Principles of Fluorescence Spectroscopy

138 TIME-DOMAIN LIFETIME MEASUREMENTS
Table 4.5. Resolution of a Two-Component Mixture of Anthranilic Acid and 2-Aminopurine,
Observed at a Single Wavelength, Using Time-Domain Data
Observa- Pre-expo- χ R 2
tion nential Fractional Number of
wave- Lifetimes (ns) factors intensities decay times
length
(nm) τ 1 τ 2 α 1 α 2 f 1 f 2 2 a 1 a
360 6.72 11.58 0.223 0.777 0.143 0.857 1.01 2.77
380 7.51 11.51 0.404 0.596 0.306 0.694 0.85 3.81
400 7.22 11.08 0.448 0.552 0.347 0.653 0.91 4.51
420 7.99 11.22 0.595 0.405 0.511 0.489 0.93 2.95
440 8.38 11.91 0.763 0.237 0.692 0.308 0.89 2.72
aRefers to a two- or one-component fit.
times were recovered at each emission wavelength. This
suggests that the actual uncertainties in the recovered lifetimes
are larger than expected from the ASEs, and then
seem to be even larger than calculated from the χ R 2 surfaces.
Furthermore, the differences in the lifetimes recovered
at each emission wavelength seem to be larger than
expected even from the χ R 2 surfaces. This illustrates the difficulties
in recovering accurate lifetimes if the values differ
by less than twofold.
Another difficulty is that the recovered amplitudes do
not follow the emission spectra expected for each component
(Table 4.5 and Problem 4.5). As the lifetimes become
closer together, the parameter values become more highly
Figure 4.51. Lifetime χ R 2 surfaces for the two-component mixture of
AA and 2-AP (Figure 4.50). The horizontal bars show the asymptotic
standard errors. From [187].
correlated, and it is difficult to know the true uncertainties.
This is not intended to be a criticism of the TD measurements,
but rather is meant to illustrate the difficulties inherent
in the analysis of multi-exponential decays.
4.10.6. Global Analysis: Multi-Wavelength
Measurements
One way to improve the resolution of closely spaced lifetimes
is to perform measurements at additional wavelengths,
and to do a global analysis (Section 4.12). The concept
of global analysis is based on the assumption that
decay times are independent of wavelength. The decay
times are global parameters because they are the same in all
data sets. The amplitudes are non-global because they are
different in each data set. Global analysis of the multiwavelength
data results in much steeper χ R 2 surfaces (Figure
4.52), and presumably a higher probability of recovery
of the correct lifetimes. The lifetimes are determined with
higher certainty from the global analysis because of the
steeper χ R 2 surfaces and the lower value of F χ with more
degrees of freedom (more data). As shown in Problem 4.5,
the amplitudes (Table 4.6) recovered from the global analysis
more closely reflect the individual emission spectra than
the amplitudes recovered from the single wavelength data.
4.10.7. Resolution of Three Closely Spaced
Lifetimes
The resolution of multi-exponential decays becomes more
difficult as the number of decay times increases. This difficulty
is illustrated by a mixture of indole (In), anthranilic
acid (AA), and 2-amino purine (2-AP) (Figure 4.53). At
380 nm all three fluorophores emit, and the decay is expected
to be a sum of three exponentials.