Principles of Fluorescence Spectroscopy

354 FLUORESCENCE ANISOTROPY
Figure 10.1. Schematic diagram for measurement of fluorescence
anisotropies.
izer. When the emission polarizer is oriented parallel (||) to
the direction of the polarized excitation the observed intensity
is called I || . Likewise, when the polarizer is perpendicular
(⊥) to the excitation the intensity is called I ⊥ . These
intensity values are used to calculate the anisotropy: 1
r I || I
I || 2I
(10.1)
The anisotropy is a dimensionless quantity that is independent
of the total intensity of the sample. This is because the
difference (I || – I ⊥ ) is normalized by the total intensity,
which is I T = I || + 2I ⊥ . The anisotropy is an intensity ratiometric
measurement. In the absence of artifacts the
anisotropy is independent of the fluorophore concentration.
In earlier publications and in the clinical literature, the
term polarization is frequently used. The polarization is
given by
P I || I
I || I
(10.2)
The polarization and anisotropy values can be interchanged
using
P 3r
2 r
r 2P
3 P
(10.3)
(10.4)
The polarization and anisotropy contain the same information,
but the use of polarization should be discouraged.
Anisotropy is preferred because it is normalized by the total
intensity I T = I || + 2I ⊥ , which results in simplification of the
equations. Suppose the sample contains several emitting
species with polarization values Pi and fractional intensities
P
f i . The polarization of this mixture ( ) is given by 2
( 1
P
1 1
) ∑
3 i
In contrast, the average anisotropy (r) is given by
r ∑ i
(10.5)
(10.6)
where r i indicates the anisotropies of the individual species.
The latter expression is clearly preferable. Furthermore, following
pulsed excitation the fluorescence anisotropy decay
r(t) of a sphere is given by
r(t) r 0e t/θ
(10.7)
where r 0 is the anisotropy at t = 0, and θ is the rotational
correlation time of the sphere. The decay of polarization is
not a single exponential, even for a spherical molecule.
Suppose that the light observed through the emission
polarizer is completely polarized along the transmission
direction of the polarizer. Then I ⊥ = 0, and P = r = 1.0. This
value can be observed for scattered light from an optically
dilute scatterer. Completely polarized emission is never
observed for fluorescence from homogeneous unoriented
samples. The measured values are smaller due to the angular
dependence of photoselection (Section 10.2.1). Completely
polarized emission can be observed for oriented
samples.
Now suppose the emission is completely depolarized.
In this case I || = I ⊥ and P = r = 0. It is important to note that
P and r are not equal for intermediate values. For the
moment we have assumed these intensities could be measured
without interference due to the polarizing properties of
the optical components, especially the emission monochromator
(Chapter 2). In Section 10.4 we will describe methods
to correct for this effect.
f ir i
f i
( 1
Pi 1
3 )