Isotropy  The property of being
directionally independent, implying no variation of specified physical
properties with direction.

Anisotropy  The property of being
directionally dependent, implying variation of specified physical
properties with direction.

Diffraction limit  The isotropic or
anisotropic limit on average of statistically significant data (also
known as the 'resolution limit'), depending on both the
properties of the crystal and the datacollection strategy.

Threshold  Criterion used to make a decision
on rejection of data.

Spherical shell  Region of reciprocal space
lying between two defined reciprocalspace radii (d*). The
statistics of both isotropic and anisotropic properties are analyzed in
spherical shells.

Diffraction cutoff  Cutoff applied to all
diffraction data outside a single closed isotropic or anisotropic
surface in reciprocal space defining the assumed boundary between, on
average, statistically significant and insignificant data. In the
case of an isotropic surface only one parameter is needed to define it,
i.e. the radius of the limiting sphere. In the general case
the surface is anisotropic and one parameter (or even a small number of
parameters) is not sufficient.

Possible data  All reflections inside the
greatest value of d* for diffraction cutoffs in all directions,
regardless of whether or not an intensity was measured (systematic
absences are excluded everywhere).

Measured data  All possible reflections with
an experimental intensity and standard uncertainty.

Unmeasured data  All possible reflections
without an experimental intensity and standard uncertainty.

Observed data  All measured reflections
inside the diffraction cutoff surface and included in the statistical
tables and the reflection output file.

Unobserved data  All measured reflections
outside the diffraction cutoff surface and excluded from the
statistical tables and the reflection output file.

Observable data  All unmeasured reflections
inside the diffraction cutoff surface (i.e. expected to be
observed).

Unobservable data  All unmeasured
reflections outside the diffraction cutoff surface (i.e.
expected to be unobserved).

Fitted ellipsoid  Ellipsoid fitted by a
multidimensional search and weighted least squares algorithm to the
reflection data immediately neighboring the diffraction cutoff
surface. Used to reduce the number of parameters required to define
the anisotropic diffraction cutoff surface and thereby estimate the
anisotropic diffraction limits and predict observable data.

DebyeWaller factor  Attenuation factor of
each measured intensity and its standard uncertainty due to thermal
motion and/or static disorder: exp(4 π^{2}
s_{h}^{T} U
s_{h}) , where s_{h} is the
reciprocallattice (column) vector,
s_{h}^{T} is the same as a row vector and
U is the overall anisotropy tensor (= B / 8
π^{2}).

Intensity prior  Expected intensity,
estimated from a spherical intensity distribution obtained from
experimental data or from a model, combined with the symmetry
enhancement factor and the isotropic or anisotropic DebyeWaller factor.

Anisotropy correction factor  The inverse
of the square root of the anisotropic DebyeWaller factor applied as a
multiplicative correction of the amplitudes after Bayesian estimation
from the intensities: exp(2 π^{2}
s_{h}^{T} ΔU
s_{h}) where ΔU is the overall
anisotropy U tensor after subtraction of U_{eq}
from its diagonal elements, where U_{eq} is the isotropic
equivalent U (mean of the eigenvalues), so that the trace of
ΔU is zero.

Completeness  Number of data as a fraction
of the number of possible data in any defined volume of reciprocal
space (e.g. within the intersection of a spherical shell with the
fitted ellipsoid).

Anisotropy ratio  Difference between the
largest and smallest eigenvalues of the overall anisotropy U
tensor divided by U_{eq} : (E_{max} 
E_{min}) / U_{eq}. This metric lies
between zero (isotropic) and 3 (maximally anisotropic).

Fractional anisotropy  The RMS deviation of
the eigenvalues from the mean, scaled to lie between zero and one:
√(1.5 Σ_{i} (E_{i} 
U_{eq})^{2} / Σ_{i}
E_{i}^{2}). Unlike the anisotropy ratio this
metric takes into account all 3 eigenvalues.

Anisotropic S/N
ratio  The maximum value over all observed reflections of the
absolute deviation of the squared anisotropy correction factor from 1,
multiplied by the local mean intensity / standard uncertainty ratio:
Max_{h} ( exp(4 π^{2}
s_{h}^{T} ΔU
s_{h})  1 
<I_{h} /
σ(I_{h})>) . Unlike the anisotropy
ratio and the fraction anisotropy this takes into account both the fact
that large anisotropies represent larger differences in intensity at
high d* and that there will be a greater contribution from
reflections with a high value of the local mean intensity / standard
uncertainty ratio. This metric is zero in the isotropic case, with
no limit in the anisotropic case.
