Eval14 Overlap

Two reflections may overlap. There is no difference in the handling of overlap between the main reflection and neighbours (from the main lattice) or between the main reflection and aliens (from the interfering lattice).

Input

Vm = volume of the nonoverlapping part of the main reflection.
Vn = volume of the nonoverlapping part of the neighbour or alien.
Vs = volume of the overlapping part of both reflections.
Im = intensity of the nonoverlapping part of the main reflection.
In = intensity of the nonoverlapping part of the alien or neighbour.
Is = intensity of the overlapping part of the two reflecions.

Calculate Split reflections

Definitions
V1 = volume of main reflection
V2 = volume of neighbour reflection
I1 = intensity of main reflection
I2 = intensity of neighbour reflection
PQ1 = peak quality main reflection
PQ2 = peak quality neighbour reflection
The overlapping volume and intensity will be distributed over two reflections by the intensity ratio f.
f = Im/(Im+In)

Split results
V1 = Vm + f*Vs
V2 = Vn + (1-f)*Vs
I1 = Im + f*Is
I2 = In + (1-f)*Is
PQ1 = I1 / SigmaBackground*sqrt(V1).
PQ2 = I2 / SigmaBackground*sqrt(V2).

Procedure

The following procedure is used the handle overlapping reflections:
  1. Calculate SharedVolumeFraction = Vs/(Vm+Vs)
  2. If the shared volume is large we sum.
    If SharedVolumeFraction > sumfactor sum.
  3. If the shared volume is small we split.
    If SharedVolumeFraction < splitfactor split.
  4. In all other cases we check whether the split peaks have a large difference in intensity. If the differences are big, we split, otherwise we sum.
    Calculate PQratio = PQ1/PQ2 (only if PQ1 > PQ2. In the other case we use PQ2/PQ1)
    If PQratio > splitpqratio split else sum.
Eval14
Eval14 commands