Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 195
one component allows the emission spectrum of the second
component to be directly recorded. This procedure is experimentally
simple and can be used to record the emission
spectra of fluorophores with closely spaced lifetimes. PSDF
is frequently used in fluorescence lifetime imaging microscopy
(Chapter 22).
5.12.1. Theory of Phase-Sensitive Detection of
Fluorescence
A phase fluorometer, when coupled with phase-sensitive
detection of fluorescence, can be used in a simple manner
to resolve heterogeneous fluorescence. Consider a sample
containing a single fluorescent species with a lifetime τ.
When excited with sinusoidally modulated light the emission
is given by
F(t) 1 m Lm sin (ωt φ)
(5.66)
where m L is the modulation of the exciting light. In this
equation, m and φ are related to the lifetime by eqs. 5.3 and
5.4. Since phase-sensitive spectra are typically measured at
a single modulation frequency the subscript ω has been
dropped for simplicity. If the sample contains more than
one fluorophore then the modulated emission at each wavelength
(λ) is given by
F(λ,t) ∑ i
(5.67)
In this expression I i (λ) are the individual emission spectra,
f i are the fractional intensities to the total steady-state intensity,
Ef i = 1.0, m i is the modulation of the ith component,
and φ i is its phase angle. Depending upon the needs of the
experiment, the steady-state spectra of each species I i (λ)
can be replaced by the steady-state spectra of the sample
I(λ) and the wavelength-dependent fractional intensities:
F(λ,t) I(λ) ∑ i
I i(λ)f im i sin (ωt φ i)
f i(λ)m i sin (ωt φ i)
(5.68)
In eqs. 5.67 and 5.68 we have assumed that the sample contains
discrete lifetimes characterized by m i and φ i , rather
than a non-exponential decay or a lifetime distribution.
Phase-sensitive detection is accomplished by multiplying
the emission F(λ,t) by a square wave, and integrating
the result over time to yield a steady-state intensity. 1–9 The
Figure 5.49. Phase-sensitive detection of fluorescence. The detector
phase (φ D ) can be in phase with the emission φ D = φ (top), out of phase
with the emission (φ D = φ + 90°, middle), or at some intermediate
value (bottom).
square wave is usually regarded as having a value of 0 or 1
depending on the angle within a single period of 2π (Figure
5.49):
{
0 from 0 to φ D
1 from φ D to φ D π
0 from φ D to φ D 2π
(5.69)
Typically the phase angle of the detector (φ D) is varied to
integrate the emission over various portions of the 0 to 2π
cycle.
The phase-sensitive detector yields a direct current signal
proportional to the modulated amplitude and to the
cosine of the phase difference between the detector phase
φ D and the phase of the sample. If an emission spectrum of
a sample containing a single fluorophore (lifetime) is
scanned using phase-sensitive detection, one observes a
steady-state spectrum whose amplitude depends on the
detector phase angle φ D and the phase angle of the fluorophore
φ 1 :
F(λ, φ D) kF(λ)m cos (φ D φ 1)
(5.70)