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Fixed_Incident_Beam_Footprint_Correction_With_Mixing

This macro is part of a collection of macros that are used to properly model the effects of a flat plat sample with a fixed angle incident beam.

There is a nice overview of their application in [1]. Individual references are given for each macro.

[1] Rowles, M. R. & Madsen, I. C. 2010, 'Whole-Pattern Profile Fitting of Powder Diffraction Data Collected in Parallel-Beam Flat-Plate Asymmetric Reflection Geometry', Journal of Applied Crystallography, vol. 43, no. 3, pp. 632-634.

Contributor: Matthew Rowles

This macro corrects the peak profile for a flat plate in fixed incident beam geometry, assuming a parallel incident beam and no diffracted optics. Theoretically, the mixing parameter should be “1” for an incident beam intensity profile of a hat, but realistically, there will be some tapering of intensity at the edges, hence the gaussian… This should be used in conjunction with Fixed_Incident_Beam_Thick_Sample_Correction.
Ref: Rowles, M. R. & Madsen, I. C. (2010). J. Appl. Cryst. 43, 632-634.

macro Fixed_Incident_Beam_Footprint_Correction_With_Mixing { FIBFCWM }
macro FIBFCWM(alpha_v, beam_v, mix_v) { FIBFCWM(, alpha_v,, beam_v,,mix_v) }
macro FIBFCWM(alpha, alpha_v, beam, beam_v, mix, mix_v)
{
   #m_argu alpha ''angle between the incident beam and the flat plate sample (in degrees)
   #m_argu beam  ''height of the beam in the vertical (in mm)
   #m_argu mix   ''the mix param between a purely hat and a purely gaussian beam profile -> 1 is pure hat
   If_Prm_Eqn_Rpt(alpha, alpha_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(beam, beam_v, min 0.0001 max 10)
   If_Prm_Eqn_Rpt(mix, mix_v, min 0 max 1)
 
   local width_ = (Sin(2 Th - CeV(alpha, alpha_v) Deg) Rad / Rs) (CeV(beam, beam_v) / Sin(CeV(alpha, alpha_v) Deg));
                 ''^the width of the footprint as seen from 2Th   ^the actual footprint on the sample
 
   hat = CeV(mix, mix_v) width_;		
   gauss_fwhm = (1-CeV(mix, mix_v)) width_;
}

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