5 Quantitative Analysis
373
For infinitely thick layers
L
and
L
0
reduce to
L
∞
(
µ
n
i
, µ
n
j
, µ
n
λ
, ψ , ψ
)
=
µ
n
j
sin
ψ
µ
n
λ
ln
1 +
µ
n
λ
µ
n
j
sin
ψ
+
µ
n
j
sin
ψ
µ
n
i
ln
1 +
µ
n
i
µ
n
j
sin
ψ
(5.104a)
L
0
(
µ
1
, µ
2
, µ
n
, T
→ ∞
) =
µ
n
µ
1
ln
1 +
µ
1
µ
n
.
(5.104b)
For a bulk sample
N
ij
reduces to
N
ij
=
1
2
ε
ij
ε
jλ
Ω
4
π
sin
ψ
L
∞
(
µ
i
, µ
j
, µ
λ
, ψ , ψ
)
C
i
C
j
µ
λ
+
µ
i
τ
jλ
τ
ij
µ
sj
.
(5.105)
Interlayer Secondary Fluorescence
For interlayer secondary ﬂuorescence, two cases are distinguished: enhance-
ment by an element in a layer below the layer of the analyte or by an element
in a layer above the layer of the analyte. The first is denoted by
N
↑
and the
latter by
N
↓
:
N
↑
kn
ij
=
1
2
ε
jλ
ε
ij
Ω
4
π
sin
ψ
A
1
,n
−
1
λ
i
,ψ
C
n
i
C
k
j
τ
jλ
τ
ij
A
1
,k
−
1
λ,ψ
X
µ
k
λ
sin
ψ
,
µ
n
i
sin
ψ
, µ
n
j
, d
n
, µ
k
j
, T
k
,
k
−
1
b
=
n
+1
µ
b
j
T
b
N
↓
kn
ij
=
1
2
ε
jλ
ε
ij
Ω
4
π
sin
ψ
A
1
,n
−
1
λ
i
,ψ
C
n
i
C
k
j
τ
jλ
τ
ij
A
1
,k
−
1
λ,ψ
X
µ
n
i
sin
ψ
,
µ
k
λ
sin
ψ
, µ
k
j
, T
k
, µ
n
j
, T
n
,
n
−
1
b
=
k
+1
µ
b
j
T
b
(5.106a)
with
X
(
p, q, µ
1
, T
1
, µ
2
, T
2
, M
) =
1
q
Y
−
p, µ
2
,
µ
1
T
1
+