¶: Called when the full process is finished

process_started()¶: Called when the full processing is started

result_processing(algorithm)¶: Called before the result of an algorithm is computed

class pyFAI.average.AverageWriter¶

Bases: object

Interface for using writer in Average process.

close()¶: Close the writer. Must not be used anymore.

write_header(merged_files, nb_frames, monitor_name)¶

Write the header of the average

Parameters

merged_files (list) – List of files used to generate this output
nb_frames (int) – Number of frames used
monitor_name (str) – Name of the monitor used. Can be None.

write_reduction(algorithm, data)¶

Write one reduction

Parameters

algorithm (ImageReductionFilter) – Algorithm used
data (object) – Data of this reduction

class pyFAI.average.ImageAccumulatorFilter¶

Bases: pyFAI.average.ImageReductionFilter

Filter applied in a set of images in which it is possible to reduce data step by step into a single merged image.

add_image(image)¶

Add an image to the filter.

Parameters: image (numpy.ndarray) – image to add

get_result()¶

Get the result of the filter.

Returns: result filter
Return type: numpy.ndarray

init(max_images=None)¶

Initialize the filter before using it.

Parameters: max_images (int) – Max images supported by the filter

class pyFAI.average.ImageReductionFilter¶

Bases: object

Generic filter applied in a set of images.

add_image(image)¶

Add an image to the filter.

Parameters: image (numpy.ndarray) – image to add

get_parameters()¶

Return a dictionary containing filter parameters

Return type: dict

get_result()¶

Get the result of the filter.

Returns: result filter

init(max_images=None)¶

Initialize the filter before using it.

Parameters: max_images (int) – Max images supported by the filter

class pyFAI.average.ImageStackFilter¶

Bases: pyFAI.average.ImageReductionFilter

Filter creating a stack from all images and computing everything at the end.

add_image(image)¶

Add an image to the filter.

Parameters: image (numpy.ndarray) – image to add

get_result()¶

Get the result of the filter.

Returns: result filter

init(max_images=None)¶

Initialize the filter before using it.

Parameters: max_images (int) – Max images supported by the filter

class pyFAI.average.MaxAveraging¶

Bases: pyFAI.average.ImageAccumulatorFilter

name = 'max'¶

class pyFAI.average.MeanAveraging¶

Bases: pyFAI.average.SumAveraging

get_result()¶

Get the result of the filter.

Returns: result filter
Return type: numpy.ndarray

name = 'mean'¶

class pyFAI.average.MinAveraging¶

Bases: pyFAI.average.ImageAccumulatorFilter

name = 'min'¶

class pyFAI.average.MultiFilesAverageWriter(file_name_pattern, file_format, dry_run=False)¶

Bases: pyFAI.average.AverageWriter

Write reductions into multi files. File headers are duplicated.

__init__(file_name_pattern, file_format, dry_run=False)¶

Parameters

file_name_pattern (str) – File name pattern for the output files. If it contains “{method_name}”, it is updated for each reduction writing with the name of the reduction.
file_format (str) – File format used. It is the default extension file.
dry_run (bool) – If dry_run, the file is created on memory but not saved on the file system at the end

close()¶: Close the writer. Must not be used anymore.

get_fabio_image(algorithm)¶

Get the constructed fabio image

Return type: fabio.fabioimage.FabioImage

write_header(merged_files, nb_frames, monitor_name)¶

Write the header of the average

Parameters

merged_files (list) – List of files used to generate this output
nb_frames (int) – Number of frames used
monitor_name (str) – Name of the monitor used. Can be None.

write_reduction(algorithm, data)¶

Write one reduction

Parameters

algorithm (ImageReductionFilter) – Algorithm used
data (object) – Data of this reduction

class pyFAI.average.SumAveraging¶

Bases: pyFAI.average.ImageAccumulatorFilter

name = 'sum'¶

pyFAI.average.average_dark(lstimg, center_method='mean', cutoff=None, quantiles=(0.5, 0.5))¶

Averages a serie of dark (or flat) images. Centers the result on the mean or the median … but averages all frames within cutoff*std

Parameters

lstimg – list of 2D images or a 3D stack
center_method (str) – is the center calculated by a “mean”, “median”, “quantile”, “std”
cutoff (float or None) – keep all data where (I-center)/std < cutoff
quantiles (tuple(float, float) or None) – 2-tuple of floats average out data between the two quantiles

Returns

2D image averaged

pyFAI.average.average_images(listImages, output=None, threshold=0.1, minimum=None, maximum=None, darks=None, flats=None, filter_='mean', correct_flat_from_dark=False, cutoff=None, quantiles=None, fformat='edf', monitor_key=None)¶

Takes a list of filenames and create an average frame discarding all: saturated pixels.

Parameters

listImages – list of string representing the filenames
output – name of the optional output file
threshold – what is the upper limit? all pixel > max*(1-threshold) are discareded.
minimum – minimum valid value or True
maximum – maximum valid value
darks – list of dark current images for subtraction
flats – list of flat field images for division
filter – can be “min”, “max”, “median”, “mean”, “sum”, “quantiles” (default=’mean’)
correct_flat_from_dark – shall the flat be re-corrected ?
cutoff – keep all data where (I-center)/std < cutoff
quantiles – 2-tuple containing the lower and upper quantile (0<q<1) to average out.
fformat – file format of the output image, default: edf
str (monitor_key) – Key containing the monitor. Can be none.

Returns

filename with the data or the data ndarray in case format=None

pyFAI.average.bounding_box(img)¶

Tries to guess the bounding box around a valid massif

Parameters: img – 2D array like
Returns: 4-typle (d0_min, d1_min, d0_max, d1_max)

pyFAI.average.common_prefix(string_list)¶

Return the common prefix of a list of strings

TODO: move it into utils package

Parameters: string_list (list(str)) – List of strings
Return type: str

pyFAI.average.create_algorithm(filter_name, cut_off=None, quantiles=None)¶

Factory to create algorithm according to parameters

Parameters

cutoff (float or None) – keep all data where (I-center)/std < cutoff
quantiles (tuple(float, float) or None) – 2-tuple of floats average out data between the two quantiles

Returns

An algorithm

Return type

ImageReductionFilter

Raises

AlgorithmCreationError – If it is not possible to create the algorithm

pyFAI.average.is_algorithm_name_exists(filter_name)¶: Return true if the name is a name of a filter algorithm

pyFAI.average.remove_saturated_pixel(ds, threshold=0.1, minimum=None, maximum=None)¶

Remove saturated fixes from an array inplace.

Parameters

ds – a dataset as ndarray
threshold (float) – what is the upper limit? all pixel > max*(1-threshold) are discareded.
minimum (float) – minumum valid value (or True for auto-guess)
maximum (float) – maximum valid value

Returns

the input dataset

`azimuthalIntegrator` Module¶

class pyFAI.azimuthalIntegrator.AzimuthalIntegrator(dist=1, poni1=0, poni2=0, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None)¶

Bases: pyFAI.geometry.Geometry

This class is an azimuthal integrator based on P. Boesecke’s geometry and histogram algorithm by Manolo S. del Rio and V.A Sole

All geometry calculation are done in the Geometry class

main methods are:

>>> tth, I = ai.integrate1d(data, npt, unit="2th_deg")
>>> q, I, sigma = ai.integrate1d(data, npt, unit="q_nm^-1", error_model="poisson")
>>> regrouped = ai.integrate2d(data, npt_rad, npt_azim, unit="q_nm^-1")[0]

DEFAULT_METHOD_1D = IntegrationMethod(1d int, full split, histogram, cython)¶

DEFAULT_METHOD_2D = IntegrationMethod(2d int, pseudo split, histogram, cython)¶: Fail-safe low-memory integrator

USE_LEGACY_MASK_NORMALIZATION = True¶

If true, the Python engine integrator will normalize the mask to use the most frequent value of the mask as the non-masking value.

This behaviour is not consistant with other engines and is now deprecated. This flag will be turned off in the comming releases.

Turning off this flag force the user to provide a mask with 0 as non-masking value. And any non-zero as masking value (negative or positive value). A boolean mask is also accepted (True is the masking value).

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

Parameters

dist (float) – distance sample - detector plan (orthogonal distance, not along the beam), in meter.
poni1 (float) – coordinate of the point of normal incidence along the detector’s first dimension, in meter
poni2 (float) – coordinate of the point of normal incidence along the detector’s second dimension, in meter
rot1 (float) – first rotation from sample ref to detector’s ref, in radians
rot2 (float) – second rotation from sample ref to detector’s ref, in radians
rot3 (float) – 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

create_mask(data, mask=None, dummy=None, delta_dummy=None, unit=None, radial_range=None, azimuth_range=None, mode='normal')¶

Combines various masks into another one.

Parameters

data (ndarray) – input array of data
mask (ndarray) – input mask (if none, self.mask is used)
dummy (float) – value of dead pixels
delta_dumy – precision of dummy pixels
mode (str) – can be “normal” or “numpy” (inverted) or “where” applied to the mask

Returns

the new mask

Return type

ndarray of bool

This method combine two masks (dynamic mask from data & dummy and mask) to generate a new one with the ‘or’ binary operation. One can adjust the level, with the dummy and the delta_dummy parameter, when you consider the data values needs to be masked out.

This method can work in two different mode:

“normal”: False for valid pixels, True for bad pixels

“numpy”: True for valid pixels, false for others

“where”: does a numpy.where on the “numpy” output

This method tries to accomodate various types of masks (like valid=0 & masked=-1, …)

Note for the developper: we use a lot of numpy.logical_or in this method, the out= argument allows to recycle buffers and save considerable time in allocating temporary arrays.

dark_correction(data, dark=None)¶

Correct for Dark-current effects. If dark is not defined, correct for a dark set by “set_darkfiles”

Parameters

data – input ndarray with the image
dark – ndarray with dark noise or None

Returns

2tuple: corrected_data, dark_actually used (or None)

property darkcurrent¶

property darkfiles¶

property empty¶

flat_correction(data, flat=None)¶

Correct for flat field. If flat is not defined, correct for a flat set by “set_flatfiles”

Parameters

data – input ndarray with the image
flat – ndarray with flatfield or None for no correction

Returns

2tuple: corrected_data, flat_actually used (or None)

property flatfield¶

property flatfiles¶

get_darkcurrent()¶

get_empty()¶

get_flatfield()¶

inpainting(data, mask, npt_rad=1024, npt_azim=512, unit='r_m', method='splitpixel', poissonian=False, grow_mask=3)¶

Re-invent the values of masked pixels

Parameters

data – input image as 2d numpy array
mask – masked out pixels array
npt_rad – number of radial points
npt_azim – number of azimuthal points
unit – unit to be used for integration
method – pathway for integration
poissonian – If True, add some poisonian noise to the data to make then more realistic
grow_mask – grow mask in polar coordinated to accomodate pixel splitting algoritm

Returns

inpainting object which contains the restored image as .data

integrate1d(data, npt, filename=None, correctSolidAngle=True, variance=None, error_model=None, radial_range=None, azimuth_range=None, mask=None, dummy=None, delta_dummy=None, polarization_factor=None, dark=None, flat=None, method='csr', unit=q_nm^-1, safe=True, normalization_factor=1.0, block_size=32, profile=False, all=False, metadata=None)¶

Calculate the azimuthal integrated Saxs curve in q(nm^-1) by default

Multi algorithm implementation (tries to be bullet proof), suitable for SAXS, WAXS, … and much more

Parameters

data (ndarray) – 2D array from the Detector/CCD camera
npt (int) – number of points in the output pattern
filename (str) – output filename in 2/3 column ascii format
correctSolidAngle (bool) – correct for solid angle of each pixel if True
variance (ndarray) – array containing the variance of the data. If not available, no error propagation is done
error_model (str) – When the variance is unknown, an error model can be given: “poisson” (variance = I), “azimuthal” (variance = (I-)^2)
radial_range ((float, float), optional) – The lower and upper range of the radial unit. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored.
azimuth_range ((float, float), optional) – The lower and upper range of the azimuthal angle in degree. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored.
mask (ndarray) – array (same size as image) with 1 for masked pixels, and 0 for valid pixels
dummy (float) – value for dead/masked pixels
delta_dummy (float) – precision for dummy value
polarization_factor (float) – polarization factor between -1 (vertical) and +1 (horizontal). 0 for circular polarization or random, None for no correction, True for using the former correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
method (can be Method named tuple, IntegrationMethod instance or str to be parsed) – can be “numpy”, “cython”, “BBox” or “splitpixel”, “lut”, “csr”, “nosplit_csr”, “full_csr”, “lut_ocl” and “csr_ocl” if you want to go on GPU. To Specify the device: “csr_ocl_1,2”
unit (pyFAI.units.Unit) – Output units, can be “q_nm^-1”, “q_A^-1”, “2th_deg”, “2th_rad”, “r_mm” for now
safe (bool) – Do some extra checks to ensure LUT/CSR is still valid. False is faster.
normalization_factor (float) – Value of a normalization monitor
block_size – size of the block for OpenCL integration (unused?)
profile – set to True to enable profiling in OpenCL
all (bool) – if true return a dictionary with many more parameters (deprecated, please refer to the documentation of Integrate1dResult).
metadata – JSON serializable object containing the metadata, usually a dictionary.

Returns

q/2th/r bins center positions and regrouped intensity (and error array if variance or variance model provided), uneless all==True.

Return type

Integrate1dResult, dict

integrate2d(data, npt_rad, npt_azim=360, filename=None, correctSolidAngle=True, variance=None, error_model=None, radial_range=None, azimuth_range=None, mask=None, dummy=None, delta_dummy=None, polarization_factor=None, dark=None, flat=None, method=None, unit=q_nm^-1, safe=True, normalization_factor=1.0, all=False, metadata=None)¶

Calculate the azimuthal regrouped 2d image in q(nm^-1)/chi(deg) by default

Multi algorithm implementation (tries to be bullet proof)

Parameters

data (ndarray) – 2D array from the Detector/CCD camera
npt_rad (int) – number of points in the radial direction
npt_azim (int) – number of points in the azimuthal direction
filename (str) – output image (as edf format)
correctSolidAngle (bool) – correct for solid angle of each pixel if True
variance (ndarray) – array containing the variance of the data. If not available, no error propagation is done
error_model (str) – When the variance is unknown, an error model can be given: “poisson” (variance = I), “azimuthal” (variance = (I-)^2)
radial_range ((float, float), optional) – The lower and upper range of the radial unit. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored.
azimuth_range ((float, float), optional) – The lower and upper range of the azimuthal angle in degree. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored.
mask (ndarray) – array (same size as image) with 1 for masked pixels, and 0 for valid pixels
dummy (float) – value for dead/masked pixels
delta_dummy (float) – precision for dummy value
polarization_factor (float) – polarization factor between -1 (vertical) and +1 (horizontal). 0 for circular polarization or random, None for no correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
method (str) – can be “numpy”, “cython”, “BBox” or “splitpixel”, “lut”, “csr; “lut_ocl” and “csr_ocl” if you want to go on GPU. To Specify the device: “csr_ocl_1,2”
unit (pyFAI.units.Unit) – Output units, can be “q_nm^-1”, “q_A^-1”, “2th_deg”, “2th_rad”, “r_mm” for now
safe (bool) – Do some extra checks to ensure LUT is still valid. False is faster.
normalization_factor (float) – Value of a normalization monitor
all (bool) – if true, return many more intermediate results as a dict (deprecated, please refer to the documentation of Integrate2dResult).
metadata – JSON serializable object containing the metadata, usually a dictionary.

Returns

azimuthaly regrouped intensity, q/2theta/r pos. and chi pos.

Return type

Integrate2dResult, dict

integrate_radial(data, npt, npt_rad=100, correctSolidAngle=True, radial_range=None, azimuth_range=None, mask=None, dummy=None, delta_dummy=None, polarization_factor=None, dark=None, flat=None, method='csr', unit=chi_deg, radial_unit=q_nm^-1, normalization_factor=1.0)¶

Calculate the radial integrated profile curve as I = f(chi)

Parameters

data (ndarray) – 2D array from the Detector/CCD camera
npt (int) – number of points in the output pattern
npt_rad (int) – number of points in the radial space. Too few points may lead to huge rounding errors.
filename (str) – output filename in 2/3 column ascii format
correctSolidAngle (bool) – correct for solid angle of each pixel if True
radial_range (Tuple(float, float)) – The lower and upper range of the radial unit. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored. Optional.
azimuth_range (Tuple(float, float)) – The lower and upper range of the azimuthal angle in degree. If not provided, range is simply (data.min(), data.max()). Values outside the range are ignored. Optional.
mask (ndarray) – array (same size as image) with 1 for masked pixels, and 0 for valid pixels
dummy (float) – value for dead/masked pixels
delta_dummy (float) – precision for dummy value
polarization_factor (float) – polarization factor between -1 (vertical) and +1 (horizontal). * 0 for circular polarization or random, * None for no correction, * True for using the former correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
method (str) – can be “numpy”, “cython”, “BBox” or “splitpixel”, “lut”, “csr”, “nosplit_csr”, “full_csr”, “lut_ocl” and “csr_ocl” if you want to go on GPU. To Specify the device: “csr_ocl_1,2”
unit (pyFAI.units.Unit) – Output units, can be “chi_deg” or “chi_rad”
radial_unit (pyFAI.units.Unit) – unit used for radial representation, can be “q_nm^-1”, “q_A^-1”, “2th_deg”, “2th_rad”, “r_mm” for now
normalization_factor (float) – Value of a normalization monitor

Returns

chi bins center positions and regrouped intensity

Return type

Integrate1dResult

medfilt1d(data, npt_rad=1024, npt_azim=512, correctSolidAngle=True, polarization_factor=None, dark=None, flat=None, method='splitpixel', unit=q_nm^-1, percentile=50, dummy=None, delta_dummy=None, mask=None, normalization_factor=1.0, metadata=None)¶

Perform the 2D integration and filter along each row using a median filter

Parameters

data – input image as numpy array
npt_rad – number of radial points
npt_azim – number of azimuthal points
correctSolidAngle (bool) – correct for solid angle of each pixel if True
polarization_factor (float) – polarization factor between -1 (vertical) and +1 (horizontal). 0 for circular polarization or random, None for no correction, True for using the former correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
unit – unit to be used for integration
method – pathway for integration and sort
percentile – which percentile use for cutting out percentil can be a 2-tuple to specify a region to average out
mask – masked out pixels array
normalization_factor (float) – Value of a normalization monitor
metadata (JSON serializable dict) – any other metadata,

Returns

Integrate1D like result like

reset()¶: Reset azimuthal integrator in addition to other arrays.

reset_engines()¶: Urgently free memory by deleting all regrid-engines

save1D(filename, dim1, I, error=None, dim1_unit=2th_deg, has_dark=False, has_flat=False, polarization_factor=None, normalization_factor=None)¶

This method save the result of a 1D integration.

Deprecated on 13/06/2017

Parameters

filename (str) – the filename used to save the 1D integration
dim1 (numpy.ndarray) – the x coordinates of the integrated curve
I (numpy.mdarray) – The integrated intensity
error (numpy.ndarray or None) – the error bar for each intensity
dim1_unit (pyFAI.units.Unit) – the unit of the dim1 array
has_dark (bool) – save the darks filenames (default: no)
has_flat (bool) – save the flat filenames (default: no)
polarization_factor (float) – the polarization factor
normalization_factor (float) – the monitor value

save2D(filename, I, dim1, dim2, error=None, dim1_unit=2th_deg, has_dark=False, has_flat=False, polarization_factor=None, normalization_factor=None)¶

This method save the result of a 2D integration.

Deprecated on 13/06/2017

Parameters

filename (str) – the filename used to save the 2D histogram
dim1 (numpy.ndarray) – the 1st coordinates of the histogram
dim1 – the 2nd coordinates of the histogram
I (numpy.mdarray) – The integrated intensity
error (numpy.ndarray or None) – the error bar for each intensity
dim1_unit (pyFAI.units.Unit) – the unit of the dim1 array
has_dark (bool) – save the darks filenames (default: no)
has_flat (bool) – save the flat filenames (default: no)
polarization_factor (float) – the polarization factor
normalization_factor (float) – the monitor value

separate(data, npt_rad=1024, npt_azim=512, unit='2th_deg', method='splitpixel', percentile=50, mask=None, restore_mask=True)¶

Separate bragg signal from powder/amorphous signal using azimuthal integration, median filering and projected back before subtraction.

Parameters

data – input image as numpy array
npt_rad – number of radial points
npt_azim – number of azimuthal points
unit – unit to be used for integration
method – pathway for integration and sort
percentile – which percentile use for cutting out
mask – masked out pixels array
restore_mask – masked pixels have the same value as input data provided

Returns

SeparateResult which the bragg & amorphous signal

Note: the filtered 1D spectrum can be retrieved from SeparateResult.radial and SeparateResult.intensity

set_darkcurrent(dark)¶

set_darkfiles(files=None, method='mean')¶

Set the dark current from one or mutliple files, avaraged according to the method provided.

Moved to Detector.

Parameters

files (str or list(str) or None) – file(s) used to compute the dark.
method (str) – method used to compute the dark, “mean” or “median”

set_empty(value)¶

set_flatfield(flat)¶

set_flatfiles(files, method='mean')¶

Set the flat field from one or mutliple files, averaged according to the method provided.

Moved to Detector.

Parameters

files (str or list(str) or None) – file(s) used to compute the flat-field.
method (str) – method used to compute the dark, “mean” or “median”

setup_CSR(shape, npt, mask=None, pos0_range=None, pos1_range=None, mask_checksum=None, unit=2th_deg, split='bbox')¶

Prepare a look-up-table

Parameters

shape ((int, int)) – shape of the dataset
npt (int or (int, int)) – number of points in the the output pattern
mask (ndarray) – array with masked pixel (1=masked)
pos0_range ((float, float)) – range in radial dimension
pos1_range ((float, float)) – range in azimuthal dimension
mask_checksum (int (or anything else ...)) – checksum of the mask buffer
unit (pyFAI.units.Unit) – use to propagate the LUT object for further checkings
split – Splitting scheme: valid options are “no”, “bbox”, “full”

This method is called when a look-up table needs to be set-up. The shape parameter, correspond to the shape of the original datatset. It is possible to customize the number of point of the output histogram with the npt parameter which can be either an integer for an 1D integration or a 2-tuple of integer in case of a 2D integration. The LUT will have a different shape: (npt, lut_max_size), the later parameter being calculated during the instanciation of the splitBBoxLUT class.

It is possible to prepare the LUT with a predefine mask. This operation can speedup the computation of the later integrations. Instead of applying the patch on the dataset, it is taken into account during the histogram computation. If provided the mask_checksum prevent the re-calculation of the mask. When the mask changes, its checksum is used to reset (or not) the LUT (which is a very time consuming operation !)

It is also possible to restrain the range of the 1D or 2D pattern with the pos1_range and pos2_range.

The unit parameter is just propagated to the LUT integrator for further checkings: The aim is to prevent an integration to be performed in 2th-space when the LUT was setup in q space.

setup_LUT(shape, npt, mask=None, pos0_range=None, pos1_range=None, mask_checksum=None, unit=2th_deg)¶

Prepare a look-up-table

Parameters

shape ((int, int)) – shape of the dataset
npt (int or (int, int)) – number of points in the the output pattern
mask (ndarray) – array with masked pixel (1=masked)
pos0_range ((float, float)) – range in radial dimension
pos1_range ((float, float)) – range in azimuthal dimension
mask_checksum (int (or anything else ...)) – checksum of the mask buffer
unit (pyFAI.units.Unit) – use to propagate the LUT object for further checkings

This method is called when a look-up table needs to be set-up. The shape parameter, correspond to the shape of the original datatset. It is possible to customize the number of point of the output histogram with the npt parameter which can be either an integer for an 1D integration or a 2-tuple of integer in case of a 2D integration. The LUT will have a different shape: (npt, lut_max_size), the later parameter being calculated during the instanciation of the splitBBoxLUT class.

It is possible to prepare the LUT with a predefine mask. This operation can speedup the computation of the later integrations. Instead of applying the patch on the dataset, it is taken into account during the histogram computation. If provided the mask_checksum prevent the re-calculation of the mask. When the mask changes, its checksum is used to reset (or not) the LUT (which is a very time consuming operation !)

It is also possible to restrain the range of the 1D or 2D pattern with the pos1_range and pos2_range.

The unit parameter is just propagated to the LUT integrator for further checkings: The aim is to prevent an integration to be performed in 2th-space when the LUT was setup in q space.

sigma_clip(data, npt_rad=1024, npt_azim=512, correctSolidAngle=True, polarization_factor=None, dark=None, flat=None, method='splitpixel', unit=q_nm^-1, thres=3, max_iter=5, dummy=None, delta_dummy=None, mask=None, normalization_factor=1.0, metadata=None)¶

Perform the 2D integration and perform a sigm-clipping iterative filter along each row. see the doc of scipy.stats.sigmaclip for the options.

Parameters

data – input image as numpy array
npt_rad – number of radial points
npt_azim – number of azimuthal points
correctSolidAngle (bool) – correct for solid angle of each pixel if True
polarization_factor (float) –
polarization factor between -1 (vertical) and +1 (horizontal).
- 0 for circular polarization or random,
- None for no correction,
- True for using the former correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
unit – unit to be used for integration
method – pathway for integration and sort
thres – cut-off for n*sigma: discard any values with (I-)/sigma > thres. The threshold can be a 2-tuple with sigma_low and sigma_high.
max_iter – maximum number of iterations :param mask: masked out pixels array
normalization_factor (float) – Value of a normalization monitor
metadata (JSON serializable dict) – any other metadata,

Returns

Integrate1D like result like

sigma_clip_ng(data, npt=1024, correctSolidAngle=True, polarization_factor=None, variance=None, error_model=None, dark=None, flat=None, method=('no', 'csr', 'cython'), unit=q_nm^-1, thres=5.0, max_iter=5, dummy=None, delta_dummy=None, mask=None, normalization_factor=1.0, metadata=None, safe=True, **kwargs)¶

Performs iteratively the 1D integration with variance propagation and performs a sigm-clipping at each iteration, i.e. all pixel which intensity differs more than thres*std is discarded for next iteration.

Keep only pixels with intensty:

|I - | < thres * std(I)

This enforces a gaussian distibution and is very good at extracting background or amorphous isotropic scattering out of Bragg peaks.

Parameters

data – input image as numpy array
npt_rad – number of radial points
correctSolidAngle (bool) – correct for solid angle of each pixel if True
polarization_factor (float) – polarization factor between: -1 (vertical) +1 (horizontal). - 0 for circular polarization or random, - None for no correction, - True for using the former correction
dark (ndarray) – dark noise image
flat (ndarray) – flat field image
variance (ndarray) – the variance of the
unit – unit to be used for integration
method – pathway for integration and sort
thres – cut-off for n*sigma: discard any values with (I-)/sigma > thres.
max_iter – maximum number of iterations
mask – masked out pixels array
normalization_factor (float) – Value of a normalization monitor
metadata (JSON serializable dict) – any other metadata,
safe – set to False to skip some tests

Returns

Integrate1D like result like

The difference with the previous version is that there is not The standard deviation is usually smaller the the signal cleaner. It is also slightly faster.

The In

xrpd_OpenCL(data, npt, filename=None, correctSolidAngle=True, dark=None, flat=None, tthRange=None, mask=None, dummy=None, delta_dummy=None, devicetype='gpu', useFp64=True, platformid=None, deviceid=None, safe=True)¶

Calculate the powder diffraction pattern from a set of data, an image.

This is (now) a pure pyopencl implementation so it just needs pyopencl which requires a clean OpenCL installation. This implementation is not slower than the previous Cython and is less problematic for compilation/installation.

Parameters

data (ndarray) – 2D array from the CCD camera
npt (integer) – number of points in the output pattern
filename (str) – file to save data in ascii format 2 column
correctSolidAngle (bool or int) – solid angle correction, order 1 or 3 (like fit2d)
tthRange ((float, float), optional) – The lower and upper range of the 2theta
mask (ndarray) – array with 1 for masked pixels, and 0 for valid pixels
dummy (float) – value for dead/masked pixels (dynamic mask)
delta_dummy (float) – precision for dummy value

OpenCL specific parameters:

Parameters

devicetype (str) – possible values “cpu”, “gpu”, “all” or “def”
useFp64 (bool) – shall histogram be done in double precision (strongly adviced)
platformid (int) – platform number
deviceid (int) – device number
safe (bool) – set to False if your GPU is already set-up correctly

Returns

(2theta, I) angle being in degrees

Return type

2-tuple of 1D arrays

This method compute the powder diffraction pattern, from a given data image. The number of point of the pattern is given by the npt parameter. If you give a filename, the powder diffraction is also saved as a two column text file. The powder diffraction is computed internally using an histogram which by default use should be done in 64bits. One can switch to 32 bits with the useFp64 parameter set to False. In 32bit mode; do not expect better than 1% error and one can even observe overflows ! 32 bits is only left for testing hardware capabilities and should NEVER be used in any real experiment analysis.

It is possible to correct or not the powder diffraction pattern using the correctSolidAngle parameter. The weight of a pixel is ponderate by its solid angle.

The 2theta range of the powder diffraction pattern can be set using the tthRange parameter. If not given the maximum available range is used. Indeed pixel outside this range are ignored.

Each pixel of the data image has also a chi coordinate. So it is possible to restrain the chi range of the pixels to consider in the powder diffraction pattern. You just need to set the range with the chiRange parameter; like the tthRange parameter, value outside this range are ignored.

Sometimes one needs to mask a few pixels (beamstop, hot pixels, …), to ignore a few of them you just need to provide a mask array with a value of 1 for those pixels. To take a pixel into account you just need to set a value of 0 in the mask array. Indeed the shape of the mask array should be idential to the data shape (size of the array _must_ be the same).

Bad pixels can also be masked by setting them to an impossible value (-1) and calling this value the “dummy value”. Some Pilatus detectors are setting non existing pixel to -1 and dead pixels to -2. Then use dummy=-2 & delta_dummy=1.5 so that any value between -3.5 and -0.5 are considered as bad.

devicetype, platformid and deviceid, parameters are specific to the OpenCL implementation. If you set devicetype to ‘all’, ‘cpu’, ‘gpu’, ‘def’ you can force the device used to perform the computation; the program will select the device accordinly. By setting platformid and deviceid, you can directly address a specific device (which is computer specific).

The safe parameter is specific to the integrator object, located on the OpenCL device. You can set it to False if you think the integrator is already setup correcty (device, geometric arrays, mask, 2theta/chi range). Unless many tests will be done at each integration.

Nota: this deprecated code is maintained until a new histograming on GPU is available

`multi_geometry` Module¶

Module for treating simultaneously multiple detector configuration within a single integration

class pyFAI.multi_geometry.MultiGeometry(ais, unit='2th_deg', radial_range=(0, 180), azimuth_range=(-180, 180), wavelength=None, empty=0.0, chi_disc=180)¶

Bases: object

This is an Azimuthal integrator containing multiple geometries, for example when the detector is on a goniometer arm

__init__(ais, unit='2th_deg', radial_range=(0, 180), azimuth_range=(-180, 180), wavelength=None, empty=0.0, chi_disc=180)¶: Constructor of the multi-geometry integrator :param ais: list of azimuthal integrators :param radial_range: common range for integration :param azimuthal_range: common range for integration :param empty: value for empty pixels :param chi_disc: if 0, set the chi_discontinuity at

integrate1d(lst_data, npt=1800, correctSolidAngle=True, lst_variance=None, error_model=None, polarization_factor=None, normalization_factor=None, all=False, lst_mask=None, lst_flat=None, method='splitpixel')¶

Perform 1D azimuthal integration

Parameters

lst_data – list of numpy array
npt – number of points int the integration
correctSolidAngle – correct for solid angle (all processing are then done in absolute solid angle !)
lst_variance (list of ndarray) – list of array containing the variance of the data. If not available, no error propagation is done
error_model (str) – When the variance is unknown, an error model can be given: “poisson” (variance = I), “azimuthal” (variance = (I-)^2)
polarization_factor – Apply polarization correction ? is None: not applies. Else provide a value from -1 to +1
normalization_factor – normalization monitors value (list of floats)
all – return a dict with all information in it (deprecated, please refer to the documentation of Integrate1dResult).
lst_mask – numpy.Array or list of numpy.array which mask the lst_data.
lst_flat – numpy.Array or list of numpy.array which flat the lst_data.
method – integration method, a string or a registered method

Returns

2th/I or a dict with everything depending on “all”

Return type

Integrate1dResult, dict

integrate2d(lst_data, npt_rad=1800, npt_azim=3600, correctSolidAngle=True, lst_variance=None, error_model=None, polarization_factor=None, normalization_factor=None, all=False, lst_mask=None, lst_flat=None, method='splitpixel')¶

Performs 2D azimuthal integration of multiples frames, one for each geometry

Parameters

lst_data – list of numpy array
npt – number of points int the integration
correctSolidAngle – correct for solid angle (all processing are then done in absolute solid angle !)
lst_variance (list of ndarray) – list of array containing the variance of the data. If not available, no error propagation is done
error_model (str) – When the variance is unknown, an error model can be given: “poisson” (variance = I), “azimuthal” (variance = (I-)^2)
polarization_factor – Apply polarization correction ? is None: not applies. Else provide a value from -1 to +1
normalization_factor – normalization monitors value (list of floats)
all – return a dict with all information in it (deprecated, please refer to the documentation of Integrate2dResult).
lst_mask – numpy.Array or list of numpy.array which mask the lst_data.
lst_flat – numpy.Array or list of numpy.array which flat the lst_data.
method – integration method (or its name)

Returns

I/2th/chi or a dict with everything depending on “all”

Return type

Integrate2dResult, dict

set_wavelength(value)¶: Changes the wavelength of a group of azimuthal integrators

`geometry` 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.Geometry(dist=1, poni1=0, poni2=0, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None)¶

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:

Axis 1 is allong first dimension of detector (when not tilted), this is the slow dimension of the image array in C or Y
In[5]:= x1={1,0,0}
Out[5]= {1,0,0}
 Axis 2 is allong second dimension of detector (when not tilted), this is the fast dimension of the image in C or X
In[6]:= x2={0,1,0}
Out[6]= {0,1,0}
Axis 3 is along the incident X-Ray beam
In[7]:= x3={0,0,1}
Out[7]= {0,0,1}
In[9]:= id3={x1,x2,x3}
Out[9]= {{1,0,0},{0,1,0},{0,0,1}}
In[10]:= {{1,0,0},{0,1,0},{0,0,1}}
Out[10]= {{1,0,0},{0,1,0},{0,0,1}}
In[11]:= rotM1=RotationMatrix[rot1,x1]
Out[11]= {{1,0,0},{0,Cos[rot1],-Sin[rot1]},{0,Sin[rot1],Cos[rot1]}}
In[12]:= rotM2 =  RotationMatrix[rot2,x2]
Out[12]= {{Cos[rot2],0,Sin[rot2]},{0,1,0},{-Sin[rot2],0,Cos[rot2]}}
In[13]:= rotM3 =  RotationMatrix[rot3,x3]
Out[13]= {{Cos[rot3],-Sin[rot3],0},{Sin[rot3],Cos[rot3],0},{0,0,1}}
Rotations of the detector are applied first Rot around axis 1, then axis 2 and finally around axis 3
In[14]:= R=rotM3.rotM2.rotM1
Out[14]= {{Cos[rot2] Cos[rot3],Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3],Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3]},{Cos[rot2] Sin[rot3],Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3],-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3]},{-Sin[rot2],Cos[rot2] Sin[rot1],Cos[rot1] Cos[rot2]}}
In[15]:= CForm[R.x1]

Out[15]//CForm=
List(Cos(rot2)*Cos(rot3),Cos(rot2)*Sin(rot3),-Sin(rot2))
In[16]:= CForm[R.x2]

Out[16]//CForm=
List(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3),Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3),Cos(rot2)*Sin(rot1))
In[17]:= CForm[R.x3]
Out[17]//CForm=
List(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3),-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3),Cos(rot1)*Cos(rot2))
In[18]:= CForm[Det[R]]
Out[18]//CForm=
Power(Cos(rot1),2)*Power(Cos(rot2),2)*Power(Cos(rot3),2) + Power(Cos(rot2),2)*Power(Cos(rot3),2)*Power(Sin(rot1),2) + Power(Cos(rot1),2)*Power(Cos(rot3),2)*Power(Sin(rot2),2) +
   Power(Cos(rot3),2)*Power(Sin(rot1),2)*Power(Sin(rot2),2) + Power(Cos(rot1),2)*Power(Cos(rot2),2)*Power(Sin(rot3),2) + Power(Cos(rot2),2)*Power(Sin(rot1),2)*Power(Sin(rot3),2) +
   Power(Cos(rot1),2)*Power(Sin(rot2),2)*Power(Sin(rot3),2) + Power(Sin(rot1),2)*Power(Sin(rot2),2)*Power(Sin(rot3),2)
In[13]:=
Any pixel on detector plan at coordianate (d1, d2) in meters. Detector is at z=L

In[22]:= P={d1,d2,L}
CForm[R.P]

Out[22]= {d1,d2,L}
Out[23]//CForm=
List(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
   d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))
In[24]:= t1 = R.P.x1
CForm[t1]
Out[24]= d1 Cos[rot2] Cos[rot3]+d2 (Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3])+L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3])
Out[25]//CForm=
d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))
In[26]:= t2 = R.P.x2
CForm[t2]
Out[26]= d1 Cos[rot2] Sin[rot3]+L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3])+d2 (Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3])
Out[27]//CForm=
d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3))
In[28]:= t3=R.P.x3
CForm[t3]
Out[28]= L Cos[rot1] Cos[rot2]+d2 Cos[rot2] Sin[rot1]-d1 Sin[rot2]
Out[29]//CForm=
L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2)
Distance sample to detector point (d1,d2)
(no Mathematica translations)
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ImageSizeRaw->{14, 14},
PlotRange->{{0, 14}, {0, 14}}]


In[30]:= dist = Norm[R.P]
CForm[dist]
Out[30]= √(Abs[L Cos[rot1] Cos[rot2]+d2 Cos[rot2] Sin[rot1]-d1 Sin[rot2]]^2+Abs[d1 Cos[rot2] Cos[rot3]+d2 (Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3])+L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3])]^2+Abs[d1 Cos[rot2] Sin[rot3]+L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3])+d2 (Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3])]^2)
Out[31]//CForm=
Sqrt(Power(Abs(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2)),2) + Power(Abs(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
       L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))),2) + Power(Abs(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3))),
     2))
cos(2theta) can be defined as (R.P component along x3) over the distance |R.P|
In[32]:= tthc = ArcCos [-(R.P).x3/Norm[R.P]]
CForm[tthc]

Out[32]= ArcCos[(-L Cos[rot1] Cos[rot2]-d2 Cos[rot2] Sin[rot1]+d1 Sin[rot2])/(√(Abs[L Cos[rot1] Cos[rot2]+d2 Cos[rot2] Sin[rot1]-d1 Sin[rot2]]^2+Abs[d1 Cos[rot2] Cos[rot3]+d2 (Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3])+L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3])]^2+Abs[d1 Cos[rot2] Sin[rot3]+L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3])+d2 (Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3])]^2))]
Out[33]//CForm=
ArcCos((-(L*Cos(rot1)*Cos(rot2)) - d2*Cos(rot2)*Sin(rot1) + d1*Sin(rot2))/
    Sqrt(Power(Abs(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2)),2) + Power(Abs(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
         L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))),2) + Power(Abs(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) +
         d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3))),2)))



In[41]:= ttht = ArcTan[t3,Sqrt[t1^2 + t2^2]]

CForm[ttht]


Out[41]= ArcTan[L Cos[rot1] Cos[rot2]+d2 Cos[rot2] Sin[rot1]-d1 Sin[rot2],√((d1 Cos[rot2] Cos[rot3]+d2 (Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3])+L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3]))^2+(d1 Cos[rot2] Sin[rot3]+L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3])+d2 (Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3]))^2)]
Out[42]//CForm=
ArcTan(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
      2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
Tangeant of angle chi is defined as (R.P component along x1) over (R.P component along x2). Arctan2 should be used in actual calculation
In[36]:= chi =ArcTan[t1  , t2]
CForm[chi]
Out[36]= ArcTan[d1 Cos[rot2] Cos[rot3]+d2 (Cos[rot3] Sin[rot1] Sin[rot2]-Cos[rot1] Sin[rot3])+L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3]),d1 Cos[rot2] Sin[rot3]+L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3])+d2 (Cos[rot1] Cos[rot3]+Sin[rot1] Sin[rot2] Sin[rot3])]
Out[37]//CForm=
ArcTan(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
   d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))
Coodinates of the Point of Normal Incidence

In[38]:= PONI = R.{0,0,L}
CForm[PONI]
Out[38]= {L (Cos[rot1] Cos[rot3] Sin[rot2]+Sin[rot1] Sin[rot3]),L (-Cos[rot3] Sin[rot1]+Cos[rot1] Sin[rot2] Sin[rot3]),L Cos[rot1] Cos[rot2]}
Out[39]//CForm=
List(L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)),L*Cos(rot1)*Cos(rot2))
Derivatives of 2Theta
In[43]:= CForm[D[ttht,d1]]
Out[43]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*Cos(rot2)*Cos(rot3)*(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
           L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))) + 2*Cos(rot2)*Sin(rot3)*
         (d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
    (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
      (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     + (Sin(rot2)*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))/
    (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
       2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))
In[44]:= CForm[D[ttht,d2]]

Out[44]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3))*
         (d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))) +
        2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3))*(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
    (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
      (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     - (Cos(rot2)*Sin(rot1)*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))/
    (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
       2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))
In[47]:= CForm[D[ttht,L]]
Out[47]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))*
         (d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))) +
        2*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3))*(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
    (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
      (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     - (Cos(rot1)*Cos(rot2)*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))/
    (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
       2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))
In[48]:= CForm[D[ttht,rot1]]
Out[48]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*(L*(-(Cos(rot3)*Sin(rot1)*Sin(rot2)) + Cos(rot1)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)))*
         (d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))) +
        2*(d2*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + L*(-(Cos(rot1)*Cos(rot3)) - Sin(rot1)*Sin(rot2)*Sin(rot3)))*
         (d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
    (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
      (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     - ((d2*Cos(rot1)*Cos(rot2) - L*Cos(rot2)*Sin(rot1))*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))/
    (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),
       2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))
In[49]:= CForm[D[ttht,rot2]]
Out[49]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*(L*Cos(rot1)*Cos(rot2)*Cos(rot3) + d2*Cos(rot2)*Cos(rot3)*Sin(rot1) - d1*Cos(rot3)*Sin(rot2))*
         (d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3))) +
        2*(L*Cos(rot1)*Cos(rot2)*Sin(rot3) + d2*Cos(rot2)*Sin(rot1)*Sin(rot3) - d1*Sin(rot2)*Sin(rot3))*
         (d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
    (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
        Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
      (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     - ((-(d1*Cos(rot2)) - L*Cos(rot1)*Sin(rot2) - d2*Sin(rot1)*Sin(rot2))*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
          L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))
     /(Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
        L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))
In[50]:= CForm[D[ttht,rot3]]
Out[50]//CForm=
((L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2))*(2*(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)))*
        (-(d1*Cos(rot2)*Sin(rot3)) + L*(Cos(rot3)*Sin(rot1) - Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(-(Cos(rot1)*Cos(rot3)) - Sin(rot1)*Sin(rot2)*Sin(rot3))) +
       2*(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)))*
        (d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)))))/
   (2.*Sqrt(Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) + L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) +
       Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2))*
     (Power(L*Cos(rot1)*Cos(rot2) + d2*Cos(rot2)*Sin(rot1) - d1*Sin(rot2),2) + Power(d1*Cos(rot2)*Cos(rot3) + d2*(Cos(rot3)*Sin(rot1)*Sin(rot2) - Cos(rot1)*Sin(rot3)) +
         L*(Cos(rot1)*Cos(rot3)*Sin(rot2) + Sin(rot1)*Sin(rot3)),2) + Power(d1*Cos(rot2)*Sin(rot3) + L*(-(Cos(rot3)*Sin(rot1)) + Cos(rot1)*Sin(rot2)*Sin(rot3)) + d2*(Cos(rot1)*Cos(rot3) + Sin(rot1)*Sin(rot2)*Sin(rot3)),2)))

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

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

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.Enum) – can be Q, TTH, R for now
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)¶

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)

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

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

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

Parameters

d1 – 1d or 2d set of points in pixel coord
d2 – 1d or 2d set of points in pixel coord

Returns

cosine of the incidence angle

del_chia()¶

del_dssa()¶

del_qa()¶

del_ra()¶

del_ttha()¶

delta2Theta(shape=None)¶

Generate a 3D array of the given shape with (i,j) with the max distance between the center and any corner in 2 theta

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 3D array of the given shape with (i,j) 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 (i,j) 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 (mm)

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)

deltaRd2(shape=None)¶

Generate a 2D array of the given shape with (i,j) 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 (i,j) (delta-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

3d array with shape=(*shape,4,2) the two elements are:

dim3[0]: radial angle 2th, q, r…
dim3[1]: azimuthal angle chi

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

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

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_mask()¶

get_maskfile()¶

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()¶

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 for the

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 pixel1¶

property pixel2¶

polarization(shape=None, factor=None, axis_offset=0, with_checksum=False)¶

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

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 !!!)

Returns

2D array with polarization correction array (intensity/polarisation)

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)¶

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)

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

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

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)¶

Set the Fit2D-like parameter set: For geometry description see HPR 1996 (14) pp-240

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

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

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_mask(mask)¶

set_maskfile(maskfile)¶

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/21)

set_spline(spline)¶

set_splineFile(splineFile)¶

set_ttha(_)¶

set_wavelength(value)¶

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 Gerometry of AzimuthalIntegrator set-up with the parameter from the file.

solidAngleArray(shape=None, order=3, absolute=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:

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.PolarizationArray(array, checksum)¶

Bases: tuple

property array¶: Alias for field number 0

property checksum¶: Alias for field number 1

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

Bases: tuple

property axis_offset¶: Alias for field number 1

property polarization_factor¶: Alias for field number 0

`geometryRefinement` Module¶

Module used to perform the geometric refinement of the model

class pyFAI.geometryRefinement.GeometryRefinement(data=None, dist=1, poni1=None, poni2=None, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None, calibrant=None)¶

Bases: pyFAI.azimuthalIntegrator.AzimuthalIntegrator

__init__(data=None, dist=1, poni1=None, poni2=None, rot1=0, rot2=0, rot3=0, pixel1=None, pixel2=None, splineFile=None, detector=None, wavelength=None, calibrant=None)¶

Parameters

data – ndarray float64 shape = n, 3 col0: pos in dim0 (in pixels) col1: pos in dim1 (in pixels) col2: ring index in calibrant object
dist – guessed sample-detector distance (optional, in m)
poni1 – guessed PONI coordinate along the Y axis (optional, in m)
poni2 – guessed PONI coordinate along the X axis (optional, in m)
rot1 – guessed tilt of the detector around the Y axis (optional, in rad)
rot2 – guessed tilt of the detector around the X axis (optional, in rad)
rot3 – guessed tilt of the detector around the incoming beam axis (optional, in rad)
pixel1 – Pixel size along the vertical direction of the detector (in m), almost mandatory
pixel2 – Pixel size along the horizontal direction of the detector (in m), almost mandatory
splineFile – file describing the detector as 2 cubic splines. Replaces pixel1 & pixel2
detector – name of the detector or Detector instance. Replaces splineFile, pixel1 & pixel2
wavelength – wavelength in m (1.54e-10)
calibrant – instance of pyFAI.calibrant.Calibrant containing the d-Spacing

anneal(maxiter=1000000)¶

calc_2th(rings, wavelength=None)¶

Parameters

rings – indices of the rings. starts at 0 and self.dSpacing should be long enough !!!
wavelength – wavelength in meter

chi2(param=None)¶

chi2_wavelength(param=None)¶

confidence(with_rot=True)¶

Confidence interval obtained from the second derivative of the error function next to its minimum value.

Note the confidence interval increases with the number of points which is “surprizing”

Parameters: with_rot – if true include rot1 & rot2 in the parameter set.
Returns: std_dev, confidence

curve_fit(with_rot=True)¶

Refine the geometry and provide confidence interval Use curve_fit from scipy.optimize to not only refine the geometry (unconstrained fit)

Parameters: with_rot – include rotation intro error measurment
Returns: std_dev, confidence

property dist_max¶

property dist_min¶

get_dist_max()¶

get_dist_min()¶

get_poni1_max()¶

get_poni1_min()¶

get_poni2_max()¶

get_poni2_min()¶

get_rot1_max()¶

get_rot1_min()¶

get_rot2_max()¶

get_rot2_min()¶

get_rot3_max()¶

get_rot3_min()¶

get_wavelength_max()¶

get_wavelength_min()¶

guess_poni(fixed=None)¶

PONI can be guessed by the centroid of the ring with lowest 2Theta

It may try to fit an ellipse and sometimes it works

property poni1_max¶

property poni1_min¶

property poni2_max¶

property poni2_min¶

refine1()¶

refine2(maxiter=1000000, fix=None)¶

refine2_wavelength(maxiter=1000000, fix=None)¶

Refine all parameters including the wavelength.

This implies that it enforces an upper limit to the wavelength depending on the number of rings.

residu1(param, d1, d2, rings)¶

residu1_wavelength(param, d1, d2, rings)¶

residu2(param, d1, d2, rings)¶

residu2_wavelength(param, d1, d2, rings)¶

residu2_wavelength_weighted(param, d1, d2, rings, weight)¶

residu2_weighted(param, d1, d2, rings, weight)¶

roca()¶: run roca to optimise the parameter set

property rot1_max¶

property rot1_min¶

property rot2_max¶

property rot2_min¶

property rot3_max¶

property rot3_min¶

set_dist_max(value)¶

set_dist_min(value)¶

set_poni1_max(value)¶

set_poni1_min(value)¶

set_poni2_max(value)¶

set_poni2_min(value)¶

set_rot1_max(value)¶

set_rot1_min(value)¶

set_rot2_max(value)¶

set_rot2_min(value)¶

set_rot3_max(value)¶

set_rot3_min(value)¶

set_tolerance(value=10)¶

Set the tolerance for a refinement of the geometry; in percent of the original value

Parameters: value – Tolerance as a percentage

set_wavelength_max(value)¶

set_wavelength_min(value)¶

simplex(maxiter=1000000)¶

update_values(dist=None, wavelength=None, poni1=None, poni2=None, rot1=None, rot2=None, rot3=None, fixed=None)¶: Update values taking care of fixed parameters.

property wavelength_max¶

property wavelength_min¶

`goniometer` Module¶

Everything you need to calibrate a detector mounted on a goniometer or any translation table

class pyFAI.goniometer.BaseTransformation(funct, param_names, pos_names=None)¶

Bases: object

This class, once instanciated, behaves like a function (via the __call__ method). It is responsible for taking any input geometry and translate it into a set of parameters compatible with pyFAI, i.e. a tuple with: (dist, poni1, poni2, rot1, rot2, rot3)

This class relies on a user provided function which does the work.

__init__(funct, param_names, pos_names=None)¶

Constructor of the class

Parameters

funct – function which takes as parameter the param_names and the pos_name
param_names – list of names of the parameters used in the model
pos_names – list of motor names for gonio with >1 degree of freedom

to_dict()¶: Export the instance representation for serialization as a dictionary

class pyFAI.goniometer.ExtendedTransformation(dist_expr=None, poni1_expr=None, poni2_expr=None, rot1_expr=None, rot2_expr=None, rot3_expr=None, wavelength_expr=None, param_names=None, pos_names=None, constants=None, content=None)¶

Bases: object

This class behaves like GeometryTransformation and extends transformation to the wavelength parameter.

This function uses numexpr for formula evaluation.

__init__(dist_expr=None, poni1_expr=None, poni2_expr=None, rot1_expr=None, rot2_expr=None, rot3_expr=None, wavelength_expr=None, param_names=None, pos_names=None, constants=None, content=None)¶

Constructor of the class

Parameters

dist_expr – formula (as string) providing with the dist
poni1_expr – formula (as string) providing with the poni1
poni2_expr – formula (as string) providing with the poni2
rot1_expr – formula (as string) providing with the rot1
rot2_expr – formula (as string) providing with the rot2
rot3_expr – formula (as string) providing with the rot3
wavelength_expr – formula (as a string) to calculate wavelength used in angstrom
param_names – list of names of the parameters used in the model
pos_names – list of motor names for gonio with >1 degree of freedom
constants – a dictionary with some constants the user may want to use
content – Should be None or the name of the class (may be used in the future to dispatch to multiple derivative classes)

to_dict()¶: Export the instance representation for serialization as a dictionary

class pyFAI.goniometer.GeometryTransformation(dist_expr, poni1_expr, poni2_expr, rot1_expr, rot2_expr, rot3_expr, param_names, pos_names=None, constants=None, content=None)¶

Bases: object

This class, once instanciated, behaves like a function (via the __call__ method). It is responsible for taking any input geometry and translate it into a set of parameters compatible with pyFAI, i.e. a tuple with: (dist, poni1, poni2, rot1, rot2, rot3) This function uses numexpr for formula evaluation.

__init__(dist_expr, poni1_expr, poni2_expr, rot1_expr, rot2_expr, rot3_expr, param_names, pos_names=None, constants=None, content=None)¶

Constructor of the class

Parameters

dist_expr – formula (as string) providing with the dist
poni1_expr – formula (as string) providing with the poni1
poni2_expr – formula (as string) providing with the poni2
rot1_expr – formula (as string) providing with the rot1
rot2_expr – formula (as string) providing with the rot2
rot3_expr – formula (as string) providing with the rot3
param_names – list of names of the parameters used in the model
pos_names – list of motor names for gonio with >1 degree of freedom
constants – a dictionary with some constants the user may want to use
content – Should be None or the name of the class (may be used in the future to dispatch to multiple derivative classes)

to_dict()¶: Export the instance representation for serialization as a dictionary

pyFAI.goniometer.GeometryTranslation¶: alias of pyFAI.goniometer.GeometryTransformation

class pyFAI.goniometer.Goniometer(param, trans_function, detector='Detector', wavelength=None, param_names=None, pos_names=None)¶

Bases: object

This class represents the goniometer model. Unlike this name suggests, it may include translation in addition to rotations

__init__(param, trans_function, detector='Detector', wavelength=None, param_names=None, pos_names=None)¶

Constructor of the Goniometer class.

Parameters

param – vector of parameter to refine for defining the detector position on the goniometer
trans_function – function taking the parameters of the goniometer and the goniometer position and return the 6 parameters [dist, poni1, poni2, rot1, rot2, rot3]
detector – detector mounted on the moving arm
wavelength – the wavelength used for the experiment
param_names – list of names to “label” the param vector.
pos_names – list of names to “label” the position vector of the gonio.

file_version = 'Goniometer calibration v2'¶

get_ai(position)¶

Creates an azimuthal integrator from the motor position

Parameters: position – the goniometer position, a float for a 1 axis goniometer
Returns: A freshly build AzimuthalIntegrator

get_mg(positions)¶

Creates a MultiGeometry integrator from a list of goniometer positions.

Parameters: positions – A list of goniometer positions
Returns: A freshly build multi-geometry

save(filename)¶

Save the goniometer configuration to file

Parameters: filename – name of the file to save configuration to

classmethod sload(filename)¶

Class method for instanciating a Goniometer object from a JSON file

Parameters: filename – name of the JSON file
Returns: Goniometer object

to_dict()¶

Export the goniometer configuration to a dictionary

Returns: Ordered dictionary

write(filename)¶

Save the goniometer configuration to file

Parameters: filename – name of the file to save configuration to

class pyFAI.goniometer.GoniometerRefinement(param, pos_function, trans_function, detector='Detector', wavelength=None, param_names=None, pos_names=None, bounds=None)¶

Bases: pyFAI.goniometer.Goniometer

This class allow the translation of a goniometer geometry into a pyFAI geometry using a set of parameter to refine.

__init__(param, pos_function, trans_function, detector='Detector', wavelength=None, param_names=None, pos_names=None, bounds=None)¶

Constructor of the GoniometerRefinement class

Parameters

param – vector of parameter to refine for defining the detector position on the goniometer
pos_function – a function taking metadata and extracting the goniometer position
trans_function – function taking the parameters of the goniometer and the gonopmeter position and return the 6/7 parameters [dist, poni1, poni2, rot1, rot2, rot3, wavelength]
detector – detector mounted on the moving arm
wavelength – the wavelength used for the experiment
param_names – list of names to “label” the param vector.
pos_names – list of names to “label” the position vector of the gonio.
bounds – list of 2-tuple with the lower and upper bound of each function

chi2(param=None)¶: Calculate the average of the square of the error for a given parameter set

new_geometry(label, image=None, metadata=None, control_points=None, calibrant=None, geometry=None)¶

Add a new geometry for calibration

Parameters

label – usually a string
image – 2D numpy array with the Debye scherrer rings
metadata – some metadata
control_points – an instance of ControlPoints
calibrant – the calibrant used for calibrating
geometry – poni or AzimuthalIntegrator instance.

refine2(method='slsqp', **options)¶

Geometry refinement tool

See https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.minimize.html

Parameters

method – name of the minimizer
options – options for the minimizer

residu2(param)¶: Actually performs the calulation of the average of the error squared

set_bounds(name, mini=None, maxi=None)¶

Redefines the bounds for the refinement

Parameters

name – name of the parameter or index in the parameter set
mini – minimum value
maxi – maximum value

classmethod sload(filename, pos_function=None)¶

Class method for instanciating a Goniometer object from a JSON file

Parameters

filename – name of the JSON file
pos_function – a function taking metadata and extracting the goniometer position

Returns

Goniometer object

class pyFAI.goniometer.PoniParam(dist, poni1, poni2, rot1, rot2, rot3)¶

Bases: tuple

property dist¶: Alias for field number 0

property poni1¶: Alias for field number 1

property poni2¶: Alias for field number 2

property rot1¶: Alias for field number 3

property rot2¶: Alias for field number 4

property rot3¶: Alias for field number 5

class pyFAI.goniometer.SingleGeometry(label, image=None, metadata=None, pos_function=None, control_points=None, calibrant=None, detector=None, geometry=None)¶

Bases: object

This class represents a single geometry of a detector position on a goniometer arm

__init__(label, image=None, metadata=None, pos_function=None, control_points=None, calibrant=None, detector=None, geometry=None)¶

Constructor of the SingleGeometry class, used for calibrating a multi-geometry setup with a moving detector.

Parameters

label – name of the geometry, a string or anything unmutable
image – image with Debye-Scherrer rings as 2d numpy array
metadata – anything which contains the goniometer position
pos_function – a function which takes the metadata as input and returns the goniometer arm position
control_points – a pyFAI.control_points.ControlPoints instance (optional parameter)
calibrant – a pyFAI.calibrant.Calibrant instance. Contains the wavelength to be used (optional parameter)
detector – a pyFAI.detectors.Detector instance or something like that Contains the mask to be used (optional parameter)
geometry – an azimuthal integrator or a ponifile (or a dict with the geometry) (optional parameter)

extract_cp(max_rings=None, pts_per_deg=1.0, Imin=0)¶

Performs an automatic keypoint extraction and update the geometry refinement part

Parameters

max_ring – extract at most N rings from the image
pts_per_deg – number of control points per azimuthal degree (increase for better precision)

get_ai()¶

Create a new azimuthal integrator to be used.

Returns: Azimuthal Integrator instance

get_position()¶: This method is in charge of calculating the motor position from metadata/label/…

`spline` Module¶

This is piece of software aims at manipulating spline files describing for geometric corrections of the 2D detectors using cubic-spline.

Mainly used at ESRF with FReLoN CCD camera.

class pyFAI.spline.Spline(filename=None)¶

Bases: object

This class is a python representation of the spline file

Those file represent cubic splines for 2D detector distortions and makes heavy use of fitpack (dierckx in netlib) — A Python-C wrapper to FITPACK (by P. Dierckx). FITPACK is a collection of FORTRAN programs for curve and surface fitting with splines and tensor product splines. See _http://www.cs.kuleuven.ac.be/cwis/research/nalag/research/topics/fitpack.html or _http://www.netlib.org/dierckx/index.html

__init__(filename=None)¶

This is the constructor of the Spline class.

Parameters: filename (str) – name of the ascii file containing the spline

array2spline(smoothing=1000, timing=False)¶

Calculates the spline coefficients from the displacements matrix using fitpack.

Parameters

smoothing (float) – the greater the smoothing, the fewer the number of knots remaining
timing (bool) – print the profiling of the calculation

bin(binning=None)¶

Performs the binning of a spline (same camera with different binning)

Parameters: binning – binning factor as integer or 2-tuple of integers
Type: int or (int, int)

comparison(ref, verbose=False)¶

Compares the current spline distortion with a reference

Parameters

ref (Spline) – another spline file
verbose (bool) – print or not pylab plots

Returns

True or False depending if the splines are the same or not

Return type

bool

correct(pos)¶

fliplr(fit=True)¶

Flip the spline horizontally

Parameters: fit (bool) – set to False to disable fitting of the coef, or provide a value for the smoothing factor
Returns: new spline object

fliplrud(fit=True)¶

Flip the spline upside-down and horizontally

Parameters: fit (bool) – set to False to disable fitting of the coef, or provide a value for the smoothing factor
Returns: new spline object

flipud(fit=True)¶

Flip the spline upside-down

Parameters: fit (bool) – set to False to disable fitting of the coef, or provide a value for the smoothing factor
Returns: new spline object

getDetectorSize()¶

Returns the size of the detector.

Return type: Tuple[int,int]
Returns: Size y then x

getPixelSize()¶

Return the size of the pixel from as a 2-tuple of floats expressed in meters.

Returns: the size of the pixel from a 2D detector
Return type: 2-tuple of floats expressed in meter.

read(filename)¶

read an ascii spline file from file

Parameters: filename (str) – file containing the cubic spline distortion file

setPixelSize(pixelSize)¶

Sets the size of the pixel from a 2-tuple of floats expressed in meters.

Param: pixel size in meter

spline2array(timing=False)¶

Calculates the displacement matrix using fitpack bisplev(x, y, tck, dx = 0, dy = 0)

Parameters: timing (bool) – profile the calculation or not
Returns: xDispArray, yDispArray
Return type: 2-tuple of ndarray

Evaluate a bivariate B-spline and its derivatives. Return a rank-2 array of spline function values (or spline derivative values) at points given by the cross-product of the rank-1 arrays x and y. In special cases, return an array or just a float if either x or y or both are floats.

splineFuncX(x, y, list_of_points=False)¶

Calculates the displacement matrix using fitpack for the X direction on the given grid.

Parameters

x (ndarray) – points of the grid in the x direction
y (ndarray) – points of the grid in the y direction
list_of_points – if true, consider the zip(x,y) instead of the of the square array

Returns

displacement matrix for the X direction

Return type

ndarray

splineFuncY(x, y, list_of_points=False)¶

calculates the displacement matrix using fitpack for the Y direction

Parameters

x (ndarray) – points in the x direction
y (ndarray) – points in the y direction
list_of_points – if true, consider the zip(x,y) instead of the of the square array

Returns

displacement matrix for the Y direction

Return type

ndarray

tilt(center=(0.0, 0.0), tiltAngle=0.0, tiltPlanRot=0.0, distanceSampleDetector=1.0, timing=False)¶

The tilt method apply a virtual tilt on the detector, the point of tilt is given by the center

Parameters

center (2-tuple of floats) – position of the point of tilt, this point will not be moved.
tiltAngle (float in the range [-90:+90] degrees) – the value of the tilt in degrees
tiltPlanRot (Float in the range [-180:180]) – the rotation of the tilt plan with the Ox axis (0 deg for y axis invariant, 90 deg for x axis invariant)
distanceSampleDetector (float) – the distance from sample to detector in meter (along the beam, so distance from sample to center)

Returns

tilted Spline instance

Return type

Spline

write(filename)¶

save the cubic spline in an ascii file usable with Fit2D or SPD

Parameters: filename (str) – name of the file containing the cubic spline distortion file

writeEDF(basename)¶

save the distortion matrices into a couple of files called basename-x.edf and basename-y.edf

Parameters: basename (str) – base of the name used to save the data

zeros(xmin=0.0, ymin=0.0, xmax=2048.0, ymax=2048.0, pixSize=None)¶

Defines a spline file with no ( zero ) displacement.

Parameters

xmin (float) – minimum coordinate in x, usually zero
xmax (float) – maximum coordinate in x (+1) usually 2048
ymin (float) – minimum coordinate in y, usually zero
ymax (float) – maximum coordinate y (+1) usually 2048
pixSize (float) – size of the pixel

zeros_like(other)¶

Defines a spline file with no ( zero ) displacement with the same shape as the other one given.

Parameters: other (Spline instance) – another Spline instance

`control_points` Module¶

ControlPoints: a set of control points associated with a calibration image

PointGroup: a group of points

class pyFAI.control_points.ControlPoints(filename=None, calibrant=None, wavelength=None)¶

Bases: object

This class contains a set of control points with (optionally) their ring number hence d-spacing and diffraction 2Theta angle…

__init__(filename=None, calibrant=None, wavelength=None)¶: Initialize self. See help(type(self)) for accurate signature.

append(points, ring=None, annotate=None, plot=None)¶

Append a group of points to a given ring

Parameters

point – list of points
ring – ring number
annotate – matplotlib.annotate reference
plot – matplotlib.plot reference

Returns

PointGroup instance

append_2theta_deg(points, angle=None, ring=None)¶

Append a group of points to a given ring

Parameters

point – list of points
angle – 2-theta angle in degrees

Param

ring: ring number

check()¶: check internal consistency of the class, disabled for now

property dSpacing¶

get(ring=None, lbl=None)¶

Retireves the last group of points for a given ring (by default the last)

Parameters

ring – index of ring to search for
lbl – label of the group to retrieve

getList()¶: Retrieve the list of control points suitable for geometry refinement with ring number

getList2theta()¶: Retrieve the list of control points suitable for geometry refinement

getListRing()¶: Retrieve the list of control points suitable for geometry refinement with ring number

getWeightedList(image)¶

Retrieve the list of control points suitable for geometry refinement with ring number and intensities :param image: :return: a (x,4) array with pos0, pos1, ring nr and intensity

#TODO: refine the value of the intensity using 2nd order polynomia

get_dSpacing()¶

get_labels()¶

Retieve the list of labels

Returns: list of labels as string

get_wavelength()¶

load(filename)¶: load all control points from a file

pop(ring=None, lbl=None)¶

Remove the set of points, either from its code or from a given ring (by default the last)

Parameters

ring – index of ring of which remove the last group
lbl – code of the ring to remove

readRingNrFromKeyboard()¶: Ask the ring number values for the given points

reset()¶: remove all stored values and resets them to default

save(filename)¶: Save a set of control points to a file :param filename: name of the file :return: None

setWavelength_change2th(value=None)¶

setWavelength_changeDs(value=None)¶: This is probably not a good idea, but who knows !

set_dSpacing(lst)¶

set_wavelength(value=None)¶

property wavelength¶

class pyFAI.control_points.PointGroup(points=None, ring=None, annotate=None, plot=None, force_label=None)¶

Bases: object

Class contains a group of points … They all belong to the same Debye-Scherrer ring

__init__(points=None, ring=None, annotate=None, plot=None, force_label=None)¶

Constructor

Parameters

points – list of points
ring – ring number
annotate – reference to the matplotlib annotate output
plot – reference to the matplotlib plot
force_label – allows to enforce the label

property code¶: Numerical value for the label: mainly for sorting

classmethod get_label()¶: return the next label

get_ring()¶

property label¶

last_label = 0¶

classmethod reset_label()¶: reset intenal counter

property ring¶

classmethod set_label(label)¶: update the internal counter if needed

set_ring(value)¶

`massif` Module¶

class pyFAI.massif.Massif(data=None, mask=None)¶

Bases: object

A massif is defined as an area around a peak, it is used to find neighboring peaks

TARGET_SIZE = 1024¶

__init__(data=None, mask=None)¶

Constructor of the class…

Parameters

data – 2D array or filename (discouraged)
mask – array with non zero for invalid data

calculate_massif(x)¶: defines a map of the massif around x and returns the mask

property cleaned_data¶

find_peaks(x, nmax=200, annotate=None, massif_contour=None, stdout=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='UTF-8'>)¶

All in one function that finds a maximum from the given seed (x) then calculates the region extension and extract position of the neighboring peaks.

Parameters

x (Tuple[int]) – coordinates of the peak, seed for the calculation
nmax (int) – maximum number of peak per region
annotate – callback method taking number of points + coordinate as input.
massif_contour – callback to show the contour of a massif with the given index.
stdout – this is the file where output is written by default.

Returns

list of peaks

getBinnedData()¶

getBluredData()¶

getLabeledMassif(pattern=None)¶

getMedianData()¶

get_binned_data()¶

Returns: binned data

get_blurred_data()¶

Returns: a blurred image

get_labeled_massif(pattern=None, reconstruct=True)¶

Parameters

pattern – 3x3 matrix
reconstruct – if False, split massif at masked position, else reconstruct missing part.

Returns

an image composed of int with a different value for each massif

get_median_data()¶

Returns: a spatial median filtered image 3x3

initValleySize()¶

init_valley_size()¶

log_info = None¶: If true, more information is displayed in the logger relative to picking.

nearest_peak(x)¶

Parameters: x – coordinates of the peak
Returns: the coordinates of the nearest peak

peaks_from_area(mask, Imin=-1.7976931348623157e+308, keep=1000, dmin=0.0, seed=None, **kwarg)¶

Return the list of peaks within an area

Parameters

mask – 2d array with mask.
Imin – minimum of intensity above the background to keep the point
keep – maximum number of points to keep
kwarg – ignored parameters
dmin – minimum distance to another peak
seed – list of good guesses to start with

Returns

list of peaks [y,x], [y,x], …]

property valley_size¶: Defines the minimum distance between two massifs

`blob_detection` Module¶

class pyFAI.blob_detection.BlobDetection(img, cur_sigma=0.25, init_sigma=0.5, dest_sigma=1, scale_per_octave=2, mask=None)¶

Bases: object

Performs a blob detection: http://en.wikipedia.org/wiki/Blob_detection using a Difference of Gaussian + Pyramid of Gaussians

__init__(img, cur_sigma=0.25, init_sigma=0.5, dest_sigma=1, scale_per_octave=2, mask=None)¶

Performs a blob detection: http://en.wikipedia.org/wiki/Blob_detection using a Difference of Gaussian + Pyramid of Gaussians

Parameters

img – input image
cur_sigma – estimated smoothing of the input image. 0.25 correspond to no interaction between pixels.
init_sigma – start searching at this scale (sigma=0.5: 10% interaction with first neighbor)
dest_sigma – sigma at which the resolution is lowered (change of octave)
scale_per_octave – Number of scale to be performed per octave
mask – mask where pixel are not valid

direction()¶: Perform and plot the two main directions of the peaks, considering their previously calculated scale ,by calculating the Hessian at different sizes as the combination of gaussians and their first and second derivatives

nearest_peak(p, refine=True, Imin=None)¶

Return the nearest peak from a position

Parameters

p – input position (y,x) 2-tuple of float
refine – shall the position be refined on the raw data
Imin – minimum of intensity above the background

peaks_from_area(mask, keep=None, refine=True, Imin=None, dmin=0.0, **kwargs)¶

Return the list of peaks within an area

Parameters

mask – 2d array with mask.
refine – shall the position be refined on the raw data
Imin – minimum of intensity above the background
kwarg – ignored parameters

Returns

list of peaks [y,x], [y,x], …]

process(max_octave=None)¶: Perform the keypoint extraction for max_octave cycles or until all octaves have been processed. :param max_octave: number of octave to process

refine_Hessian(kpx, kpy, kps)¶

Refine the keypoint location based on a 3 point derivative, and delete non-coherent keypoints.

Parameters

kpx – x_pos of keypoint
kpy – y_pos of keypoint
kps – s_pos of keypoint

Returns

arrays of corrected coordinates of keypoints, values and locations of keypoints

refine_Hessian_SG(kpx, kpy, kps)¶: Savitzky Golay algorithm to check if a point is really the maximum :param kpx: x_pos of keypoint :param kpy: y_pos of keypoint :param kps: s_pos of keypoint :return: array of corrected keypoints

refinement()¶

show_neighboor()¶

show_stats()¶: Shows a window with the repartition of keypoint in function of scale/intensity

tresh = 0.6¶

pyFAI.blob_detection.image_test()¶

pyFAI.blob_detection.local_max(dogs, mask=None, n_5=True)¶

Parameters

dogs – 3d array with (sigma,y,x) containing difference of gaussians
mask – mask out keypoint next to the mask (or inside the mask)
n_5 – look for a larger neighborhood

pyFAI.blob_detection.make_gaussian(im, sigma, xc, yc)¶

`calibrant` Module¶

Calibrant

A module containing classical calibrant and also tools to generate d-spacing.

Interesting formula: http://geoweb3.princeton.edu/research/MineralPhy/xtalgeometry.pdf

pyFAI.calibrant.CALIBRANT_FACTORY = Calibrants available: Al, LaB6, TiO2, Ni, CuO, quartz, Si, mock, Si_SRM640e, LaB6_SRM660a, PBBA, cristobaltite, Si_SRM640, NaCl, AgBh, CrOx, LaB6_SRM660c, C14H30O, Si_SRM640a, Au, alpha_Al2O3, ZnO, Si_SRM640d, Cr2O3, Si_SRM640c, LaB6_SRM660b, Si_SRM640b, CeO2¶: Default calibration factory provided by the library.

class pyFAI.calibrant.Calibrant(filename=None, dSpacing=None, wavelength=None)¶

Bases: object

A calibrant is a reference compound where the d-spacing (interplanar distances) are known. They are expressed in Angstrom (in the file)

__init__(filename=None, dSpacing=None, wavelength=None)¶: Initialize self. See help(type(self)) for accurate signature.

append_2th(value)¶

append_dSpacing(value)¶

count_registered_dSpacing()¶: Count of registered dSpacing positons.

property dSpacing¶

fake_calibration_image(ai, shape=None, Imax=1.0, U=0, V=0, W=0.0001)¶

Generates a fake calibration image from an azimuthal integrator

Parameters

ai – azimuthal integrator
Imax – maximum intensity of rings
V, W (U,) – width of the peak from Caglioti’s law (FWHM^2 = Utan(th)^2 + Vtan(th) + W)

property filename¶

get_2th()¶: Returns the 2theta positions for all peaks (cached)

get_2th_index(angle, delta=None)¶

Returns the index in the 2theta angle index

Parameters

angle – expected angle in radians
delta – precision on angle

Returns

0-based index or None

get_dSpacing()¶

get_filename()¶

get_max_wavelength(index=None)¶: Calculate the maximum wavelength assuming the ring at index is visible :param index: Ring number, otherwise assumes all rings are visible :return: the maximum visible wavelength

get_peaks(unit='2th_deg')¶: Calculate the peak position as :return: numpy array (unlike other methods which return lists)

get_wavelength()¶

load_file(filename=None)¶

save_dSpacing(filename=None)¶: save the d-spacing to a file

setWavelength_change2th(value=None)¶

setWavelength_changeDs(value=None)¶: This is probably not a good idea, but who knows !

set_dSpacing(lst)¶

set_wavelength(value=None)¶

property wavelength¶

class pyFAI.calibrant.CalibrantFactory(basedir=None)¶

Bases: object

Behaves like a dict but is actually a factory:

Each time one retrieves an object it is a new geniune new calibrant (unmodified)

__init__(basedir=None)¶

Constructor

Parameters: basedir – directory name where to search for the calibrants

get(what, notfound=None)¶

has_key(k)¶

items()¶

keys()¶

values()¶

class pyFAI.calibrant.Cell(a=1, b=1, c=1, alpha=90, beta=90, gamma=90, lattice='triclinic', lattice_type='P')¶

Bases: object

This is a cell object, able to calculate the volume and d-spacing according to formula from:

http://geoweb3.princeton.edu/research/MineralPhy/xtalgeometry.pdf

__init__(a=1, b=1, c=1, alpha=90, beta=90, gamma=90, lattice='triclinic', lattice_type='P')¶

Constructor of the Cell class:

Crystalographic units are Angstrom for distances and degrees for angles !

Parameters

a,b,c – unit cell length in Angstrom
beta, gamma (alpha,) – unit cell angle in degrees
lattice – “cubic”, “tetragonal”, “hexagonal”, “rhombohedral”, “orthorhombic”, “monoclinic”, “triclinic”
lattice_type – P, I, F, C or R

classmethod cubic(a, lattice_type='P')¶

Factory for cubic lattices

Parameters: a – unit cell length

d(hkl)¶

Calculate the actual d-spacing for a 3-tuple of integer representing a family of Miller plans

Parameters: hkl – 3-tuple of integers
Returns: the inter-planar distance

d_spacing(dmin=1.0)¶

Calculate all d-spacing down to dmin

applies selection rules

Parameters: dmin – minimum value of spacing requested
Returns: dict d-spacing as string, list of tuple with Miller indices preceded with the numerical value

classmethod diamond(a)¶

Factory for Diamond type FCC like Si and Ge

Parameters: a – unit cell length

get_type()¶

classmethod hexagonal(a, c, lattice_type='P')¶

Factory for hexagonal lattices

Parameters

a – unit cell length
c – unit cell length

lattices = ['cubic', 'tetragonal', 'hexagonal', 'rhombohedral', 'orthorhombic', 'monoclinic', 'triclinic']¶

classmethod monoclinic(a, b, c, beta, lattice_type='P')¶

Factory for hexagonal lattices

Parameters

a – unit cell length
b – unit cell length
c – unit cell length
beta – unit cell angle

classmethod orthorhombic(a, b, c, lattice_type='P')¶

Factory for orthorhombic lattices

Parameters

a – unit cell length
b – unit cell length
c – unit cell length

classmethod rhombohedral(a, alpha, lattice_type='P')¶

Factory for hexagonal lattices

Parameters

a – unit cell length
alpha – unit cell angle

save(name, long_name=None, doi=None, dmin=1.0, dest_dir=None)¶

Save informations about the cell in a d-spacing file, usable as Calibrant

Parameters

name – name of the calibrant
doi – reference of the publication used to parametrize the cell
dmin – minimal d-spacing
dest_dir – name of the directory where to save the result

selection_rules = None¶: contains a list of functions returning True(allowed)/False(forbiden)/None(unknown)

set_type(lattice_type)¶

classmethod tetragonal(a, c, lattice_type='P')¶

Factory for tetragonal lattices

Parameters

a – unit cell length
c – unit cell length

property type¶

types = {'C': 'Side centered', 'F': 'Face centered', 'I': 'Body centered', 'P': 'Primitive', 'R': 'Rhombohedral'}¶

property volume¶

pyFAI.calibrant.calibrant_factory(basedir=None)¶

pyFAI.calibrant.get_calibrant(calibrant_name)¶

Returns a new instance of the calibrant by it’s name.

Parameters: calibrant_name (str) – Name of the calibrant

pyFAI.calibrant.names()¶

Returns the list of registred calibrant names.

Return type: str

`distortion` Module¶

class pyFAI.distortion.Distortion(detector='detector', shape=None, resize=False, empty=0, mask=None, method='CSR', device=None, workgroup=8)¶

Bases: object

This class applies a distortion correction on an image.

New version compatible both with CSR and LUT…

__init__(detector='detector', shape=None, resize=False, empty=0, mask=None, method='CSR', device=None, workgroup=8)¶

Parameters

detector – detector instance or detector name
shape – shape of the output image
resize – allow the output shape to be different from the input shape
empty – value to be given for empty bins
method – “lut” or “csr”, the former is faster
device – Name of the device: None for OpenMP, “cpu” or “gpu” or the id of the OpenCL device a 2-tuple of integer
workgroup – workgroup size for CSR on OpenCL

calc_LUT(use_common=True)¶

Calculate the Look-up table

Returns: look up table either in CSR or LUT format depending on serl.method

calc_init()¶: Initialize all arrays

calc_pos(use_cython=True)¶

Calculate the pixel boundary position on the regular grid

Returns: pixel corner positions (in pixel units) on the regular grid
Return type: ndarray of shape (nrow, ncol, 4, 2)

calc_size(use_cython=True)¶

Calculate the number of pixels falling into every single bin and

Returns: max of pixel falling into a single bin

Considering the “half-CCD” spline from ID11 which describes a (1025,2048) detector, the physical location of pixels should go from: [-17.48634 : 1027.0543, -22.768829 : 2028.3689] We chose to discard pixels falling outside the [0:1025,0:2048] range with a lose of intensity

correct(image, dummy=None, delta_dummy=None)¶

Correct an image based on the look-up table calculated …

Parameters

image – 2D-array with the image
dummy – value suggested for bad pixels
delta_dummy – precision of the dummy value

Returns

corrected 2D image

reset(method=None, device=None, workgroup=None, prepare=True)¶

reset the distortion correction and re-calculate the look-up table

Parameters

method – can be “lut” or “csr”, “lut” looks faster
device – can be None, “cpu” or “gpu” or the id as a 2-tuple of integer
worgroup – enforce the workgroup size for CSR.
prepare – set to false to only reset and not re-initialize

property shape_out¶

Calculate/cache the output shape

Returns: output shape

uncorrect(image, use_cython=False)¶

Take an image which has been corrected and transform it into it’s raw (with loss of information)

Parameters: image – 2D-array with the image
Returns: uncorrected 2D image

Nota: to retrieve the input mask on can do:

>>> msk =  dis.uncorrect(numpy.ones(dis._shape_out)) <= 0

class pyFAI.distortion.Quad(buffer)¶

Bases: object

Quad modelisation.

__init__(buffer)¶: Initialize self. See help(type(self)) for accurate signature.

calc_area()¶

calc_area_AB(I1, I2)¶

calc_area_BC(J1, J2)¶

calc_area_CD(K1, K2)¶

calc_area_DA(L1, L2)¶

calc_area_old()¶

calc_area_vectorial()¶

get_box(i, j)¶

get_box_size0()¶

get_box_size1()¶

get_idx(i, j)¶

get_offset0()¶

get_offset1()¶

init_slope()¶

integrateAB(start, stop, calc_area)¶

populate_box()¶

reinit(A0, A1, B0, B1, C0, C1, D0, D1)¶

`worker` Module¶

This module contains the Worker class:

A tool able to perform azimuthal integration with: additional saving capabilities like

save as 2/3D structure in a HDF5 File
read from HDF5 files

Aims at being integrated into a plugin like LImA or as model for the GUI

The configuration of this class is mainly done via a dictionary transmitted as a JSON string: Here are the valid keys:

“dist”
“poni1”
“poni2”
“rot1”
“rot3”
“rot2”
“pixel1”
“pixel2”
“splineFile”
“wavelength”
“poni” #path of the file
“chi_discontinuity_at_0”
“do_mask”
“do_dark”
“do_azimuthal_range”
“do_flat”
“do_2D”
“azimuth_range_min”
“azimuth_range_max”
“polarization_factor”
“nbpt_rad”
“do_solid_angle”
“do_radial_range”
“do_poisson”
“delta_dummy”
“nbpt_azim”
“flat_field”
“radial_range_min”
“dark_current”
“do_polarization”
“mask_file”
“detector”
“unit”
“radial_range_max”
“val_dummy”
“do_dummy”
“method”

class pyFAI.worker.DistortionWorker(detector=None, dark=None, flat=None, solidangle=None, polarization=None, mask=None, dummy=None, delta_dummy=None, device=None)¶

Bases: object

Simple worker doing dark, flat, solid angle and polarization correction

__init__(detector=None, dark=None, flat=None, solidangle=None, polarization=None, mask=None, dummy=None, delta_dummy=None, device=None)¶: Constructor of the worker :param dark: array :param flat: array :param solidangle: solid-angle array :param polarization: numpy array with 2D polarization corrections :param device: Used to influance OpenCL behavour: can be “cpu”, “GPU”, “Acc” or even an OpenCL context

process(data, variance=None, normalization_factor=1.0)¶: Process the data and apply a normalization factor :param data: input data :param variance: the variance associated to the data :param normalization: normalization factor :return: processed data

class pyFAI.worker.PixelwiseWorker(dark=None, flat=None, solidangle=None, polarization=None, mask=None, dummy=None, delta_dummy=None, device=None, empty=None, dtype='float32')¶

Bases: object

Simple worker doing dark, flat, solid angle and polarization correction

__init__(dark=None, flat=None, solidangle=None, polarization=None, mask=None, dummy=None, delta_dummy=None, device=None, empty=None, dtype='float32')¶

Constructor of the worker

Parameters

dark – array
flat – array
solidangle – solid-angle array
polarization – numpy array with 2D polarization corrections
device – Used to influance OpenCL behavour: can be “cpu”, “GPU”, “Acc” or even an OpenCL context
empty – value given for empty pixels by default
dtype – unit (and precision) in which to perform calculation: float32 or float64

process(data, variance=None, normalization_factor=None, use_cython=True)¶: Process the data and apply a normalization factor :param data: input data :param variance: the variance associated to the data :param normalization: normalization factor :return: processed data, optionally with the assiciated error if variance is provided

class pyFAI.worker.Worker(azimuthalIntegrator=None, shapeIn=(2048, 2048), shapeOut=(360, 500), unit='r_mm', dummy=None, delta_dummy=None)¶

Bases: object

__init__(azimuthalIntegrator=None, shapeIn=(2048, 2048), shapeOut=(360, 500), unit='r_mm', dummy=None, delta_dummy=None)¶

Parameters

azimuthalIntegrator (AzimuthalIntegrator) – An AzimuthalIntegrator instance
shapeIn – image size in input
shapeOut – Integrated size: can be (1,2000) for 1D integration
unit – can be “2th_deg, r_mm or q_nm^-1 …

do_2D()¶

property error_model¶

get_config()¶

Returns the configuration as a dictionary.

FIXME: The returned dictionary is not exhaustive.

get_error_model()¶

get_json_config()¶: return configuration as a JSON string

get_normalization_factor()¶

get_unit()¶

property normalization_factor¶

process(data, variance=None, normalization_factor=1.0, writer=None, metadata=None)¶

Process a frame #TODO: dark, flat, sa are missing

Parameters

data – numpy array containing the input image
writer – An open writer in which ‘write’ will be called with the result of the integration

reconfig(shape=(2048, 2048), sync=False)¶

This is just to force the integrator to initialize with a given input image shape

Parameters

shape – shape of the input image
sync – return only when synchronized

reset()¶: this is just to force the integrator to initialize

save_config(filename=None)¶: Save the configuration as a JSON file

setDarkcurrentFile(imagefile)¶

setExtension(ext)¶: enforce the extension of the processed data file written

setFlatfieldFile(imagefile)¶

setJsonConfig(json_file)¶

setSubdir(path)¶: Set the relative or absolute path for processed data

set_config(config, consume_keys=False)¶

Configure the working from the dictionary.

Parameters

config (dict) – Key-value configuration
consume_keys (bool) – If true the keys from the dictionary will be consumed when used.

set_dark_current_file(imagefile)¶

set_error_model(value)¶

set_flat_field_file(imagefile)¶

set_json_config(json_file)¶

set_method(method='csr')¶: Set the integration method

set_normalization_factor(value)¶

set_unit(value)¶

property unit¶

warmup(sync=False)¶

Process a dummy image to ensure everything is initialized

Parameters: sync – wait for processing to be finished

pyFAI.worker.make_ai(config, consume_keys=False)¶

Create an Azimuthal integrator from the configuration.

Parameters

config – Key-value dictionary with all parameters
consume_keys (bool) – If true the keys from the dictionary will be consumed when used.

Returns

A configured (but uninitialized) AzimuthalIntgrator.

pyFAI package¶

`pyFAI` Package¶

`average` Module¶

`azimuthalIntegrator` Module¶

`multi_geometry` Module¶

`geometry` Module¶

`geometryRefinement` Module¶

`goniometer` Module¶

`spline` Module¶

`control_points` Module¶

`massif` Module¶

`blob_detection` Module¶

`calibrant` Module¶

`distortion` Module¶

`worker` Module¶

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pyFAI package¶

pyFAI Package¶

average Module¶

azimuthalIntegrator Module¶

multi_geometry Module¶

geometry Module¶

geometryRefinement Module¶

goniometer Module¶

spline Module¶

control_points Module¶

massif Module¶

blob_detection Module¶

calibrant Module¶

distortion Module¶

worker Module¶

`pyFAI` Package¶

`average` Module¶

`azimuthalIntegrator` Module¶

`multi_geometry` Module¶

`geometry` Module¶

`geometryRefinement` Module¶

`goniometer` Module¶

`spline` Module¶

`control_points` Module¶

`massif` Module¶

`blob_detection` Module¶

`calibrant` Module¶

`distortion` Module¶

`worker` Module¶