Chemistry Reference
In-Depth Information
APPENDIX:
Multichannel ("Stroboscopic") Optical Spectrum Analyser
The principle of the MOSA operation was suggested by L.S. Dolin. The
refracted light forming an image of the ruffled water surface in the image
plane of a lens passes through a screen with narrow periodic slits. Then the
light intensity of the image
I(x,y,t)
is integrated by a photo receiver. The
output signal
i
(
t
) can be written in the form
f
f
³³
i
(
t
)
~
W
(
x
,
y
)
I
(
x
,
y
,
s
)
R
(
x
Vt
)
dxdy
(A.1)
f
f
where
R(x)
describes the screen transparency (we assume that the slits are
parallel to the
y
-axis),
W
is a "window function", which for a rectangular
window can be written in the following form
>
@
>
@
W
(
x
,
y
)
1
x
D
)
1
x
D
)
1
y
D
)
1
y
D
)
(A.2)
x
x
y
y
Here
D
x
and
D
y
are the window scales in the
x
- and
y
- directions. In
(A.1) we assumed that the slits move in the
x
-direction with velocity
V
,
practically it can be achieved using a rotating disk with radial slits, if the
radius of the disk is large compared with the size of an analysed image.
The periodic function
R(x
) can be represented by a Fourier series as
¦
R x
()
A
exp(
inKx
)
(A.3)
n
Then it follows from (A.1)-(A.3) and (1) that the spectrum
i
(Z
of
i(t)
can be written in the form
>
¦
f
i
(
Z
)
~
A
G
(
Z
nKV
)
F
(
nK
,
0
n
0
(A.4)
º
³
c
W
(
x
,
y
)
I
(
x
)
s
(
x
,
y
,
Z
nKV
)
exp(
inKx
)
dxdy
¼
0
f
Here
f
³
F
(
nK
,
)
W
(
x
,
y
)
I
(
x
)
exp(
inKx
)
dxdy
(A.5)
0
0
f
is the wave number spectrum of the mean intensity for an undisturbed wa-
ter surface multiplied by the window function
W(x,y.,
In (A.4)
s(x,y,
Z
)
is
the amplitude frequency spectrum of wave slopes. The first term in the
r.h.s. of (A.4) corresponds to an undisturbed water surface and does not
contain information about surface waves. This "flat surface spectrum" has
