Principles of Fluorescence Spectroscopy

14 INTRODUCTION TO FLUORESCENCE
1.7. STEADY-STATE AND TIME-RESOLVED
FLUORESCENCE
Fluorescence measurements can be broadly classified into
two types of measurements: steady-state and time-resolved.
Steady-state measurements, the most common type, are
those performed with constant illumination and observation.
The sample is illuminated with a continuous beam of
light, and the intensity or emission spectrum is recorded
(Figure 1.17). Because of the ns timescale of fluorescence,
most measurements are steady-state measurements. When
the sample is first exposed to light, steady state is reached
almost immediately.
The second type of measurement is time-resolved,
which is used for measuring intensity decays or anisotropy
decays. For these measurements the sample is exposed to a
pulse of light, where the pulse width is typically shorter
than the decay time of the sample (Figure 1.17). This intensity
decay is recorded with a high-speed detection system
that permits the intensity or anisotropy to be measured on
the ns timescale.
It is important to understand the relationship between
steady-state and time-resolved measurements. A steadystate
observation is simply an average of the time-resolved
phenomena over the intensity decay of the sample. For
instance, consider a fluorophore that displays a single decay
time (τ) and a single rotational correlation time (θ). The
intensity and anisotropy decays are given by
I(t) I 0 e t/τ
r(t) r 0 e t/θ
(1.13)
(1.14)
where I 0 and r 0 are the intensities and anisotropies at t = 0,
immediately following the excitation pulse, respectively.
Equations 1.13 and 1.14 can be used to illustrate how
the decay time determines what can be observed using fluorescence.
The steady-state anisotropy (r) is given by the
average of r(t) weighted by I(t):
r
∞
0 r(t)I(t)dt
∞
0 I(t)dt
(1.15)
In this equation the denominator is present to normalize the
anisotropy to be independent of total intensity. In the
numerator the anisotropy at any time t contributes to the
steady-state anisotropy according to the intensity at time t.
Figure 1.17. Comparison of steady-state and time-resolved fluorescence
spectroscopy.
Substitution of eqs. 1.13 and 1.14 into 1.15 yields the Perrin
equation, 1.10.
Perhaps a simpler example is how the steady-state
intensity (I SS ) is related to the decay time. The steady-state
intensity is given by
∞
ISS I0 e
0
t/τ dt I0τ (1.16)
The value of I 0 can be considered to be a parameter that
depends on the fluorophore concentration and a number
of instrumental parameters. Hence, in molecular terms,
the steady-state intensity is proportional to the lifetime.
This makes sense in consideration of eqs. 1.1 and 1.2,
which showed that the quantum yield is proportional to
the lifetime.
1.7.1. Why Time-Resolved Measurements?
While steady-state fluorescence measurements are simple,
nanosecond time-resolved measurements typically require
complex and expensive instrumentation. Given the relationship
between steady-state and time-resolved measurements,
what is the value of these more complex measurements? It
turns out that much of the molecular information available
from fluorescence is lost during the time averaging process.
For example, anisotropy decays of fluorescent macromolecules
are frequently more complex than a single exponential
(eq. 1.14). The precise shape of the anisotropy decay
contains information about the shape of the macromolecule
and its flexibility. Unfortunately, this shape information is
lost during averaging of the anisotropy over the decay time
(eq. 1.15). Irrespective of the form of r(t), eq. 1.15 yields a