====== Documentation for FitTEY ======

The program FitTEY is a toolbox to fit the total electron yield (TEY) or calculated spectra to off-resonant tables (optical constants delta, beta or scattering factors f1, f2) and to do Kramers-Kronig calculations in one step.
Furthermore it can create new optical constants for compounds.

==== Fit ====

Usage:
FitTEY is a console application.

<code>
FitTEY.exe fit mode file1 file2 element model cutmin cutmax fitmin1 fitmax1 fitmin2 fitmax2 a b c shift
</code>

== fit [string] ==
This is the command and should be exactly this string

== mode [string] ==
"db" or "ff" or "cF" dependent what you want to fit
  * mode="ff": atomic conductivity to atomic scattering factor
  * mode="F" : atomic conductivity tensor to atomic scattering tensor
  * mode="db": conductivity to refractive index


== file1 [string] ==
file containing the measured or calculated data dependent on the mode variable.                   
  * mode="ff": filename with data to merge with columns [energy 0 conductivity]
  * mode="F" : filename with columns [energy conductivity tensor(18 entries)]
  * mode="db": filename with data to merge with columns [energy 0 conductivity]
Look in the file formats section of this documentation for more information


== file2 [string] ==
File containing the off-resonant data dependent on the mode variable
  * mode="ff": filename with columns [energy f1 f2]
  * mode="db": filename with columns [energy delta beta]
  * mode="F" : filename with columns [energy f1 f2]
Look in the file formats section of this documentation for more information

== element [string] ==
Chemical element or Chemical formula dependent on the mode variable
  * mode="ff": chemical element e.g. Ni
  * mode="F" : chemical element e.g. Ni
  * mode="db": chemical formula e.g. LaNiO3

== model [string] ==

the model describes the different fitting models

^ model      ^ mode       ^ formula          ^ fit parameters ^ fixed parameters ^ Comments ^
| A    | db     | beta(E) = (t(E) / E) * a + b + c * E      | a b c | |
| B    | db     | beta(E) = (t(E) / E * a + b + c * E      | a b   | c |
| C    | db     | beta(E) = (t(E) / E) * a + b + c * E      | a     | b c |
| N    | db     | beta(E) = (t(E) / E) * a + b + c * E      |       | a b c |
| D    | db     | beta(E) = (t(E)*a*sin( c*pi/180. ) / (1. - t*a) / b) / ((5.067769e-4 * E * 2.) | a b | c |
| E    | db     | beta(E) = (t(E)*a*sin( c*pi/180. ) / (1. - t*a) / b) / ((5.067769e-4 * E * 2.) | a | b c |
| F    | db     | beta(E) = (t(E) / E) * (a + c * E) + b    | a b c | 
| A    | ff     | f2(E) = (t(E) * E) * a + b + c * E        | a b c | 
| B    | ff     | f2(E) = (t(E) * E) * a + b + c * E        | a b   | c |
| C    | ff     | f2(E) = (t(E) * E) * a + b + c * E        | a     | b c |
| F    | ff     | f2(E) = (t(E) * E) * (a + c * E) + b      | a b c |
| G    | db/ff  | beta(E)/ff(E) = t(E) * a + b + c * E      | a b c | | not officially supported|
| H    | db/ff  | beta(E)/ff(E) = t(E) * a + b + c * E      | a b   | c | not officially supported|
| I    | db/ff  | beta(E)/ff(E) = t(E) * a + b + c * E      | a     | b c | not officially supported|
| J    | db/ff  | beta(E)/ff(E) = t(E) * a + b + c * E      |       | a b c | not officially supported|
| K    | ff     | ff(E) = t(E)*E*E * a + b + c * E       | a b c |  | not officially supported|

In all models the parameters a acts like a scaling factor for the TEY data.
The variables t is the TEY signal and the parameter e is the energy in eV.

Model D and E take the self-absorption into account. (Reiko Nakajima "Electron-yield saturation effects in L-edge x-ray magnetic circular dichroism spectra of Fe, Co and Ni" PRB Volume 59, Number 9 (1999) ) by the formulas

<m> mu lambda_e = {t sin(theta) } / {1 - t} </m>  with <m> mu = 2 k_0 beta </m>  \\

Parameter a is a scaling factor for the TEY signal. 
Parameter b is the escape length  <m>lambda_e</m> of the electrons in Angstrom.
Paramter c corresponds to the Variable <m>theta</m> and is the angle (in degrees) of the incoming beam (perpendicular incoming ray is c=90).
Variable k0 is the wavenumber of the incoming ray.

== cutmin [number], cutmax [number] ==
Energy range in eV for the measurement which should be merged with the off-resonance data. 

== fitmin1 [number], fitmax1 [number] ==
Energy range used for fit before resonance

== fitmin2 [number], fitmax2 [number] ==
Energy range used for fit after resonance


== a [number] ==
Initial value for fit parameter a. Depends on the used model. In most cases a good initial value is a = 1.

== b [number] ==
Initial value for fit parameter b Depends on the used model. Good initial starting could be b = 0.

== c [number] ==
Initial value for fit parameter c. Depends on the used model. Good initial starting could be c = 0.

== shift [number] ==
Energy shift of the measurement. If unsure set it to zero. 

=== output merged.?? ===
The output of the program is a file called merged.db or merged.ff with the fitted and merged TEY-data. It is dependent on the mode variable
  * mode="ff": filename with columns [energy f1 f2]
  * mode="db": filename with columns [energy delta beta]
  * mode="F" : filename with columns [energy conductivity tensor(18 entries)]

==== Create ====

To create the off resonant values of the refractive index for a compound you can use following command
<code>
FitTEY.exe create chemical_formula density shift
</code>

== density [number] ==
density of the compound in units of g/cm^3

== shift [number] ==
Energy shift of the off resonant values. If unsure set it to zero. 

==== Convert ====

This command converts the fitted refractive index to atomic scattering factors

<code>
FitTEY.exe convert file1 chemical_formula density element cutmin cutmax shift
</code>

== file1 ==
fitted .db file with resonances

== element ==
Element to extract from the file

== cutmin, cutmax ==
Lowest and highest energy values for the resonance you want to merge.

== shift [number] ==
Energy shift of the off resonant values. If unsure set it to zero.