Subsections

• Correction for Polarisation Effects

 Powder Diffraction Ring Integration

Included in the FIT sub-menu are a number of commands concerned with integrating 2-D images of powder diffraction rings to 1-D ``scans''. These commands have been placed within the FIT sub-menu since they all allow arbitrary regions of the data to be ``masked-off'' and therefore not be included in the integration. Thus all the commands relating to defining or un-defining the ``mask'' are relevant to powder diffraction, as are the commands TILT/BEAM CENTRE and POWDER DIFFRACTION.

TILT/BEAM CENTRE allows any non-orthogonality of the detector with respect to the beam to be fitted from the shape of one or more powder rings. Similarly the beam centre on the detector can be refined.

From the tilt and beam centre found by TILT/BEAM CENTRE or input by the user, the ROI may be re-binned to a 1-D equal angle or equal radial distance bin scan using the POWDER DIFFRACTION command. This allows the option or simultaneously correcting spatial distortion.

Users of these commands are kindly asked to acknowledge and cite:

A P Hammersley, S O Svensson, M Hanfland, A N Fitch, and D Häusermann, ``Two-Dimensional Detector Software: From Real Detector to Idealised Image or Two-Theta Scan'', High Pressure Research, 14, pp235-248, (1996)

(Note: Other options to allow more flexible integration as a function of azimuth are under development. At present R/THETA RE-BINNING performs a polar transformation to the ROI, with user control of the number and size of radial and azimuthal pixels.)

Correction for Polarisation Effects

The commands POWDER DIFFRACTION and R/THETA RE-BINNING re-bin 2-D powder rings to one or more 1-D spectra. In order that the relative intensities are correct it is important to consider both the effect of polarisation and the Lorentz correction factor.

In general the effect of polarisation is dependent on both the 2$\theta$ angle and the azimuthal angle of diffracted radiation. Thus, it is important to correct for polarisation when the data is being converted from a 2-D image to one or more 1-D spectra. If the polarisation correction is to be applied the user will be prompted for the polarisation degree of the X-ray beam and the geometry of the experiment. The beam polarisation is defined as:

$$P = \frac{(I_h - I_v)}{(I_h + I_v)}$$ (6)

where: $I_h$ is the horizontal component of the intensity, and $I_v$ is the vertical component.

At a synchrotron the X-rays are usually highly horizontally polarised, so $P \approx 1.0$, but the beam-line scientists should be able to supply an appropriate number for their beam-lines.

The correction applied is based on the formula of Kahn [16].

Having corrected for polarisation it is important that subsequent software does not also apply a polarisation correction !