Handbook of Biomedical Optics

594 Handbook of Biomedical Optics

modulation depth and a phase delay relative to the excitation

signal, as illustrated in Figure 28.3.

e uorescence lifetime can be determined from measure-

ments of the relative modulation, m, and the phase delay, 

(Lakowicz 2006). For an ideal single exponential decay, the life-

time can be calculated from  or m using the following equations:

τ

ω

φ

ϕ

=

1

tan (28.3)

τ

ω

m

m

= −

⎛

⎝

⎜

⎞

⎠

⎟

1 1

1

2

1

2

(28.4)

If the uorescence excitation is not a pure sinusoid, the

frequency-domain approach is still applicable since the lifetime

can be calculated using the Fourier components of any modu-

lated uorescence signa ...