Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 385
Figure 11.2. Frequency-domain measurements of anisotropy decays.
For simplicity the average intensity is assumed equal for both polarized
components. From [2].
The experimental procedures and the form of the data
are different for frequency-domain of the anisotropy decay
measurements. 2 The sample is excited with amplitude-modulated
light, which is vertically polarized (Figure 11.2). The
emission is observed through a polarizer that is rotated
between the parallel and perpendicular orientations. In the
frequency domain there are two observable quantities that
characterize the anisotropy decay. These are the phase shift
∆ ω , at the modulation frequency ω, between the perpendicular
(φ ⊥ ) and parallel (φ || ) components of the emission:
and the ratio
∆ ω φ φ ||
Λ ω m ||/m
(11.6)
(11.7)
of the parallel (m || ) and perpendicular (m ⊥ ) components of
the modulated emission. To avoid confusion, we stress that
Λ ω is the ratio of the modulated amplitudes of the polarized
components, not the ratio of the modulation of each polarized
component. The ratio Λ ω is often presented as the frequency-dependent
anisotropy (r ω ), which is defined by
r ω Λ ω 1
Λ ω 2
(11.8)
The form of the frequency-domain anisotropy data is
illustrated in Figures 11.3 and 11.4. Analogous to the timedomain
measurements, one could measure the phase and
modulation of the polarized components relative to scat-
Figure 11.3. Simulated FD data for an anisotropy decay, τ = 10 ns and
θ = 10 ns, showing the phase and actual modulation (m || ' and m ⊥ ') of
the polarized components of the emission, relative to the modulated
excitation or scattered light. The dashed line shows the rotation-free
phase and modulation values for the total emission. From [1].
Figure 11.4. Differential phase (∆ ω ) and modulated (Λ ω ) anisotropy
for τ = 10 ns, θ = 10 ns, and r 0 = 0.4. From [1].
tered light (Figure 11.3, solid lines). The phase angle of the
parallel component (φ || ) will be smaller than the rotationfree
phase angle for the total emission, and the modulation
of the parallel component will be larger than that of the
rotation-free modulation (dashed). These effects are the
result of the shorter mean decay time of the vertically polarized
decay (Figure 11.1). Similarly, the phase angle of the
perpendicular component is larger, and the modulation
smaller, because this component is being repopulated by the
excess population in the parallel orientation, resulting in a
longer mean decay time for the perpendicular component.