Multi-geometry azimuthal integration

Or how it is possible to perform an azimuthal regrouping using multiple detectors or by moving a single (small) detector to cover more solid angle.

Idea

Azimuthal integration or azimuthal regrouping is (roughly) the averaging of all pixel intensities with the same Q value (or 2theta), as described in this publication chapter 3.2 and 3.3.

By taking multiple images at various places in space one covers more solid angle, allowing either a better statistics or a larger Q-range coverage.

As described in the publication, the average is calculated by the ratio of the (intensity-) weighted histogram by the unweighted histogram. By enforcing a same bin position over multiple geometries, one can create a combined weighted and unweighted histograms by simply summing all partial histograms from each geometry.

The resulting pattern is obtained as usual by the ration of weighted/unweighted

How it works

Lets assume you are able to know where your detector is in space, either calibrated, either calculated from the goniometer position. A diffrection image (img_i) has been acquired using a geometry which is stored in a poni-file (poni_i) useable by pyFAI.

To define a multi-geometry integrator, one needs all poni-files and one needs to define the output space so that all individual integrators use the same bins.

import glob
import fabio
from pyFAI.multi_geometry import MultiGeometry

img_files = glob.glob("*.cbf")
img_data = [fabio.open(i).data for i in img_files]
ais = [i[:-4]+".poni" for i in img_files]
mg = MultiGeometry(ais, unit="q_A^-1", radial_range=(0, 50), wavelength=1e-10)
q, I = mg.integrate1d(img_data, 10000)

What is automatic

  • MultiGeometry takes care of defining the same output space with the same bin position,
  • It performs the normalization of the solid angle (absolute solid angle, unlike AzimuthalIntegrator !)
  • It can handle polarization correction if needed
  • It can normalize by a monitor (I1 normalization) or correct for exposure time

What is not

For PDF measurement, data needs to be properly prepared, especially:

  • Dark current subtraction
  • Flat-field correction
  • Exposure time correction (if all images are not taken with the same exposure time)

Conclusion

MultiGeometry is a unique feature of PyFAI ... While extremely powerful, it need careful understanding of the numerical treatement going on underneath.