Chemistry Reference
In-Depth Information
a maximum at
n=0
and decreases with wave number approximately as
sin(
nKD
x
)/
nKD
x
. The second term in r.h.s. of (A.4), corresponding to a
signal from a rough surface, can be discriminated, in general, from the "flat
surface spectrum”, since it is shifted from the frequencies
nKV
; the shift
from a given frequency
nKV
is equal to the frequency of surface waves
with a wave number
nK
.
The power frequency spectrum of the MOSA signal
s
(
Ȧ
) = < |
i
(
Ȧ
)|
2
>
(<..> denotes statistical averaging) can be written in the form (1)
2
¦
s
(
Z
)
~
FSS
(
A
c
l
)
2
F
(
nK
,
0
Z
nKV
)
(A.6)
n
0
where
F
2
(
nK
,
Z
nKV
)
D
2
D
(A.7)
sh
D
(
2
D
x
)
y
ª
º
x
³ ³
4
dy
dx
(
2
D
y
)
x
cos(
nKx
)
B
(
x
,
y
,
Z
nKV
)
¬
¼
y
D
0
0
In (A.7)
B
(
x
,
y
,
Ȧ
) = <
s
(
x
+
ȟ
,
y
+
Ș
,
Ȧ
)·
s
(
ȟ
,
Ș
,
Ȧ
) > is the slope correlation
function. It is easy to see that if the correlation lengths are small compared
with
D
x
,
D
y
,
Į
1
-1
then
F
in formula (A.7) in the first approximation is equal
to the wave number-frequency spectrum of slopes convolved with the
spectrum of the window spectrum, i.e.
sh
(
D
2
D
)
F
(
nK
,
Z
nKV
)
2
D
x
y
D
>
@
(A.7a)
>
@
f
2
sin
2
D
k
2
sin
2
D
(
k
nK
)
³
y
y
F
(
k
,
k
,
Z
nKV
)
x
x
dk
dk
x
y
x
y
k
nK
k
f
x
y
