Absorption
probability (referred to electric dipolar absorption) for a molecular transition with its electric
transition (dipole) moment at an
angle
with the electric vector of the light is proportional to
.
For the whole sample it is proportional to the orientation factor
,
averaged over all sample molecules. This average is
for a sample with all transition moments perfectly aligned along the electric vector of the light,
for an
isotropic sample and
for a sample where all transition moments are perpendicular to the electric vector.
Notes:
 The directional cosines provide, especially for uniaxial samples, a simple description of exactly those orientation properties of the sample that are relevant for light absorption. With the principal coordinate system
(,
,
),
forming angles
with the light electric vector in the
direction, all orientation effects induced by light absorption are contained in
.
Since the sum of
for three perpendicular molecular axes is equal to
,
only two independent parameters are required to describe the orientation effects on light absorption.

A related, commonly used description is based on diagonalized Saupe matrices:
The principal (molecular) coordinate system
(
,
,
)
forming angles
with the light electric vector should be chosen such that the matrix
and the tensor
are diagonal.
To describe processes involving two or more photons, such as
luminescence of a uniaxial, aligned sample, an expansion of the directional cosines to the fourth
power is required.
 Order parameters (related to Wigner matrices) are an alternative to the
directional cosinebased description of molecular alignment. Orderparameter
methods also work well for nonuniaxial samples and provide a seemingly more complex,
but in other ways convenient, description of molecular orientation distributions.
Wigner matrices are used as a basis set for an expansion of the orientation–distribution
function.
Source:
PAC, 2007, 79, 293
(Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006))
on page 371
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML online corrected version: http://goldbook.iupac.org (2006) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0967855098.
doi:10.1351/goldbook.