Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 169
stand. There can be systematic errors in the phase or modulation
values, and the direction of the errors is not always
intuitively obvious. Fortunately, the color effects are minor
with presently used side-window dynode PMTs, and the
effect appears to be negligible with microchannel plate
PMTs. Although no reports have appeared, it is likely that
color effects are minimal with the TO-8 compact PMTs
(Section 4.6.3.). Systematic errors due to the wavelengthdependent
time response are easily corrected using lifetime
standards.
In order to correct for a wavelength-dependent
response one uses a lifetime standard in place of the scatterer
in the sample turret (Figure 5.7). The standard should
display a single-exponential decay of known lifetime τ R .
The lifetime of the standard should be as short as possible,
typically near 1 ns, to avoid demodulation that results in
decreased precision of the phase-angle measurements.
Another advantage of short-lifetime standards is the minimal
effect of dissolved oxygen on the lifetimes. Short lifetimes
can be obtained with collisional quenching, but this is
not recommended because such samples display non-exponential
decays. Lifetime standards are summarized in
Appendix II. The chosen standard should absorb and emit
at wavelengths comparable to the sample, so that the sample
and reference can be observed with the same emission
filter and/or monochromator setting. Under these conditions
the PMT observes essentially the same wavelength for
both sample and reference measurements, so the color
effects are eliminated.
The decay time of the reference results in a phase delay
(φ R ) and demodulation (m R ) of the reference emission compared
to that which would have been observed using a scatterer
with a lifetime of zero. Of course, φ R and m R depend
on the modulation frequency. The measured values (φ T obs
and m T obs) need to be corrected for this effect. The corrected
values are given by
φ ω φ obs
ω φ R
m ω m obs
ω m R m obs
ω /√1 ω 2 τ 2 R
(5.16)
(5.17)
where φ T obs and m T obs are the observed values measured relative
to the lifetime standard. These equations can be understood
by noting that the observed phase angle is smaller
than the actual phase angle due to the phase angle of the reference
(φ T obs = φ T – φ R ). Similarly, the observed modulation
is the ratio of the modulation of the sample relative to the
reference (m T obs = m T/m R). We find this simple approach
adequate for all samples we have encountered. Somewhat
different methods have also been proposed. 67–68
5.3.2. Background Correction in Frequency-
Domain Measurements
Correction for background fluorescence from the sample is
somewhat complex when using the FD method. 69–70 In
time-domain measurements, correction for autofluorescence
can be accomplished by a relatively straightforward
subtraction of the data file measured for the blank from that
measured for the sample, with error propagation of Poisson
noise if the background level is high. In the frequency
domain it is not possible to perform a simple subtraction of
the background signal. The background may be due to scattered
light with a zero decay time, due to impurities with
finite lifetimes, or a combination of scattered light and autofluorescence.
The phase (φ TB ) and modulation (m TB ) of the
background can be measured at each light modulation frequency.
However, the measured values φ TB and m TB cannot
be subtracted from the sample data unless the intensities are
known and the correction is properly weighted.
Background correction of the FD data is possible, but
the procedure is somewhat complex and degrades the resolution
of the measurements. It is preferable to perform the
FD measurements under conditions where background correction
is not necessary. If needed, the correction is performed
by measuring the frequency response of the background,
and its fractional contribution (f B ) to the steadystate
intensity of the sample. If the background level is low,
then the values of φ TB and m TB have large uncertainties due
to the weak signals. However, this is not usually a problem
because if the background is low its weighted contribution
to the sample data is small, so that minimal additional
uncertainty is added to the data. If the background is larger,
its significance is greater, but it can also be measured with
higher precision.
A data file corrected for background is created by the
following procedure. 66 Let
N ωB m ωB sin φ ωB
D ωB m ωB cos φ ωB
(5.18)
(5.19)
represent the sine and cosine transforms. In these equations
φ TB and m TB represent the measured values for the phase