Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mput
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
11
,
No.
1
,
Febr
uar
y
2021
, pp.
38
3
~
389
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v11
i
1
.
pp
38
3
-
389
383
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om
Foc
us
ed a
nd
collim
ate
d
G
aussian
l
aser be
am
s
cintil
lation
i
n
w
eakly
t
urbu
lent
m
arine
a
tmo
spheri
c
m
ediu
m
Ah
med
A.
Abbas
1
,
H
amz
a Gerç
ekci
oğlu
2
, H
.
H
aldun G
ök
t
aş
3
1
Coll
ege of
Enginee
ring
,
Univ
ersity
o
f
Anbar
,
Ira
q
2
Ministr
y
of Tra
nsport,
Mari
ti
m
e
Affai
rs
an
d
Co
m
m
unic
at
ions, T
urke
y
3
Coll
ege of
Enginee
ring
,
Ankar
a Yıldı
rım Be
y
a
zıt
Univer
sit
y
,
Tur
ke
y
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Dec
10
, 201
9
Re
vised
Jun
1
0
,
20
20
Accepte
d
J
u
n
28
, 20
20
The
scintill
at
io
n
inde
x
on
the
axi
s
for
Gauss
ia
n
bea
m
s
f
ocuse
d
an
d
col
li
m
ated
in
w
ea
k
m
ari
n
e
turb
ule
nc
e
is
form
ul
at
ed
via
the
usa
ge
of
R
y
t
ov
m
et
hod.
The
a
ver
age
bi
t
err
or
r
at
e
<BE
R
>
is
eva
lua
t
ed
using
thi
s
form
ula
ti
on.
Th
e
scintill
at
ion
in
dex
and
<BE
R>
ver
sus
propa
gation
dista
n
c
e
and
source
siz
e
ar
e
de
te
rm
i
n
ed
b
y
using
t
he
log
-
norm
al
distri
bute
d
.
I
nte
nsit
y
for
th
e
collimat
ed
a
nd
foc
used.
Gauss
ia
n
be
ams
,
which
a
r
e
exhi
bited
for
wa
vel
eng
th,
source
size
,
foc
al
l
ength,
and
<SNR>.
The
foc
used
bea
m
s
are
rev
e
al
ing
m
ore
adv
ant
ag
eous
tha
n
col
li
m
a
te
d
be
ams
in
an
at
m
o
spheric
m
ar
ine
env
ironment
.
Th
e
find
ings
o
f
thi
s
stud
y
are
signifi
c
ant
for
optical c
om
m
unic
at
ion
s
y
st
e
m
per
form
anc
e
i
n
thi
s
lay
e
r.
Ke
yw
or
d
s
:
Atm
os
ph
eric
pro
pa
gation
Atm
os
ph
eric t
urb
ulence
Fr
ee
-
sp
ace
O
ptica
l com
m
un
ic
at
io
n
Scinti
ll
at
ion
This
is an
op
en
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Ah
m
ed
A
. Ab
ba
s,
Coll
ege
of
En
gi
neer
in
g
,
The U
niv
er
sit
y o
f
A
nbar
,
Anba
r
,
Ir
a
q.
Em
a
il
:
ah
m
ed.
abb
a
s@
uo
a
nba
r.
e
du.iq
1.
INT
R
ODU
CTION
The
at
m
os
ph
e
r
ic
m
arine
env
i
ronm
ent
is
one
that
is
in
i
m
m
ediat
e
con
ta
ct
with
water
and
directl
y
i
m
pacted b
y sea
s an
d ocea
ns
. In
this m
edia, the o
cea
n
a
nd
a
t
m
os
ph
e
re alt
ern
at
e be
twee
n
trem
end
ous am
ount
s
of
m
oistur
e,
he
at
,
and
m
o
m
entum
par
ti
cularl
y
by
turb
ule
nt
trans
port.
Th
us,
stud
yi
ng
tur
bule
nce
in
the
m
arine
env
i
ronm
ent
is
i
m
po
rtant
t
o
ens
ur
e
e
ff
ic
ie
nt
op
ti
cal
com
m
un
ic
at
ion
syst
e
m
s
and
in
t
he
de
sig
n
of
na
utica
l
la
ser
rad
a
r.
Atm
os
ph
eric
tur
bu
le
nce
is
con
si
der
e
d
on
e
of
t
he
extrem
el
y
i
m
portant
fact
o
r
s
for
eff
ic
ie
ncy
-
li
m
i
ti
ng
of
the
com
m
un
ic
at
ion
li
nk
s
in
fr
e
e
-
sp
ace
op
ti
ca
l
(F
SO).
Sci
ntil
la
ti
on
is
a
vital
conseq
ue
nce
of
the
tu
rbul
ence,
w
hich
gen
e
rates
de
pt
h
inco
ns
ta
nc
y
within
the
sign
al
received
a
nd
conseq
ue
ntly
l
eads
to
li
nk
unreli
abili
ty
.
In
this
s
tud
y,
t
he
fo
c
us
is
sci
nt
il
la
t
ion
in
the
m
arine
en
vironm
ent.
The
fi
nd
i
ngs
on
the
sci
ntil
la
ti
on
i
nd
e
x
of
f
oc
us
e
d
an
d
coll
i
m
at
ed
Gau
ssi
an
la
ser
beam
s
prop
a
gatin
g
i
n
this
env
i
ronm
ent ar
e all
r
ep
or
te
d [
1,
2].
Nu
m
erous
stu
dies
hav
e
bee
n
co
nducted
on
var
i
ous
eff
e
ct
s
of
disti
nct
turbulence
on
the
m
arine
atm
os
ph
e
re.
In
this
pa
per,
on
ly
the
i
m
po
rta
nt
posit
ive
ex
pressi
ons
a
re
re
ported
.
I
n
the
m
arine
atm
os
phere
,
the
powe
r
s
pec
tra
are
sta
te
d
i
n
[
3,
4].
Util
iz
ing
on
-
a
xis
sci
ntil
la
ti
on
from
higher
orde
r
la
ser
beam
s
in
a
wea
k
tur
bu
le
nt
m
ari
ne
e
nv
i
ronm
ent
m
edium
wer
e
assesse
d
a
nd
pr
ese
nted
in
[5,
6].
Starti
ng
a
gen
e
rali
zed
m
arit
i
m
e
atm
os
ph
e
ric
s
pectr
um
m
od
el
to
pr
ese
nt
Gau
s
sia
n
bea
m
wav
es
pro
pag
at
in
g
th
r
ough
non
-
K
ol
m
og
oro
v
m
arit
i
m
e
atm
os
pheric
e
nviro
nm
ent
wh
e
re
an
a
naly
ti
c
ex
pr
essi
on
is
deri
ved
of
a
ver
a
ge
sci
ntil
la
ti
on
ind
e
x
wh
ic
h
is
asso
c
ia
te
d
with
the
receiver
-
a
per
t
ure
[7
]
.
The
m
a
rine
at
m
os
pher
ic
tur
bu
le
nce
m
od
ulati
on
t
ra
ns
fe
r
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
383
-
389
384
functi
on
c
har
a
ct
erizes
the
re
su
lt
s
of
m
arin
e
at
m
os
ph
eric
tur
bu
le
nce
on
a
syst
e
m
with
opti
cal
i
m
a
gin
g
[
8].
The
s
pr
ea
d
a
nd
wa
nder
bea
m
s
of
a
Gau
ss
ia
n
beam
wave
wer
e
a
natom
iz
ed
by
pr
op
a
gating
t
hro
ugh
m
arine
atm
os
ph
e
ric
tu
rbulence
[
9].
The
beam
wave
fr
ont
co
rr
ect
ion
in
m
arit
i
me
atm
os
ph
e
re
was
stu
died
by
us
ing
adap
ti
ve
opti
cs
[10,
11]
.
U
sing
ra
ndom
ai
r
-
w
at
e
r
inter
face
thr
ough
an
ada
ptive
opti
cs
syst
e
m
cause
d
m
itigati
ng
si
gnal
dist
or
ti
ons
there
f
or
e
t
his
ne
w
c
oncept
descr
i
bed
in
[
12
]
.
I
n
t
he
m
arit
i
m
e
env
ir
onm
ent,
fiel
d
m
easur
e
m
ents
are
us
e
d
to
offer
m
os
t
i
m
po
rtant
co
ntributi
on
s
pec
ifie
d
by
the
ty
pe
of
m
et
h
odol
og
y
t
o
com
pu
te
the
prob
a
bili
ty
d
ensi
ty
f
unct
ion o
f
t
he
la
ser
b
eam
intensit
y [
13
]
.
T
he
ang
le
of
arr
ival
fluctu
at
ion
s
in
the
m
arit
i
m
e
atm
o
sp
he
ric
tur
bu
l
ence
is
exam
i
ned
[
14,
15]
.
Am
on
g
key
interi
m
data
i
s
irra
diance
s
ci
ntil
la
ti
on
'
s
t
e
m
po
ral
powe
r
sp
ect
ra
ove
r
wea
ke
ned
m
arine
disturba
nce
w
hich
is
exam
ined
analy
ti
cal
ly
and
num
erical
ly
in
each
el
em
ent
[1
6].
I
n
add
it
io
n,
s
uch
to
key
interi
m
data
is
to
de
pict
the
c
orrelat
ion
of
ir
rad
ia
nce
inc
on
sta
ncy
at
uniq
ue
tim
e
sit
uatio
ns
[
17]
.
I
n
t
his
stud
y
,
we
de
rive
d
an
d
eval
uated
the
.
Scinti
ll
at
ion
ind
e
x
th
rou
gh
weak
e
ne
d
at
m
os
phe
ric
m
arin
e
turbulence
by
us
in
g
Ry
tov
m
et
ho
d.
O
ur
goal
is
to
com
pr
ehe
nd
how
the
us
e
of
fo
c
us
e
d
a
nd
c
ollim
at
ed
Gaussi
an
beam
s
helps
in
sh
ri
nk
i
ng the
on
-
a
xis sci
ntil
la
t
ion
i
n wirele
ss
op
ti
cal
c
om
m
u
nicat
ion
i
n h
or
i
zon
ta
l l
in
ks
i
n t
his lay
er.
2.
FOR
M
ULAT
ION
This
sect
io
n
is
der
i
ved
f
or
the
sci
ntil
la
ti
on
in
dex
on
th
e
axis
f
or
Ga
us
sia
n
beam
s
fo
c
us
e
d
a
nd
collim
at
ed
in
weak
m
arine
tur
bule
nce.
T
he
power
s
pectrum
of
m
arine
ref
racti
ve
in
de
x
fluctuati
on
in
s
p
at
ia
l
do
m
ai
n
is as
fol
lows
[1,
2]:
Φ
(
)
=
0
.
033
2
2
[
1
−
0
.
061
/
+
2
.
836
7
/
6
/
7
/
6
]
(
−
2
/
2
)
(
0
2
+
2
)
11
/
6
,
(1)
w
he
re
=
3
.
14
0
,
0
=
1
0
,
the
scal
es
of
tu
rbulenc
e
oute
r
a
nd
i
nner
0
an
d
0
,
re
fers
to
the
wav
e
nu
m
ber
(
sp
at
ia
l
)
f
or
0
≤
<
∞
.
T
he
sci
ntil
la
ti
on
in
dex
base
d
on
Ry
to
v
a
ppr
ox
im
at
ion
for
hom
og
en
eous
a
nd
isot
ropi
c
tur
bu
le
nce is
presente
d
as
[1
7
].
2
=
4
{
∫
∫
∫
[
1
(
,
,
)
+
2
(
,
,
)
]
2
0
∞
0
0
Φ
(
)
}
,
(2)
In
w
hich
(
κ
,
θ)
in
dicat
e
to
the
pola
r
c
oor
din
at
e
il
lustrati
on
of
t
he
two
-
dim
ension
al
s
patia
l
fr
e
qu
e
ncy
,
de
noti
ng
a
le
ngth along
t
he
pro
pa
gation
a
xis
w
hich
is
a v
a
riab
le
,
L
is
the
pro
pag
at
io
n
dista
nc
e
of
the li
nk
an
d R
e (
*)
de
no
te
s
th
e re
al
par
t
of th
e ar
gu
m
ent
[17
]
.
The
e
xpr
es
sion
s
in
the i
nteg
rand
of
(
2) are
1
(
,
,
)
=
−
2
2
(
)
1
(
1
+
)
2
[
−
(
−
)
(
1
+
)
2
(
1
+
)
]
,
(3)
2
(
,
,
)
=
2
|
(
)
|
2
1
(
1
+
)
(
1
−
∗
)
[
−
(
−
)
2
(
1
+
1
+
−
1
−
∗
1
−
∗
)
2
]
,
(4)
(
)
=
1
/
(
1
+
)
,
(5)
wh
e
re
“*”
is
t
he
c
om
plex.
C
onjug
at
e,
=
(−
1)
0.
5,
=
2
/
is
a
wa
ve
nu
m
ber
,
=
1
(
)
2
+
he
re
a
nd
are
th
e
s
ou
rce
siz
e
a
nd
f
ocal
le
ngth
of
the
Gaussi
an
beam
and
in
ci
de
nt
f
ie
ld
e
xpressio
n
i
s
(
−
1
/
2
2
)
[
18,
19]
.
Inse
rting
(
3),
(4)
a
nd
the
po
wer
s
pectr
um
of
m
arine
i
n
(
2),
act
ing
the
inte
gr
at
ion
ov
e
r
fr
om
[20].
The
n,
th
e
sci
ntil
la
ti
on
ind
ex
on
the
ax
is
fo
r
Ga
us
sia
n
beam
s
fo
cu
s
ed
an
d
colli
m
at
ed.
In
wea
ke
ned m
arine t
urbu
le
nc
e is f
ound a
nd
dem
on
strat
ed
a
s:
2
=
1
.
39
2
2
{
∫
∑
1
!
∞
=
0
[
[
(
0
2
)
−
5
6
Γ
(
−
+
5
6
)
Γ
(
+
1
)
]
0
×
[
(
−
1
2
(
)
(
1
+
)
2
)
[
−
(
(
−
)
(
1
+
)
(
1
+
)
+
1
2
)
]
+
(
1
|
(
)
|
2
(
1
+
)
(
1
−
∗
)
)
×
[
−
(
(
−
)
2
(
1
+
1
+
−
1
−
∗
1
−
∗
)
+
1
2
)
]
]
−
0
.
061
[
(
0
2
)
−
1
3
Γ
(
−
+
1
3
)
×
Γ
(
+
3
2
)
]
[
(
−
1
2
(
)
(
1
+
)
2
)
[
−
(
(
−
)
(
1
+
)
(
1
+
)
+
1
2
)
]
+
(
1
|
(
)
|
2
(
1
+
)
(
1
−
∗
)
)
[
−
(
(
−
)
2
(
1
+
1
+
−
1
−
∗
1
−
∗
)
+
1
2
)
]
]
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Foc
us
ed
an
d
c
olli
ma
te
d
G
aus
sian l
as
er
b
e
am sci
ntil
lati
on
in weakly t
urb
ulent
marine
.
.
.
(
Ah
med A.
Ab
ba
s)
385
+
2
.
836
7
6
[
(
0
2
)
−
1
4
Γ
(
−
+
1
4
)
Γ
(
+
19
12
)
]
[
(
−
1
2
(
)
(
1
+
)
2
)
×
[
−
(
(
−
)
(
1
+
)
(
1
+
)
+
1
2
)
]
+
(
1
|
(
)
|
2
(
1
+
)
(
1
−
∗
)
)
[
−
(
(
−
)
2
(
1
+
1
+
−
1
−
∗
1
−
∗
)
+
1
2
)
]
]
]
}
.
(6)
Lessen
(
6
)
t
o
s
ci
ntil
la
ti
on
inde
x
in
K
olm
og
oro
v
to
af
firm
t
he
acc
ur
acy
of
our
m
od
el
a
nd
by
way
of
ta
kin
g
i
nn
e
r
s
cal
e
0
=
0
.
In
a
ddit
ion,
ne
glect
th
e
influ
e
nce
of
ou
te
r
scal
e
[
1]
.
The
sci
ntil
la
ti
on
inde
x
i
n
Ko
lm
og
or
ov
i
n
[
2
1
]
m
at
ched
with
our
m
od
el
a
fter
re
duci
ng.
BER
a
nd
SN
R
ar
e
util
iz
ed
to
det
erm
ine
the
qual
it
y
of
the
c
omm
un
ic
at
ion
syst
em
s.
BER
perf
or
m
a
nce
d
epe
nds
on
the
sci
ntil
la
ti
on
stre
ng
t
h,
re
cei
ver
no
ise
,
an
d
a
ve
rag
e
receive
d
powe
r.
I
n
wea
ken
e
d
m
arine
tur
bu
le
nce,
a
ve
rag
e
bit
er
ror
rate
<
>
is
pr
ese
nted
as
fol
lows
[22,
23]
.
<
>
=
0
.
5
∫
∞
0
(
)
(
0
.
5
<
>
√
2
)
,
(7)
wh
e
re
<
>
is
av
erag
e
sig
nal
to
no
ise
rati
o,
re
pr
e
sents
un
it
y
no
rm
ali
zed.
Sig
nal,
(.)
i
s
the fu
nction o
f c
om
ple
m
entary erro
r
, a
nd f
in
al
ly
(
)
is ex
pr
e
sse
d
in
the m
at
hem
at
ic
al
(8)
[
24
, 25]:
=
1
√
2
exp
{
−
[
ln
(
)
+
0
.
5
2
]
2
2
2
}
,
>
0
,
(8)
3.
RESU
LT
S
This
sect
ion
presents
the
nu
m
erical
resu
lt
s
fo
r
on
-
axis
sc
inti
ll
at
ion
ind
ex
for
colli
m
a
t
ed
Ga
us
sia
n
beam
s
and
fo
c
us
e
d
Ga
us
sia
n
beam
s
in
m
arine
at
m
os
ph
ere
ver
s
us
the
cha
ng
e
s
in
the
sou
rce
siz
e,
li
nk
le
ng
t
h,
fo
cal
le
ngth
,
and
wa
velen
gth
.
Additi
on
al
l
y,
<B
ER>
ver
su
s
source
si
ze,
li
nk
le
ngt
h,
a
nd
wa
ve
le
ng
th
are
al
so
prese
nt
ed
and
discu
s
sed.
All
these
resu
lt
s
are
ac
quire
d
from
(6
)
and
(
7).
Most
resu
lt
s
are
obt
ai
ned
by
re
gu
la
ti
ng
the
wa
velen
gt
h
=
1550
nm
,
inn
er
scal
e
=
2
m
m
,
ou
te
r
scal
e
0
=
1
and
str
ucture
const
ant
2
=
1
×
10
−
15
m
−
2
/
3
.
W
e
pr
e
fer
=
1550
nm
becau
se
these
l
asers
are
m
os
t
br
oa
dly
us
e
d
com
m
ercial
ly
because
they a
re s
a
fe fo
r
the
ey
es an
d
the
in
te
ns
it
y i
s att
enu
at
ed
i
n
F
SO l
ink
s
.
In
Fig
ure
1,
th
e
le
ng
th
li
nk
s
ver
s
us
sinti
ll
at
ion
in
dex
wit
h
three
s
ource
-
siz
e
values
1,
2,
an
d
3
cm
wh
e
n
the
f
oca
l
le
ngth
is
=
10
7
(c
ollim
at
ed
Ga
ussi
an
beam
s)
and
=
(
f
ocu
se
d
Gau
s
sia
n
bea
m
s).
The
colli
m
at
e
d
Ga
us
sia
n
be
a
m
s
hav
e
ap
pro
xim
at
e
ly
the
sa
m
e
sci
ntill
at
ion
s
in
com
par
is
on
with
f
ocused
Gau
s
sia
n
be
a
m
s
at
=1
cm
for
al
l
pro
pa
ga
ti
on
distanc
e
s.
T
he
lo
west
sci
ntil
la
ti
on
a
re
e
xhibit
ed
a
t
al
l
pro
pag
at
io
n for the
focu
sed
Gaussian
b
eam
A
t
=
2
,
and
3
cm
.
Figur
e
1.
The
s
ci
ntil
la
ti
on
index a
gainst t
he pr
opagati
on
di
sta
nce fo
r diffe
ren
t s
ource
sizes
=
1
,
2
,
3
cm
W
it
h
t
hr
ee
wa
velen
gth
s
78
0,
1064,
a
nd
15
50
nm
,
the
sci
ntil
la
ti
on
in
de
x
ver
s
us
the
le
ng
t
h
li
nks
ar
e
ind
ic
at
ed
in
Figure
2.
T
he
fig
ur
e
a
pp
e
ars
tha
t
sci
ntil
la
t
ion
ind
e
x
c
on
ce
r
n
on
t
he
wa
velen
gth
a
nd
will
increa
s
e
with
distance
.
The
va
riance
in
atm
os
ph
e
r
ic
m
arine
turbulence
inc
reas
es
becau
s
e
th
e
transm
issi
on
range
0
0
.
5
1
1
.
5
2
2
.
5
0
0
.
2
0
.
4
0
.
6
0
.
8
1
P
r
op
a
ga
t
i
on
di
s
t
a
nc
e
(
L
i
n
k
m
)
S
c
i
nt
i
l
l
a
t
i
on
i
nd
e
x
(
m
2
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
s
=
1
c
m
,
F
s
=L
s
=
2
c
m
,
F
s
=L
s
=
3
c
m
,
F
s
=L
s
=
1
c
m
,
F
s
=
s
=
2
c
m
,
F
s
=
s
=
3
c
m
,
F
s
=
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
383
-
389
386
increases
.
I
ncrea
sed
wav
el
e
ngth
ca
n
s
hr
i
nk
the
sci
ntil
la
ti
on
in
de
x
in
weak
m
arine
tur
bu
le
n
ce
f
or
bo
t
h
collim
at
ed
and f
ocu
se
d Ga
us
s
ia
n
beam
, but s
ci
ntil
la
ti
on
b
ec
om
es low
er
wi
th a
fo
c
us
e
d G
aussian
b
eam
.
Figure
2.
The
s
ci
ntil
la
ti
on
index a
gainst t
he pr
opagati
on
di
sta
nce f
or c
olli
m
at
ed
and c
oncentrate
d
g
a
us
s
ia
n
beam
w
it
h
dif
f
eren
t
wa
velen
gt
hs
= 0.7
8, 1.0
64, 1.
55 μ
m
Fo
r
f
ocu
se
d
Gau
s
sia
n
bea
m
s,
F
ig
ure
3
exh
i
bits
the
s
ci
ntil
la
ti
on
inde
x
ve
rs
us
sou
rce
siz
e
with
L
=
0.5,
1,
1.5,
and
2.5
km
.
The
fi
gure
in
dic
at
es
the
highes
t
so
urce
siz
e
pro
duce
lo
w
sci
ntil
la
ti
on
ind
e
x
with
al
l
L
.
The
sci
nt
il
la
t
ion
ve
rsus
L
is
sho
wn
in
F
ig
ure
4,
with
dif
fer
e
nt
f
oc
al
le
ngths
=
(
focuse
d
beam
),
10
4
,
10
5
,
a
nd
10
7
m
(co
ll
i
m
at
ed
beam
).
From
wh
ic
h
the
con
ce
ntrate
d
Gau
s
sia
n
bea
m
s
will
retur
n
the
best
sci
ntil
la
ti
on
in
dex
res
ults
in
weak
e
ne
d
m
arine
tu
r
bu
le
nc
e.
I
n
F
ig
ure
5,
lo
g
(<BER
>)
is
de
picte
d
ver
s
us
the
sou
rce
siz
e
for
t
he
f
oc
use
d
Gaussi
an
beam
at
pr
opa
gation
dista
nc
es
L
=
0.5,
1,
1.5,
an
d
2.5
km
and
<SNR>
=1
5
dB
.
Partic
ularly
at
reasonably
siz
able
sourc
e
siz
es,
the
<
BER
>
turns
in
to
extrem
el
y
s
m
al
le
r
wh
e
n
the
co
nc
entrati
ons
of
G
aussian
beam
i
s
at
the
pr
opa
ga
ti
on
Dista
nce
L
=
0.
5
km
.
Fi
g
ure
6
e
xh
i
bited
log
(<BER
>)
vers
us
L
with
=
780,
1064,
a
nd
1550
nm
.
As
L
increase
s,
s
o
<B
ER>
raises
too
.
F
or
three
values
of
wa
velen
gths,
a
m
ark
ed
i
m
pr
ov
em
en
t
is
obser
ve
d
i
n
the
perform
a
nce
in
f
ree
s
pace
li
nks
at
highe
r
wav
el
e
ng
t
hs
f
or
c
ollim
at
ed
and
focuse
d
Ga
us
sia
n
beam
,
bu
t
the
be
st
i
m
pr
ovem
ent
accrues
wit
h
the
f
oc
us
e
d
Gau
s
sia
n beam
s.
Fig
ure
7
il
lustr
at
es the p
e
rform
ance o
f
l
og <
BER
> as a d
ist
ance fu
nction
with <S
NR> =
5
a
nd
15 d
B
and
=
1
a
nd
2
c
m
.
I
n
F
ig
ure
7
t
he
<B
ER>
i
ncr
ease
s
as
L
i
ncr
ease
s
a
nd
i
m
pr
ov
es
in
li
nks
of
at
m
os
ph
eric
m
ari
ne
are
r
el
a
te
d
to
la
rg
e
r
<
SN
R>
a
nd s
ource size
for foc
us
e
d
G
aussia
n beam
s.
Figure
3.
The
s
ci
ntil
la
ti
on
index a
gainst t
he
s
ource size
f
or
var
i
ou
s
d
ist
a
nc
es of
pro
pag
at
i
on L=
0.5, 1
, 1
.5
,
and 2.5
k
m
and
=
0
0
.
5
1
1
.
5
2
2
.
5
0
0
.
2
0
.
4
0
.
6
0
.
8
1
P
r
op
a
ga
t
i
on
di
s
t
a
nc
e
(
L
i
n
k
m
)
S
c
i
nt
i
l
l
a
t
i
on
i
nd
e
x
(
m
2
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
2
c
m
=
1
5
5
0
n
m
,
F
s
=L
=
1
5
5
0
n
m
,
F
s
=
=
1
0
6
4
n
m
,
F
s
=L
=
1
0
6
4
n
m
,
F
s
=
=
7
8
0
n
m
,
F
s
=L
=
7
8
0
n
m
,
F
s
=
5
10
15
20
25
0
0
.
2
0
.
4
0
.
6
0
.
8
1
s
(
i
n
c
m
)
S
c
i
nt
i
l
l
a
t
i
on
i
nd
e
x
(
m
2
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
=
1
5
5
0
n
m
L
=
0
.
5
K
m
L
=
1
K
m
L
=
1
.
5
K
m
L
=
2
.
5
K
m
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Foc
us
ed
an
d
c
olli
ma
te
d
G
aus
sian l
as
er
b
e
am sci
ntil
lati
on
in weakly t
urb
ulent
marine
.
.
.
(
Ah
med A.
Ab
ba
s)
387
Figure
4.
The
s
ci
ntil
la
ti
on
index a
g
ai
ns
t t
he pr
opagati
on
di
sta
nce fo
r diffe
ren
t
fo
cal
le
ngths
=
(focused
b
eam
),
10
4
, 10
5
, a
nd 10
7
m
Figure
5.
<B
E
R>
ag
ai
ns
t
sou
rce size
for diff
eren
t
pro
pag
at
i
on d
ist
a
nces
L
= 0
.
5, 1,
1.5,
a
nd 2.5 km
,
<SNR> =
15
dB
and
=
Figure
6.
<B
E
R>
ag
ai
ns
t
pro
pag
at
io
n dist
an
ce f
or
dif
fer
e
nt
w
a
velen
gth
s
=
0
.
78, 1.
064,
1.55 μ
m
,
<
SN
R>
=
15
dB
0
0
.
5
1
1
.
5
2
2
.
5
0
0
.
2
0
.
4
0
.
6
0
.
8
1
P
r
op
a
ga
t
i
on
di
s
t
a
nc
e
(
L
i
n
k
m
)
S
c
i
nt
i
l
l
a
t
i
on
i
nd
e
x
(
m
2
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
4
c
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
4
c
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
s
=
4
c
m
,
=
1
5
5
0
n
m
F
s
=
L
F
s
=
1
0
4
m
F
s
=
1
0
5
m
F
s
=
1
0
7
m
5
10
15
20
25
-8
-7
-6
-5
-4
-3
-2
-1
0
s
(
i
n
c
m
)
l
o
g
(
<
B
E
R
>
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
S
N
R
=
1
5
d
B
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
S
N
R
=
1
5
d
B
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
S
N
R
=
1
5
d
B
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
F
s
=
L
,
S
N
R
=
1
5
d
B
,
=
1
5
5
0
n
m
L
=
0
.
5
K
m
L
=
1
K
m
L
=
1
.
5
K
m
L
=
2
.
5
K
m
0
0
.
5
1
1
.
5
2
2
.
5
-
1
0
-8
-6
-4
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0
pr
op
a
ga
t
i
on
di
s
t
a
nc
e
(
i
n
k
m
)
l
og
(
<
B
E
R
>
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
S
N
R
=
1
5
d
B
,
s
=
2
c
m
=
1
5
5
0
n
m
,
F
s
=L
=
1
5
5
0
n
m
,
F
s
=
=
1
0
6
4
n
m
,
F
s
=L
=
1
0
6
4
n
m
,
F
s
=
=
7
8
0
n
m
,
F
s
=L
=
7
8
0
n
m
,
F
s
=
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
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8708
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1,
Febr
uar
y
2021
:
383
-
389
388
Figure
7.
<B
E
R>
ag
ai
ns
t
pro
pag
at
io
n dist
an
ce f
or
dif
fer
e
nt
<
SN
R>
=
5 a
nd
15 d
B
, a
nd s
ource sizes
=
1
,
2
4.
CONCL
US
I
O
N
Th
e
form
ula
ti
on
a
nd
eval
uation
of
the
sci
nt
il
la
ti
on
for
Ga
us
sia
n
beam
s
f
ocused
a
nd
c
ol
lim
at
ed
in
weak
m
arine
tur
bule
nce
is
f
or
the
horiz
on
ta
l
li
nk
s
via
the
us
a
ge
of
Ry
to
v
m
e
tho
d.
The
ob
ta
ine
d
res
ults
is
f
or
sci
ntil
la
ti
on
ind
ex
a
nd
<B
ER>
ver
s
us
the
li
nk
le
ng
t
h
f
or
be
am
siz
e,
wav
el
en
gth
,
f
ocal
le
ng
th
,
an
d
<
SN
R>
.
Howe
ver,
the
res
ults
s
how
that,
l
ow
est
sci
ntil
la
ti
on
s
a
t
al
l
prop
a
gati
on
dista
nces
wh
e
ne
ver
inc
r
easi
ng
the
wa
velen
gt
h
a
nd
sou
rce
siz
e
of
the
fo
c
us
e
d
Ga
us
sia
n
beam
in
wea
k
at
m
os
phe
ric
tu
rbulence
.
Fu
rt
her
m
or
e,
t
he
at
m
os
ph
e
ric
m
arine
in
hori
zon
ta
l
li
nks,
<
BER
>
beco
m
es
sm
aller
in
th
e
case
of
s
hort
le
ng
t
h
li
nk
s,
a
nd
w
he
n
the
wav
el
e
ngth
a
nd
source
siz
e
increase.
W
e
noti
ced
t
hat
the
sci
ntil
la
ti
on
in
dex
ha
s
bee
n
reduce
d
us
i
ng
the
fo
c
us
e
d
beam
s
and
th
eref
o
re
the
a
ver
a
ge
BER
conseq
ue
ntly
has
bee
n
im
pr
ove
d.
The
fin
dings
c
an
be
a
be
nef
i
ci
al
ref
ere
nce
i
n
perform
ance
an
d
desig
n
e
va
luati
on
s
of
th
e
horiz
on
ta
l
li
nk
s
of
op
ti
cal
wirele
ss
com
m
un
ic
at
ion
t
hat
ar
e
thr
ough
m
arine
m
edia,
i.e.,
ab
ove
seas
a
nd
oceans.
Her
e
,
the
sci
ntil
la
ti
on
ind
ex
was
f
ound
j
ust
for
Ga
us
sia
n
e
xcita
ti
on
,
i
t
can
be
f
ound
fo
r
oth
er
excit
at
io
ns
li
ke
cos
-
Ga
us
sia
n,
cos
h
-
Gau
s
sia
n,
sine
-
Ga
us
sia
n,
sin
h
-
Gaussi
an
,
He
rm
it
e
-
cosh
-
Ga
us
sia
n,
Herm
it
e
-
sine
-
Ga
ussi
an,
Her
m
it
e
-
sinh
-
Gau
s
sia
n;
Herm
it
e
-
cos
-
Ga
uss
ia
n
beam
s….etc.
These
ex
ci
ta
ti
on
s
m
ay
re
du
ce
the
e
ff
ect
of
sci
ntil
la
ti
on
and im
pr
ove in
opti
cal
li
nk
s.
REFERE
NCE
S
[1]
F.
S.
Vete
li
no,
et
al
.
,
“
A
ne
w
m
ari
ne
at
m
ospheric
spec
tru
m
for
la
ser
pr
opaga
t
ion,
”
Pro
c
ee
d
ings
of
SPIE
,
At
mos
pheric
Propagati
on
I
V
,
vol
.
65
51,
2007.
[2]
K.
J.
Gra
y
shan,
et
al.
,
“
A
m
ari
n
e
at
m
ospheric
spec
trum
for
la
se
r
propa
gat
ion
,
”
Wav
e
s
in
Random
and
Co
mplex
Me
dia
,
vol
.
18
,
no.
1
,
pp
.
173
-
1
84
,
2008
.
[3]
C.
A.
Frieh
e,
et
al
.
,
“
Eff
e
ct
s
of
t
empera
ture
and
hum
idi
t
y
f
luctua
ti
ons
on
the
op
tical
r
efr
a
ct
iv
e
in
de
x
in
th
e
m
ari
n
e
boundar
y
l
a
y
er
,
”
Journal
o
f the
Opt
ic
al
Soc
i
ety of
Am
eri
ca
A
,
vo
l
.
65
,
no
.
12
,
pp
.
1502
-
1511
,
197
5.
[4]
L.
C.
Andrews
,
“
An
ana
l
y
tical
m
odel
for
the
ref
rac
t
ive
index
power
spec
trum
and
it
s
app
li
c
at
ion
to
optic
a
l
scint
illations
in
t
he
a
tmos
p
her
e
,”
J
ournal
of
Mod
e
rn
Opt
ics
,
vol.
39
,
no
.
9
,
pp
.
184
9
-
1853
,
1992
.
[5]
Y.
B
a
y
ka
l
,
“
Higher
-
orde
r
la
ser
bea
m
scintill
at
io
n
in
we
akly
tur
bule
nt
m
ari
ne
atm
ospheric
m
ediu
m
,
”
J
ournal
of
the
Opt
ic
al
Soc
i
et
y
of
Ame
rica
,
vol.
33
,
no
.
4
,
pp
.
758
-
763
,
2016
.
[6]
M
.
Q.
Tah
a,
e
t
al
.
,
“
Two
-
le
ve
l
sche
duli
ng
sch
e
m
e
for
int
egr
a
ted
4G
-
W
LAN
ne
twork,
”
Int
ernat
ional
Journal
of
El
e
ct
rica
l
and
C
omputer
Engi
n
e
ering
(
IJE
CE)
,
v
ol
.
10
,
n
o
.
3
,
pp
.
2633
-
26
43,
20
20
.
[7]
M.
Cheng,
e
t
al.
,
“
Scint
i
ll
a
ti
on
and
ape
r
ture
av
era
ging
for
Gau
ss
ia
n
bea
m
s
through
non
-
Kolmogorov
m
ari
ti
m
e
at
m
ospheric
turb
ule
nc
e cha
nne
ls,
”
Opti
cs
E
xpre
ss
,
vol
.
23
,
no
.
25
,
pp.
32606
-
3262
1
,
2015
.
[8]
L.
Cui
,
et
al.
,
“
Atm
ospheric
tur
bule
nc
e
MTF
fo
r
i
nfra
r
ed
opt
ica
l
wave
s’
prop
ag
at
ion
through
m
ari
ne
at
m
ospheri
c
turbul
en
ce
,
”
In
frared
Phy
si
cs
&
Technol
ogy
,
vo
l
.
65
,
pp.
24
-
29
,
2
01
4
.
[9]
I.
Tosel
l
i,
e
t
al.
,
“
Gauss
ia
n
bea
m
propa
gation
in
m
ari
ti
m
e
at
m
ospheric
turbu
le
n
ce
:
long
te
rm
bea
m
s
pre
ad
and
bea
m
wande
r ana
l
y
sis,
”
Proc
ee
d
ings o
f
SPIE
,
Free
-
Spa
ce
Las
er
Comm
unic
ati
ons
X
,
vol
.
7814,
2010
.
[10]
R
.
A
.
Fa
y
adh,
e
t
al
.
,
“
Esta
bl
ishm
ent
Network
by
Us
ing
FS
O
Li
nk
Based
on
MD
Code
for
Hy
brid
SC
M
-
SAC
-
OCD
MA
W
ire
les
s
Sy
stem,
”
Int
e
rnational
Journ
al
of
E
lectric
a
l
and
Computer
E
ng
ine
ering
(
IJECE)
,
v
ol
.
8
,
n
o.
6,
pp.
5107
-
5117
,
2018
.
[11]
M.
Li
and
M.
Cvij
etic
,
“
Coher
ent
fre
e
spac
e
o
pti
cs
comm
unicati
ons
over
the
m
ari
ti
m
e
at
m
osphere
with
use
of
ada
pt
ive
op
tics f
or
bea
m
wav
efr
o
nt
cor
r
ection,
”
A
ppli
ed
Opt
ics
,
v
ol
.
54
,
no
.
6
,
pp
.
1453
-
1462
,
201
5.
0
0.
5
1
1.
5
2
2.
5
-8
-6
-4
-2
0
pr
op
a
ga
t
i
on
di
s
t
a
nc
e
(
i
n
k
m
)
l
og
(
<
B
E
R
>
)
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
C
2
n
=
1
0
-
1
5
m
-
2
/
3
, l
0
=
2
m
m
,
=
1
5
5
0
n
m
s
=
1c
m
,
F
s
=
L
s
=
1c
m
,
F
s
=
s
=
2c
m
,
F
s
=
L
s
=
2c
m
,
F
s
=
s
=
1c
m
,
F
s
=L
s
=
1c
m
,
F
s
=
s
=
2c
m
F
s
=L
s
=
2c
m
,
F
s
=
S
N
R
=
5
d
B
S
N
R
=
1
5
d
B
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Foc
us
ed
an
d
c
olli
ma
te
d
G
aus
sian l
as
er
b
e
am sci
ntil
lati
on
in weakly t
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dom
ai
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wat
er
interfa
ce
:
f
ea
sibi
li
t
y
fo
r
under
-
wate
r
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m
m
unic
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ions,
”
Proc
ee
dings
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,
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Propag
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t
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on
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y
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l
ase
r
be
am
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gat
i
ng
in
the
m
aritime
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ronm
ent
,
”
O
pt
ics
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press
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F
SO
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t
her
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it
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ad
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”
Int
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al
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em
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iv
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rar
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y
t
ically
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Form
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e
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at
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ence,
”
Journal
of
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a
l
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f
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pped
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ia
n
l
as
er
bea
m
scinti
ll
ation
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wea
k
l
y
turbu
le
nt
m
arine
at
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ospheric
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edi
um
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es
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ospheric
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en
ce
fo
r
sate
l
li
t
e
l
ase
r
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”
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el
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W
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Bit
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aussian
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ams
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wea
k
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ceani
c
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ule
nc
e
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Journal
of
th
e
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ic
a
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ty
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f Ameri
ca
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BIOGR
AP
H
I
ES
OF
A
UTH
ORS
Ah
me
d
A.
Ab
b
as
is
A
hea
d
o
f
Elec
tr
ic
a
l
E
ng
ine
er
ing
Depa
r
t
m
ent
,
Col
le
ge
o
f
Engi
n
ee
ring
,
Univer
sit
y
of
A
nbar
from
2018
ti
ll
now.
He
rece
ive
d
th
e
B
.
Sc.
d
egr
ee
in
El
e
ct
r
ical
Eng
ineeri
ng/
Univer
sit
y
of
Technol
og
y
in
199
4,
he
re
ceive
d
MS
.
c
.
in
comm
unic
a
ti
on
Engi
ne
e
ring
/Unive
rsi
t
y
of
Technol
og
y
i
n
200
5
and
he
rec
e
ive
d
P
hD
in
comm
unic
at
ion
Engi
ne
eri
ng
/Ankar
a
Yı
ldı
rım
Be
y
azıt
Univer
s
ity
in
2017.
Dr.
Ahm
ed
is
re
sea
rch
er
in
optical
wav
e
propa
gat
ion
through
ran
dom
m
edi
a.
Hamz
a
Ge
rç
ek
ci
oğlu
cur
ren
t
l
y
works
at
Republ
ic
of
Turkey
Ministr
y
of
Trans
por
ta
ti
on
and
Infra
struct
ur
e,
Dire
ct
or
at
e
Gen
era
l
of
Aerona
u
ti
cs
and
Space
Te
chno
logi
es.
D
r.
Ham
za
does
rese
arc
h
in
Enginee
ring
Edu
ca
t
io
n,
E
lectr
oni
c En
gine
er
ing
and
C
om
m
unic
at
ion
E
ngine
er
ing.
H.
Hal
du
n
Göktaş
rec
ei
v
ed
the
B.
Sc.
degr
ee
in
El
e
ct
ri
ca
l
an
d
Elec
tron
ic
Eng
ine
e
ring/
Hac
et
t
epe
Univer
sit
y
in
1987
.
H
e
rec
ei
v
ed
M.Sc
.
in
Elec
tr
ic
a
l
and
El
e
ct
roni
c
Engi
ne
e
ring
/Hacet
t
epe
Univer
sit
y
in
1
990
and
r
ec
e
ived
PhD
in
Elec
tr
onic
Eng
ineeri
n
g/E
rc
i
y
es
Unive
rsit
y
in
1996
.
Prof.
Dr.
H
al
dun
is r
ese
arc
h
er in optical
f
ibe
r
co
m
m
unic
at
ion
an
d
optical fi
b
er
se
nsors
.
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