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CC1/2
Direction Cosines
Duration
Psi
Renninger score

CC1/2

Split intensities into two groups

loop over all mother reflections
if at least 2 daughters are active
- build a list of all intensities of these (active) daughters
- shuffle this list
- calculate the average intensity of the first half → half1
- calculate the average intensity of the second half → half2
  (if the list contains an odd number of intensities, the half position is randomly incremented by one)
otherwise set half1 and half2 to an invalid value.

At this stage, every mother reflection has a half1 and half2 value. These values are available via the daughter variables half1 and half2.
Splitting of the intensities is done:

after reading new data
after changing the pointgroup (pg command, and implicitly by rpg and rlaue)
with the cchalfsplit command

The calculation of CC1/2

loop over all mother reflections
if half1 and half2 are valid
- ```
x = half1
y = half2
```

                Σx*y - Σx*Σy/n
CC1/2 = ———————————————————————————————————
         √[ (Σx²-Σx*Σx/n)*(Σy²-Σy*Σy/n) ]

         2*CC
CC* = √ ——————
         1+CC

CC1/2 is calculated:

as part of list intensity
with the cchalf command

Direction Cosines

The Direction Cosines describe the orientation of a reflection normal hkl with respect to the reciprocal axes.
The orientation matrix Rmat contains the coefficients of the reciprocal axes as column vectors at goniostat position (0,0,0)

Method 1 (in diffacting position)
- the reflection hkl is in diffracting position. Calculate the rotation matrix G from the 0,0,0 position to the diffracting position.
- extract the reciprocal axes vectors from the orientation matrix Rmat → as, bs and cs
- rotate the reciprocal axes to diffracting position:
  asr = G x as
  bsr = G x bs
  csr = G x cs
  Normalize asr, bsr and csr
- Inray = (focusdist,focushor,focusver)
  Normalize Inray
- calculate cosines from scalar product:
  cosi(1) = asr·Inray
  cosi(2) = bsr·Inray
  cosi(3) = csr·Inray
- calculate Outray:
  cvec = Rmat x hkl
  cvecr = G x cvec
  cvecrl = cvecr * λ
  so |cvecrl| = 2sin(θ)
- Outray = cvecrl - Inray
- calculate cosines from scalar product:
  coso(1) = asr·Outray
  coso(2) = bsr·Outray
  coso(3) = csr·Outray
Method 2 (in 0,0,0 position)
- the reflection hkl is in diffracting position. Calculate the rotation matrix G' from the diffacting position to the the 0,0,0 position.
- extract the reciprocal axes vectors from the orientation matrix Rmat → as, bs and cs
  Normalize as, bs and cs
- Inray = (focusdist,focushor,focusver)
  Normalize Inray
- Inrayr = G' x Inray
- calculate cosines from scalar product:
  cosi(1) = as·Inrayr
  cosi(2) = bs·Inrayr
  cosi(3) = cs·Inrayr
- cvec = Rmat x hkl
  cvecl = cvec * λ
  so |cvecl| = 2sin(θ)
- Outray = cvecl - Inrayr
- calculate cosines from scalar product:
  coso(1) = as·Outray
  coso(2) = bs·Outray
  coso(3) = cs·Outray

Note, the direction cosines are written to hkl files in a specific order:
cosi(1) coso(1) cosi(2) coso(2) cosi(3) coso(3)

Duration

If the rotation axis is perpendicular to the primary beam, the reflections in the equator (i.e. reflection vectors perpendicular to the rotation axis) move with the highest velocity through the Ewald sphere. These reflections have duration 1.

The duration of a reflection is the time spent in the Ewald sphere with respect to an equatorial reflection.

variable	definition	length	description
rotax		1.0	vector along rotation axis
inray		1.0	vector pointing to primary beam
lorvec	vecprod(rotax,inray)	sin(rotax,inray)	lorentz vector (does not change during one scan)
c		2*sin(θ)/λ	c-vector in diffracting position
lor	\|(1.0/scalprod(c,lorvec)\|		the lorentz correction
duration	\|c\|*lor		theta corrected lorentz correction

Psi

A reflection in diffracting position will keep diffracting if the crystal is rotated about the reflection normal. The angle of this rotation is names psi. R₀₀₀ Orientation Matrix
ToGonio₀ = Rotate crystal to goniostat position with rotation angle 0
ToGonio = Rotate crystal to diffracting position
c₀₀₀ = R₀₀₀·h
c = ToGonio·c₀₀₀

Renninger Score

The intensity of a specific reflection can be influenced by simultaneous diffraction on two other reflections. This only occurs if the primary beam diffracts on the second reflection AND that diffracted beam diffracts again on a third reflection. This process can be ignored if the second and third reflection are weak. So there are 3 reflections: ref_A, ref_B and ref_C with corresponding intensities I_A, I_B and I_C. ref_B can have any set of indices, as long as it diffracts at the same time as ref_A.
Now if the reflection indices of ref_C are h_C = h_B - h_A, the renninger reflection will coincide with ref_A.

If renningernormalize is off
J_B = I_B
J_C = I_C
If renningernormalize is on
J_B = I_B/(sin(θ_B)/λ)
J_C = I_C/(sin(θ_C)/λ)

We can express J_B and J_C relative to the intensity of the primary beam I_PB:
s_B = J_B/I_PB and s_C = J_C/I_PB.
(The initial intensity of the primary beam is set to the intensity of the strongest reflection in the dataset)

The initial score of reflections ref_B and ref_C is defined as s_B*s_C (This score is then a number between 0.0 and 1.0).
The final score is calculated by multiplying the initial score with I_PB.

For every possible pair of renninger reflections the final score is evaluated. The renningerscore is defined as the sum of final scores for all renninger pairs.

Notes:

ref_B and ref_C should be strong. To limit the number of calculations, only reflections with an intensity larger than renningerthreshold*primarybeam are considered.
ref_B should be active at the same moment as ref_A. This is tested by bringing ref_B in the diffracting position of ref_A. ref_B will only diffract if Braggs Law is full-filled. This is tested by evaluating the length of the outray. It should be 1.0/λ, but a tolerance (renningersimult) is used to allow small missettings.

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