Parallel beam, thin-plate transmission

This is a collection of macros that are used to model the effects of a flat plate sample in transmission, either in asymmetric or symmetric geometry.

There is a (nice) overview of their application in [1]. The required equations for reflection and capillary geometry are also reviewed, as are preferred orientation issues.

Contributor: Matthew Rowles

[1] Rowles, M. R., and C. E. Buckley. 2017. "Aberration Corrections for Non-Bragg-Brentano Diffraction Geometries." Journal of Applied Crystallography 50 (1): 240-251..

These are probably the macros you'll actually put in your input files. They have all of the commonly used corrections.

''master macro to encapsulate all asymmetric transmission corrections in a single macro
macro Asymmetric_Transmission(omega, omega_v, beam, beam_v, sd, sd_v, mu, mu_v, t, t_v)
{
	Asymmetric_Transmission_Intensity_Correction(omega, omega_v, mu, mu_v, t, t_v)
	Asymmetric_Transmission_Absorption_Correction(omega, omega_v, mu, mu_v, t, t_v)
	Asymmetric_Transmission_Parallel_Footprint_Correction(omega, omega_v, beam, beam_v)
	Asymmetric_Transmission_Specimen_Displacement(omega, omega_v, sd, sd_v)
}

''master macro to encapsulate all symmetric transmission corrections in a single macro
macro Symmetric_Transmission(beam, beam_v, sd, sd_v, mu, mu_v, t, t_v)
{
	Symmetric_Transmission_Intensity_Correction(mu, mu_v, t, t_v)
	Symmetric_Transmission_Absorption_Correction(t, t_v)
	Symmetric_Transmission_Parallel_Footprint_Correction(beam, beam_v)
	Symmetric_Transmission_Specimen_Displacement(sd, sd_v)
}

These are the macros that actually do the maths.

''Intensity correction in asymmetric transmission - equation 22
macro Asymmetric_Transmission_Intensity_Correction(omega, omega_v, mu, mu_v, t, t_v)
{						
   #m_argu omega ''in degrees
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique beta = (180 - ((2 Th) Rad + CeV(omega, omega_v))); '' in degrees
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   scale_pks = 2 Exp(-mu_s CeV(t, t_v) / Sin(beta Deg)) (Sin(beta Deg) /  (Sin(CeV(omega, omega_v)  Deg) - Sin(beta Deg))) (Exp(-mu_s CeV(t, t_v) (Sin(beta Deg) - Sin(CeV(omega, omega_v)  Deg)) / (Sin(CeV(omega, omega_v)  Deg) Sin(beta Deg))) - 1);
}

''Intensity correction in symmetric transmission - equation 24
macro Symmetric_Transmission_Intensity_Correction(mu, mu_v, t, t_v)
{						
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   scale_pks = (2 mu_s CeV(t, t_v) Exp(-mu_s CeV(t, t_v) / Cos(Th))) / Cos(Th);
}

''Relative intensity scaling for buried layers in asymmetric transmission geometry -- Equation 25
macro Asymmetric_Transmission_Intensity_Correction_for_prelayers(omega, omega_v, mu, mu_v, t, t_v)
{
   #m_argu omega ''in degrees
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   scale_pks = Exp((-mu_s CeV(t, t_v)) / Sin(CeV(omega, omega_v) Deg)) ;
}

''Relative intensity scaling for buried layers in asymmetric transmission geometry -- Equation 26
macro Asymmetric_Transmission_Intensity_Correction_for_postlayers(omega, omega_v, mu, mu_v, t, t_v)
{
   #m_argu omega ''in degrees
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique beta = (180 - ((2 Th) Rad + CeV(omega, omega_v))); '' in degrees
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   scale_pks = Exp((-mu_s CeV(t, t_v)) / Sin(beta Deg) ;
}

''Relative intensity scaling for buried layers in symmetric transmission geometry -- implied from Equation 25 & 26
macro Symmetric_Transmission_Intensity_Correction_for_prepostlayers(omega, omega_v, mu, mu_v, t, t_v)
{
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
  If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   scale_pks = Exp((-mu_s CeV(t, t_v)) / Cos(Th)) ;
}

''Line profile correction due to absorption in asymmetric transmission - equation 36
macro Asymmetric_Transmission_Absorption_Correction(omega, omega_v, mu, mu_v, t, t_v)
{						
   #m_argu omega ''in degrees
   #m_argu mu    ''in cm^-1
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(mu, mu_v, min 3 max 500)
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique beta = (180 - ((2 Th) Rad + CeV(omega, omega_v))); '' in degrees
   prm #m_unique mu_s = CeV(mu, mu_v) / 10; ''converts cm^-1 --> mm^-1 for dimensional consistency
 
   prm #m_unique g = Exp(-mu_s ((X Rs/Sin(2 Th) Deg   (Sin(CeV(omega, omega_v) Deg)/Sin(beta Deg) - 1) + (ts/Sin(beta Deg))));
 
   user_defined_convolution =g; ''convolutions are automatically normalised
   	min =(-CeV(t, t_v)/Rs) (Sin2 Th)/Sin(CeV(omega, omega_v) Deg)) Rad;
   	max 0
}

''Line profile correction due to absorption in symmetric transmission - equation 37
macro Symmetric_Transmission_Absorption_Correction(t, t_v)
{						
   #m_argu t     ''in mm
   If_Prm_Eqn_Rpt(t, t_v, min 0.001 max 5)
 
   prm #m_unique eps_min = (-2 CeV(t, t_v)/Rs) Sin(Th) Rad;
 
   user_defined_convolution = -1/eps_min;
   	min =eps_min;
   	max 0
}

''Line profile correction due to footprint in asymetric transmission - equation 38
macro Asymmetric_Transmission_Parallel_Footprint_Correction(omega, omega_v, beam, beam_v)
{						
   #m_argu omega ''in degrees
   #m_argu beam  ''height in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(beam, beam_v, min 0.001 max 5)
 
   prm #m_unique beta = (180 - ((2 Th) Rad + CeV(omega, omega_v))); '' in degrees
 
   hat = ((CeV(beam, beam_v) Sin(beta Deg)) / (Rs Sin(CeV(omega, omega_v)  Deg))) Rad;
}	

''Line profile correction due to footprint in symetric transmission - implied by equation 38
macro Symmetric_Transmission_Parallel_Footprint_Correction(beam, beam_v)
{						
   #m_argu beam  ''height in mm
   If_Prm_Eqn_Rpt(beam, beam_v, min 0.001 max 5)
 
   hat = (CeV(beam, beam_v)/ Rs) Rad;
}	

''Specimen displacement in asymmetric transmission -- equation 39
macro Asymmetric_Transmission_Specimen_Displacement(omega, omega_v, sd, sd_v)
{
   #m_argu omega '' degrees
   #m_argu sd    ''displacement of the sample in mm
   If_Prm_Eqn_Rpt(omega, omega_v, min 0.0001 max 90)
   If_Prm_Eqn_Rpt(sd, sd_v, min -2 max 2)
 
   th2_offset = (CeV(sd, sd_v) / Rs) (Sin(2 Th)/Sin(CeV(omega, omega_v) Deg)) Rad;
}

''Specimen displacement in symmetric transmission -- equation 40
macro Symmetric_Transmission_Specimen_Displacement(sd, sd_v)
{
   #m_argu sd    ''displacement of the sample in mm
   If_Prm_Eqn_Rpt(sd, sd_v, min -2 max 2)
 
   th2_offset = (CeV(sd, sd_v) / Rs) (2 Sin(Th)) Rad;
}