Appendix
36
Dividing equation 11 by 12 results in a correlation of the phase angle (
Φ
m
) and the intensity
ratio of the indicator dye (A
ind
) and reference luminophore (A
ref
) :
ref
ind
ref
ref
ref
ref
ind
ref
ref
m
m
m
m
m
A
A
A
A
A
A
A
⋅
Φ
+
Φ
=
Φ
⋅
+
Φ
⋅
=
Φ
=
Φ
⋅
Φ
⋅
sin
1
cot
sin
cos
cot
sin
cos
(
13
)
In this equation, cot
Φ
m
reflects the referenced intensity of the fluorescence indicator. A linear
relation is obtained between cot (
Φ
m
) and the ratio of A
ind
/A
ref
, because the phase angle of
Φ
ref
of the reference luminophore was assumed to be constant. This method is referred to as
Dual Lifetime Referencing (
DLR
).