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itio
n
ally
,
in
c
o
r
r
ec
t
f
o
ca
l
p
o
in
t
d
eter
m
in
atio
n
r
aises
m
ain
ten
a
n
ce
co
s
ts
d
u
e
to
th
e
n
ee
d
f
o
r
f
r
eq
u
e
n
t
s
er
v
icin
g
.
T
h
er
e
f
o
r
e,
p
r
ec
is
e
f
o
ca
l
p
o
in
t
id
en
tific
atio
n
is
cr
u
cial.
I
n
r
elate
d
r
esear
ch
,
th
e
s
ec
o
n
d
ar
y
r
ef
lecto
r
g
eo
m
etr
y
o
f
a
Fre
s
n
el
-
ty
p
e
s
o
lar
co
n
ce
n
tr
ato
r
was
o
p
tim
ized
.
I
t
r
esu
lted
in
a
n
ew
d
esig
n
ca
lled
th
e
d
o
u
b
le
p
ar
a
b
o
lic
co
n
ce
n
tr
ato
r
(
DPC
)
.
T
h
is
in
n
o
v
atio
n
im
p
r
o
v
e
d
p
r
o
to
ty
p
e
ef
f
icien
cy
b
y
1
0
%
to
1
3
%,
ac
h
iev
in
g
1
0
0
% o
p
tical
ef
f
icien
cy
at
th
e
r
e
ce
iv
er
.
T
s
ek
o
u
r
as
et
a
l.
[
2
]
p
er
f
o
r
m
ed
o
p
tical
an
d
th
er
m
al
an
aly
s
es
o
n
a
lin
ea
r
Fre
s
n
el
co
lle
cto
r
with
a
tr
ap
ez
o
id
al
ca
v
ity
.
T
h
eir
f
i
n
d
in
g
s
co
n
f
ir
m
ed
th
at
c
o
n
ce
n
tr
ated
s
o
lar
co
llecto
r
s
ef
f
ec
ti
v
ely
g
e
n
er
ate
h
ea
t
b
etwe
en
1
5
0
°C
an
d
4
0
0
°C
.
Usi
n
g
r
ay
-
tr
ac
in
g
m
o
d
els,
th
e
y
d
em
o
n
s
tr
ated
s
o
lar
r
ad
iatio
n
d
is
tr
ib
u
tio
n
ac
r
o
s
s
th
e
ab
s
o
r
b
er
’
s
p
er
im
eter
.
C
o
m
p
u
tatio
n
al
f
l
u
id
d
y
n
am
ics
(
C
FD)
s
im
u
latio
n
s
f
u
r
th
er
an
aly
ze
d
tem
p
er
at
u
r
e
d
is
tr
ib
u
tio
n
in
r
ec
ei
v
er
co
m
p
o
n
en
ts
.
Al
-
Ar
ab
[
3
]
d
e
v
elo
p
ed
o
p
tic
al
d
esig
n
s
f
o
r
s
p
h
er
ical
a
n
d
p
ar
ab
o
lic
d
is
h
co
n
ce
n
tr
ato
r
s
o
f
v
a
r
y
in
g
d
iam
eter
s
.
Simu
latio
n
s
u
s
in
g
Z
E
MA
X
s
o
f
twar
e
r
ev
ea
led
th
at
b
o
th
co
n
ce
n
tr
ato
r
t
y
p
es
ca
n
ex
h
ib
it
s
p
h
er
ical
an
d
co
m
a
ab
er
r
atio
n
s
u
n
d
er
n
o
r
m
al
co
n
d
itio
n
s
.
L
i
a
n
d
Du
b
o
wsk
y
[
4
]
,
[
5
]
n
o
ted
t
h
at
p
ar
ab
o
lic
d
is
h
co
n
ce
n
tr
ato
r
s
o
f
f
er
th
e
h
ig
h
est
th
er
m
al
an
d
o
p
tical
ef
f
icien
cy
am
o
n
g
ex
is
tin
g
d
esig
n
s
.
T
h
eir
r
esear
ch
in
tr
o
d
u
ce
d
a
n
o
v
el
m
et
h
o
d
f
o
r
m
an
u
f
ac
tu
r
in
g
lar
g
e
-
s
ca
le
p
ar
ab
o
lic
d
is
h
es
b
y
o
p
tim
izin
g
s
eg
m
en
ted
m
ir
r
o
r
s
v
ia
p
ar
ticle
s
war
m
o
p
tim
izatio
n
-
g
e
n
etic
alg
o
r
ith
m
(
PS
O
-
GA)
.
T
h
e
d
esig
n
in
v
o
lv
e
d
ca
b
l
e
-
ad
ju
s
ted
p
etal
-
lik
e
s
eg
m
en
ts
an
d
an
an
aly
tical
m
o
d
el
f
o
r
s
tiff
n
ess
o
p
tim
izat
io
n
u
s
in
g
p
er
f
o
r
ated
h
o
les.
Kalid
asan
et
a
l.
[
6
]
im
p
r
o
v
e
d
lin
ea
r
ca
v
ity
r
ec
ei
v
er
ef
f
icien
cy
,
ac
h
iev
in
g
7
7
%
th
er
m
al
ef
f
icien
cy
an
d
o
p
er
atin
g
tem
p
er
atu
r
es
ex
ce
ed
in
g
6
2
7
°C
.
T
o
u
ar
ef
e
t
a
l.
[
7
]
e
n
h
an
ce
d
a
s
o
lar
d
is
till
er
’
s
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
n
au
to
m
atic
tr
ac
k
er
,
p
r
o
d
u
cin
g
1
6
0
liter
s
o
f
wate
r
i
n
1
0
h
o
u
r
s
with
7
0
.
3
% th
e
r
m
a
l e
f
f
icien
cy
.
J
u
n
g
et
a
l.
[
8
]
d
e
v
elo
p
ed
a
s
o
lar
-
en
er
g
y
-
p
lan
t
-
c
u
ltiv
atio
n
h
y
b
r
i
d
m
o
d
u
le,
r
ea
ch
in
g
5
4
%
s
o
lar
co
n
v
er
s
io
n
ef
f
icien
cy
.
Fo
u
laa
d
v
an
d
et
a
l.
[
9
]
an
aly
ze
d
h
ea
t
f
lu
x
d
is
tr
ib
u
tio
n
in
s
o
lar
c
o
l
lecto
r
s
,
co
m
p
ar
i
n
g
s
p
h
er
ical
an
d
p
ar
ab
o
lic
r
ef
lecto
r
ef
f
icien
cy
u
s
in
g
n
o
v
el
an
al
y
tical
m
eth
o
d
s
.
Haf
ez
et
a
l.
[
1
0
]
ex
am
in
ed
d
esig
n
p
ar
am
eter
s
,
m
ath
em
atica
l
m
o
d
els,
an
d
s
im
u
latio
n
s
f
o
r
p
ar
ab
o
lic
tr
o
u
g
h
co
llecto
r
s
(
PTCs
)
,
as
s
es
s
in
g
th
eir
f
ea
s
ib
ilit
y
in
d
if
f
e
r
en
t
r
e
g
io
n
s
.
T
awf
ik
et
a
l.
[
1
1
]
s
tu
d
ied
a
s
o
lar
co
o
k
er
with
a
b
o
tto
m
p
ar
ab
o
lic
r
ef
lecto
r
(
T
B
PR
)
,
ap
p
ly
in
g
4
E
(
en
e
r
g
y
,
ex
er
g
y
,
ec
o
n
o
m
ic,
en
v
ir
o
n
m
en
tal
)
an
aly
s
is
.
T
h
e
d
esig
n
i
m
p
r
o
v
e
d
ef
f
icien
cy
b
y
3
2
.
6
9
%
an
d
r
ed
u
ce
d
C
O₂
em
is
s
io
n
s
.
Kh
aled
i
et
a
l.
[
1
2
]
d
ev
elo
p
ed
a
n
a
n
o
f
lu
i
d
-
b
ased
th
er
m
al
m
o
d
el
f
o
r
co
m
p
o
u
n
d
p
ar
a
b
o
lic
c
o
n
ce
n
t
r
ato
r
s
(
C
PC
s
)
,
v
alid
atin
g
it
with
SiO₂/eth
y
len
e
g
ly
co
l
-
wate
r
n
an
o
f
lu
id
(
4
.
6
1
%
av
er
ag
e
er
r
o
r
)
.
Dr
ir
a
[
1
3
]
p
r
o
p
o
s
ed
s
em
i
-
p
ar
ab
o
lic
lin
ea
r
Fre
s
n
el
r
ef
lecto
r
s
(
SP
L
FR
s
)
as
co
s
t
-
ef
f
ec
tiv
e
alter
n
ativ
es
to
tr
ad
itio
n
al
PT
C
s
f
o
r
lo
w
-
in
co
m
e
r
eg
io
n
s
.
Li
et
a
l.
[
1
4
]
en
h
an
ce
d
p
ar
a
b
o
lic
tr
o
u
g
h
co
llecto
r
(
PTC)
p
er
f
o
r
m
an
ce
u
s
in
g
a
h
o
m
o
g
en
izer
an
d
s
p
ir
al
s
tr
u
ctu
r
e
(
R
HS
d
e
s
ig
n
)
,
r
ed
u
cin
g
th
e
r
m
al
d
ef
o
r
m
atio
n
b
y
9
6
%
an
d
im
p
r
o
v
in
g
ef
f
icien
c
y
b
y
0
.
6
3
%
–
1
.
2
%.
B
h
ar
ti
et
a
l.
[
1
5
]
o
p
tim
ized
s
ec
o
n
d
ar
y
r
ef
lecto
r
s
f
o
r
PTCs
,
f
in
d
in
g
p
ar
a
b
o
lic
r
e
f
lecto
r
s
i
n
cr
ea
s
ed
tem
p
e
r
atu
r
e
b
y
1
0
.
9
°C
co
m
p
ar
e
d
to
tr
ian
g
u
lar
(
9
.
6
°C
)
an
d
n
o
-
r
ef
lecto
r
(
7
.
4
°C
)
s
etu
p
s
.
Ma
d
ad
i
et
a
l.
[
1
6
]
e
v
alu
ated
g
la
s
s
-
co
v
er
ed
PTCs
u
n
d
er
d
if
f
er
en
t
tr
ac
k
in
g
m
o
d
es,
n
o
tin
g
a
1
0
% e
f
f
icien
c
y
d
r
o
p
with
a
6
° tilt er
r
o
r
in
f
u
ll
-
tr
ac
k
in
g
m
o
d
e.
Ma
ato
u
g
et
a
l.
[
1
7
]
m
o
d
el
ed
p
ar
ab
o
lic
cy
lin
d
r
ical
co
l
lecto
r
s
m
ath
em
atica
lly
.
T
h
e
r
esear
ch
in
v
esti
g
ated
th
e
co
n
v
er
s
io
n
o
f
s
o
lar
en
er
g
y
in
to
t
h
er
m
al
e
n
er
g
y
u
s
in
g
a
p
a
r
ab
o
lic
cy
lin
d
r
ical
co
n
ce
n
t
r
ato
r
.
T
h
e
en
er
g
y
b
alan
ce
eq
u
atio
n
f
o
r
th
e
ab
s
o
r
b
er
tu
b
e
was
s
o
lv
ed
u
s
in
g
th
e
f
in
ite
d
if
f
e
r
e
n
ce
m
eth
o
d
,
an
d
a
MA
T
L
AB
-
b
ased
co
m
p
u
ter
s
im
u
latio
n
was
d
ev
elo
p
ed
to
an
aly
ze
th
er
m
al
e
f
f
icien
cy
,
ab
s
o
r
b
er
t
u
b
e
tem
p
er
atu
r
e,
w
o
r
k
in
g
f
lu
id
tem
p
er
atu
r
e,
g
lass
tem
p
er
atu
r
e,
an
d
h
ea
t lo
s
s
co
ef
f
icien
ts
.
Ku
m
ar
et
a
l.
[
1
8
]
c
o
n
d
u
cted
an
o
p
tical
an
aly
s
is
o
f
a
cy
lin
d
r
ical
s
em
i
-
s
p
h
er
ical
r
ec
eiv
er
in
teg
r
ated
with
a
3
-
m
eter
-
d
iam
eter
p
a
r
a
b
o
lic
d
is
h
co
n
ce
n
tr
at
o
r
.
T
h
e
s
tu
d
y
u
tili
ze
d
So
lTr
ac
e
s
o
f
twar
e
to
an
aly
ze
th
e
ef
f
ec
t
o
f
v
ar
y
in
g
p
ar
am
eter
s
s
u
ch
as
r
ec
eiv
e
r
ap
e
r
tu
r
e
d
iam
eter
(
Da:
0
.
1
2
5
to
0
.
1
6
2
m
)
,
c
o
n
ce
n
tr
ato
r
s
u
r
f
ac
e
er
r
o
r
(
1
.
7
4
5
3
to
3
4
.
9
0
7
m
r
a
d
)
,
an
d
s
u
r
f
ac
e
ab
s
o
r
p
tiv
ity
(
α
:
7
5
%
to
9
5
%)
at
d
if
f
e
r
en
t
r
ec
eiv
er
d
is
tan
ce
s
(
H:
1
.
7
to
1
.
9
5
m
)
.
T
h
e
f
i
n
d
in
g
s
co
n
clu
d
ed
th
at
th
e
o
p
tim
al
o
p
tical
ef
f
icien
cy
was a
ch
iev
e
d
wh
en
th
e
r
ec
eiv
er
(
d
iam
eter
:
0
.
1
5
0
m
)
was
p
o
s
itio
n
ed
1
.
8
5
m
awa
y
f
r
o
m
th
e
c
o
n
ce
n
tr
ato
r
.
Ad
d
itio
n
ally
,
in
cr
ea
s
in
g
s
lo
p
e
er
r
o
r
s
f
r
o
m
1
.
7
4
5
3
to
1
7
.
4
5
3
m
r
ad
r
ed
u
ce
d
a
v
er
ag
e
o
p
tical
ef
f
icie
n
cy
b
y
n
ea
r
ly
5
0
% f
o
r
all
r
ec
e
iv
er
d
iam
eter
s
.
C
h
en
et
a
l.
[
1
9
]
im
p
r
o
v
ed
s
ec
o
n
d
ar
y
s
o
lar
a
p
p
licatio
n
s
u
s
in
g
h
y
b
r
id
p
ar
a
b
o
lic/s
p
h
er
ica
l
m
ir
r
o
r
s
,
v
alid
ated
v
ia
Z
em
ax
s
im
u
latio
n
s
.
C
u
ce
et
a
l.
[
2
0
]
in
teg
r
ated
th
er
m
o
elec
tr
ic
g
e
n
er
ato
r
s
(
T
E
Gs)
with
PTCs
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Geo
metrica
l d
etermin
a
tio
n
o
f
th
e
fo
ca
l p
o
in
t o
f p
a
r
a
b
o
lic
s
o
la
r
co
n
ce
n
tr
a
to
r
s
(
B
ek
z
o
d
Ma
xmu
d
o
v
)
5057
ac
h
iev
in
g
7
0
%
h
ig
h
er
ef
f
ici
en
cy
th
an
s
tan
d
alo
n
e
s
y
s
tem
s
.
L
atr
ac
h
e
et
a
l.
[
2
1
]
d
ev
elo
p
ed
g
e
o
m
etr
ic
p
ar
am
eter
s
f
o
r
co
n
ical
co
n
ce
n
tr
ato
r
s
,
d
er
iv
in
g
a
g
en
er
aliz
ed
f
o
ca
l
d
is
tan
ce
eq
u
atio
n
.
Do
n
g
a
et
a
l.
[
2
2
]
co
m
p
ar
ed
r
h
o
m
b
ic
v
s
.
cir
cu
la
r
ab
s
o
r
b
er
s
in
PTCs
,
s
h
o
win
g
2
.
8
8
%
h
ig
h
e
r
th
er
m
al
ef
f
icie
n
cy
with
r
h
o
m
b
ic
d
esig
n
s
.
Ma
llay
y
a
et
a
l.
[
2
3
]
an
aly
ze
d
p
a
r
ab
o
lic
d
is
h
co
n
ce
n
tr
ato
r
s
(
PDC
s
)
f
o
r
m
icr
o
g
as
tu
r
b
in
es
(
1
8
.
3
%
elec
tr
ical
ef
f
icien
cy
)
an
d
s
te
am
p
lan
ts
.
Nan
d
an
war
et
a
l
.
[
2
4
]
r
e
v
iewe
d
PDC
ad
v
an
ce
m
en
ts
,
in
clu
d
in
g
r
ec
eiv
er
g
e
o
m
etr
y
,
n
a
n
o
f
lu
id
s
,
an
d
th
er
m
al
s
to
r
a
g
e.
T
e
r
r
ó
n
-
Her
n
án
d
ez
et
a
l.
[
2
5
]
d
esig
n
ed
a
n
o
r
th
-
f
ac
in
g
C
P
C
s
o
lar
wate
r
h
ea
ter
with
PID
/FOP
I
D
co
n
tr
o
l
alg
o
r
ith
m
s
.
Qu
et
a
l.
[
2
6
]
r
ed
u
ce
d
co
s
i
n
e
lo
s
s
es
in
PT
C
s
u
s
in
g
r
o
tatin
g
-
a
x
is
tr
ac
k
in
g
,
b
o
o
s
tin
g
win
ter
ef
f
icien
cy
f
r
o
m
4
3
%
to
4
8
%.
T
h
is
r
esear
ch
u
n
d
e
r
s
co
r
es
th
e
im
p
o
r
tan
ce
o
f
g
eo
m
et
r
y
,
m
at
er
ials
,
an
d
o
p
tim
izatio
n
in
f
o
ca
l
p
o
in
t
d
eter
m
in
atio
n
,
en
h
a
n
cin
g
s
o
lar
en
er
g
y
ef
f
icien
cy
.
2.
M
E
T
H
O
D
Par
ab
o
lic
s
o
lar
co
n
ce
n
tr
ato
r
s
co
m
e
in
s
ev
er
al
d
is
tin
ct
co
n
f
ig
u
r
atio
n
s
,
ea
ch
tailo
r
e
d
f
o
r
s
p
ec
if
ic
ap
p
licatio
n
s
:
a.
Par
ab
o
lic
d
is
h
co
n
ce
n
tr
ato
r
s
:
h
ig
h
-
ef
f
icien
cy
s
y
s
tem
s
ty
p
ic
ally
u
s
ed
f
o
r
co
n
ce
n
tr
ated
p
h
o
to
v
o
ltaic
(
C
PV)
o
r
th
er
m
al
a
p
p
licatio
n
s
;
b.
Par
ab
o
lic
d
is
h
-
Sti
r
lin
g
s
y
s
tem
s
:
co
m
b
in
e
p
ar
a
b
o
lic
d
is
h
es w
ith
Sti
r
lin
g
en
g
in
es f
o
r
elec
tr
ic
ity
g
en
er
atio
n
;
c.
Par
ab
o
lic
tr
o
u
g
h
wate
r
h
ea
tin
g
s
y
s
tem
s
:
d
esig
n
ed
p
r
im
ar
il
y
f
o
r
in
d
u
s
tr
ial
an
d
r
esid
en
ti
al
wate
r
h
ea
tin
g
ap
p
licatio
n
s
;
d.
Par
ab
o
lic
tr
o
u
g
h
co
n
ce
n
tr
ato
r
s
:
wid
ely
u
s
ed
in
u
tili
ty
-
s
ca
le
s
o
lar
th
er
m
al
p
o
wer
p
la
n
ts
.
E
ac
h
v
ar
ian
t
ex
h
ib
its
u
n
iq
u
e
p
er
f
o
r
m
an
ce
ch
a
r
ac
ter
is
tics
,
o
p
er
atio
n
al
ef
f
icien
cies,
an
d
e
n
g
in
ee
r
in
g
s
p
ec
if
icatio
n
s
th
at
m
ak
e
th
e
m
s
u
itab
le
f
o
r
p
ar
tic
u
lar
u
s
e
ca
s
es.
T
h
e
r
esear
ch
in
v
e
s
tig
atio
n
in
clu
d
ed
co
m
p
r
eh
e
n
s
iv
e
an
aly
s
is
o
f
f
o
ca
l
p
o
in
t
id
en
tific
atio
n
m
eth
o
d
s
f
o
r
p
ar
a
b
o
lic
tr
o
u
g
h
s
y
s
tem
s
.
T
wo
p
r
in
cip
al
m
eth
o
d
o
l
o
g
ies em
er
g
e
f
o
r
t
h
is
cr
itical
alig
n
m
en
t p
r
o
ce
s
s
.
2
.
1
.
M
a
t
hema
t
ica
l f
un
ct
io
n
o
f
t
he
pa
ra
bo
lic
s
o
la
r
c
o
ncent
ra
t
o
r
I
n
t
h
i
s
m
e
t
h
o
d
,
t
h
e
m
a
t
h
e
m
a
ti
c
a
l
f
u
n
c
ti
o
n
o
f
t
h
e
p
a
r
a
b
o
l
i
c
s
o
l
a
r
c
o
n
c
e
n
t
r
a
t
o
r
m
u
s
t
b
e
k
n
o
w
n
.
F
o
r
e
x
a
m
p
l
e
,
l
e
t
u
s
d
e
t
e
r
m
i
n
e
t
h
e
f
o
c
a
l
p
o
i
n
t
o
f
t
h
e
f
u
n
c
t
i
o
n
=
2
.
T
o
f
i
n
d
t
h
e
f
o
c
a
l
p
o
i
n
t
o
f
t
h
e
f
u
n
ct
i
o
n
=
2
,
it
m
u
s
t
f
ir
s
t
b
e
r
ewr
itten
in
t
h
e
g
en
e
r
al
f
o
r
m
o
f
a
p
ar
ab
o
lic
eq
u
atio
n
.
T
h
e
e
q
u
atio
n
o
f
a
p
ar
ab
o
la
is
clo
s
ely
r
elate
d
to
its
m
at
h
em
atica
l
an
d
g
eo
m
etr
ical
p
r
o
p
er
ties
.
A
p
ar
ab
o
la
is
a
s
et
o
f
p
o
i
n
ts
in
a
p
lan
e
wh
er
e
ea
c
h
p
o
in
t
is
eq
u
id
is
tan
t
f
r
o
m
a
f
ix
ed
p
o
i
n
t
(
f
o
c
u
s
)
an
d
a
f
ix
ed
lin
e
(
d
ir
ec
t
r
ix
)
.
T
h
is
f
u
n
d
am
en
tal
g
eo
m
etr
ic
co
n
d
itio
n
d
ef
in
es th
e
s
h
ap
e
an
d
f
o
ca
l p
r
o
p
e
r
ties
o
f
th
e
p
a
r
ab
o
la
,
s
ee
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Geo
m
etr
ic
r
ep
r
esen
tatio
n
o
f
th
e
f
u
n
ctio
n
=
2
Usi
n
g
th
ese
p
r
o
p
er
ties
o
f
a
p
ar
ab
o
la,
we
ca
n
tr
an
s
f
o
r
m
th
e
f
u
n
ctio
n
=
2
in
to
th
e
g
en
er
al
f
o
r
m
o
f
a
p
ar
ab
o
lic
eq
u
atio
n
.
T
o
a
n
aly
ze
th
e
g
en
er
al
eq
u
atio
n
o
f
a
p
ar
a
b
o
la,
we
m
u
s
t
f
ir
s
t
co
n
s
id
er
its
g
eo
m
etr
ic
ch
ar
ac
ter
is
tics
.
I
f
th
e
v
er
te
x
o
f
th
e
p
ar
ab
o
la
is
at
(
0
,
0
)
,
its
eq
u
atio
n
s
atis
f
ies
th
e
f
o
llo
win
g
co
n
d
itio
n
s
:
T
h
e
d
ir
ec
tr
ix
is
g
iv
en
b
y
=
−
.
T
h
e
f
o
cu
s
is
at
(
0
,
p
)
,
wh
er
e
p
r
ep
r
e
s
en
ts
th
e
d
is
tan
ce
f
r
o
m
th
e
v
er
tex
to
th
e
d
ir
ec
tr
ix
o
r
th
e
f
o
cu
s
,
s
ee
Fig
u
r
e
2
.
Acc
o
r
d
in
g
to
t
h
e
d
ef
i
n
itio
n
o
f
a
p
a
r
ab
o
la,
th
e
p
er
p
en
d
i
cu
lar
d
is
tan
ce
f
r
o
m
an
y
p
o
i
n
t
(
x
,
y
)
o
n
th
e
p
ar
ab
o
l
a
to
th
e
d
ir
ec
tr
i
x
is
alwa
y
s
eq
u
al
to
its
d
is
tan
ce
f
r
o
m
th
e
f
o
cu
s
,
s
ee
Fig
u
r
e
3
.
B
ased
o
n
th
ese
co
n
d
itio
n
s
,
we
p
er
f
o
r
m
th
e
f
o
llo
win
g
s
tep
s
an
d
th
er
e
b
y
t
r
an
s
f
o
r
m
o
u
r
f
u
n
ctio
n
=
2
in
to
a
g
e
n
er
al
p
ar
a
b
o
lic
eq
u
atio
n
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
5
5
-
5
0
6
6
5058
T
h
e
d
is
tan
ce
b
etwe
en
a
n
ar
b
itr
ar
y
p
o
i
n
t (
x
,
y
)
a
n
d
th
e
f
o
cu
s
(
0
,
p
)
o
n
a
p
ar
ab
o
la
is
:
√
2
+
(
−
)
2
(
1
)
T
h
e
d
is
tan
ce
b
etwe
en
th
e
p
o
in
t (
x
,
y
)
an
d
t
h
e
d
ir
ec
tr
i
x
o
n
th
e
p
ar
ab
o
la
is
:
(
+
)
(
2
)
Acc
o
r
d
in
g
t
o
Fig
u
r
e
3
,
T
h
ese
t
wo
d
is
tan
ce
s
m
u
s
t b
e
eq
u
al,
t
h
er
ef
o
r
e:
√
2
+
(
−
)
2
=
(
+
)
(
3
)
L
et’
s
s
im
p
lify
th
is
ex
p
r
ess
io
n
.
W
e
cr
ea
te
th
e
f
o
llo
win
g
f
u
n
ct
io
n
:
2
+
(
−
)
2
=
(
+
)
2
(
4
)
2
+
2
−
2
+
2
=
2
+
2
+
2
(
5
)
2
−
2
=
2
(
6
)
2
=
4
(
7
)
=
2
4
(
8
)
T
h
is
f
u
n
ctio
n
=
2
4
is
a
g
en
er
al
f
u
n
ctio
n
o
f
p
ar
a
b
o
la
.
W
e
s
atis
f
y
th
e
g
i
v
en
c
o
n
d
itio
n
(
f
i
n
d
in
g
th
e
f
o
cu
s
)
b
y
co
m
p
ar
in
g
t
h
e
f
u
n
ct
io
n
=
2
to
th
e
g
en
er
al
f
u
n
ctio
n
o
f
a
p
ar
ab
o
la
=
2
4
.
=
2
=
2
4
(
9
)
1
=
1
4
(
1
0
)
=
4
(
1
1
)
=
4
(
1
2
)
T
h
er
ef
o
r
e,
th
e
v
alu
e
o
f
t
h
e
f
o
c
u
s
o
f
th
e
p
ar
a
b
o
la
p
is
eq
u
al
to
(
1
2
)
.
Fr
o
m
th
is
,
th
e
f
o
ca
l
p
o
in
t
o
f
th
e
p
ar
a
b
o
lic
f
u
n
ctio
n
=
2
g
iv
en
to
u
s
is
lo
ca
ted
o
n
th
e
v
e
r
tical
ax
is
,
an
d
its
co
o
r
d
in
ates
ar
e
(
0
,
4
)
.
T
h
u
s
,
i
t
was
d
eter
m
in
ed
b
y
m
eth
o
d
1
th
at
t
h
e
f
o
ca
l p
o
in
t o
f
th
e
f
u
n
ctio
n
=
2
is
(
0
,
4
)
.
Fig
u
r
e
2
.
E
q
u
ality
o
f
th
e
d
is
ta
n
ce
(
p
)
f
r
o
m
th
e
o
r
ig
in
o
f
th
e
p
a
r
ab
o
la
t
o
th
e
d
ir
e
ctr
ix
an
d
th
e
f
o
cu
s
Fig
u
r
e
3
.
T
h
e
d
is
tan
ce
f
r
o
m
a
n
ar
b
itra
r
y
p
o
i
n
t o
f
a
p
ar
ab
o
la
p
er
p
e
n
d
icu
lar
to
th
e
d
ir
ec
tr
ix
is
eq
u
al
to
t
h
e
d
is
tan
ce
to
th
e
f
o
c
u
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Geo
metrica
l d
etermin
a
tio
n
o
f
th
e
fo
ca
l p
o
in
t o
f p
a
r
a
b
o
lic
s
o
la
r
co
n
ce
n
tr
a
to
r
s
(
B
ek
z
o
d
Ma
xmu
d
o
v
)
5059
2
.
2
.
Det
er
m
ina
t
io
n
o
f
t
he
f
o
cus
o
f
a
pa
ra
bo
la
g
iv
en
by
t
he
equa
t
io
n
o
f
a
s
t
ra
ig
ht
l
ine
co
nv
er
t
ed
t
o
a
f
un
ct
io
n a
s
a
n a
t
t
em
pt
T
h
is
m
eth
o
d
d
eter
m
i
n
es
th
e
f
o
cu
s
o
f
th
e
g
iv
en
p
a
r
ab
o
la
th
r
o
u
g
h
th
e
eq
u
atio
n
o
f
a
s
tr
aig
h
t
lin
e
tr
an
s
f
o
r
m
ed
in
to
th
e
f
u
n
ctio
n
=
2
.
T
h
er
e
f
o
r
e,
th
e
f
o
llo
win
g
m
u
s
t
b
e
d
o
n
e
to
c
o
n
s
tr
u
ct
th
e
e
q
u
atio
n
o
f
a
s
tr
aig
h
t lin
e
tr
an
s
f
o
r
m
e
d
in
to
t
h
e
f
u
n
ctio
n
=
2
.
T
o
wr
ite
th
e
eq
u
atio
n
o
f
a
s
tr
a
ig
h
t lin
e,
we
wr
ite
th
e
f
o
llo
win
g
u
s
in
g
t
h
e
ex
p
la
n
atio
n
s
in
F
ig
u
r
e
4
.
=
(
−
0
)
(
−
0
)
=
(
−
0
)
(
−
0
)
(
1
3
)
Her
e
(
0
;
0
)
is
a
p
o
in
t
o
n
b
o
t
h
th
e
s
t
r
aig
h
t
lin
e
an
d
th
e
p
a
r
ab
o
la.
k
is
th
e
s
lo
p
e
o
f
th
e
s
tr
aig
h
t
lin
e
(
)
.
T
h
is
is
also
k
n
o
wn
to
u
s
f
r
o
m
m
ath
em
atica
l r
u
les
, s
ee
Fig
u
r
e
4
.
Fig
u
r
e
4
.
T
h
e
f
u
n
ctio
n
=
2
an
d
th
e
eq
u
atio
n
o
f
th
e
s
tr
aig
h
t lin
e
t
o
u
ch
in
g
it a
t th
e
p
o
in
t
(
0
;
0
)
Fro
m
m
ath
em
atica
l
r
u
les,
we
ca
n
also
d
er
iv
e
th
at
t
h
e
f
ir
s
t
d
er
iv
ativ
e
o
f
a
p
ar
ab
o
la
f
u
n
ctio
n
is
eq
u
al
to
th
e
s
lo
p
e
o
f
th
e
s
tr
aig
h
t
lin
e
d
r
awn
to
it
f
r
o
m
th
e
p
o
in
t
(
0
;
0
)
,
th
at
is
,
k
.
Fu
n
ctio
n
=
2
;
its
d
er
iv
at
iv
e
=
2
.
=
2
=
(
)
(
14
)
Sin
ce
th
e
p
o
in
t
(
0
;
0
)
b
elo
n
g
s
to
b
o
t
h
th
e
p
ar
a
b
o
la
an
d
th
e
s
tr
aig
h
t
lin
e:
=
2
0
(
15
)
0
=
0
2
(
1
6
)
C
o
n
s
id
er
in
g
th
e
ab
o
v
e:
(
−
0
)
=
(
−
0
)
(
1
7
)
(
−
0
2
)
=
2
0
(
−
0
)
(
1
8
)
B
y
o
p
er
atin
g
,
we
g
et
(
1
9
)
a
n
d
(
2
0
)
:
=
2
0
−
2
0
2
+
0
2
(
1
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
5
5
-
5
0
6
6
5060
=
2
0
−
0
2
(
2
0
)
So
,
th
e
eq
u
atio
n
o
f
t
h
e
s
tr
aig
h
t
lin
e
d
r
awn
th
r
o
u
g
h
th
e
p
o
i
n
t
(
0
;
0
)
as
a
f
u
n
ctio
n
=
2
h
as
th
e
f
o
r
m
=
2
0
−
0
2
.
T
h
is
was
n
ec
ess
ar
y
f
o
r
u
s
to
b
etter
u
n
d
e
r
s
tan
d
t
h
e
n
u
m
e
r
ical
v
al
u
e
o
f
0
;
0
,
wh
at
is
,
an
d
its
lo
ca
tio
n
h
er
e
.
B
e
ca
u
s
e,
in
m
eth
o
d
2
,
th
ese
a
r
e
o
f
g
r
ea
t
im
p
o
r
tan
ce
.
Fo
r
e
x
am
p
le,
let
u
s
co
n
s
id
er
th
e
p
r
o
b
lem
o
f
d
eter
m
in
in
g
th
e
f
o
c
u
s
o
f
a
p
ar
a
b
o
l
a
with
an
u
n
k
n
o
wn
f
u
n
ctio
n
.
Su
ch
a
s
itu
atio
n
is
en
co
u
n
ter
e
d
in
en
er
g
y
an
d
en
g
in
ee
r
in
g
wo
r
k
.
T
ec
h
n
ical
m
ea
s
u
r
em
en
ts
o
f
th
e
v
alu
es
o
f
0
;
0
,
th
e
an
g
u
lar
v
alu
e
o
f
α
ca
n
b
e
ca
r
r
ie
d
o
u
t
u
s
in
g
an
en
g
i
n
ee
r
in
g
r
u
ler
.
W
e
r
ely
o
n
th
e
f
ac
t
th
at
“th
e
d
is
ta
n
ce
fr
o
m
a
n
a
r
b
itr
a
r
y
p
o
in
t
o
f
a
p
a
r
a
b
o
la
p
erp
en
d
ic
u
la
r
to
th
e
d
ir
ec
tr
ix
i
s
eq
u
a
l
to
th
e
d
is
ta
n
ce
to
th
e
fo
cu
s
”
.
T
h
is
ca
n
also
b
e
s
ee
n
b
elo
w
,
s
ee
Fig
u
r
e
5
.
A
r
ay
in
cid
en
t
o
n
a
p
ar
ab
o
la
at
p
o
in
t
0
;
0
is
d
ir
ec
te
d
t
o
war
d
s
th
e
f
o
c
u
s
.
T
h
e
len
g
t
h
o
f
th
e
r
a
y
f
r
o
m
p
o
i
n
t
0
;
0
to
th
e
f
o
cu
s
is
eq
u
al
to
+
0
,
s
ee
Fig
u
r
e
6
.
A
r
a
y
in
cid
en
t
o
n
a
p
ar
a
b
o
la
at
p
o
i
n
t
0
;
0
r
etu
r
n
s
to
th
e
f
o
cu
s
at
th
e
s
am
e
an
g
le
as
th
e
r
ay
in
cid
en
t
o
n
p
o
in
t
0
;
0
.
T
h
e
v
alu
e
o
f
t
h
is
an
g
l
e
is
eq
u
al
to
90
−
,
s
ee
Fig
u
r
e
7
.
Usi
n
g
Fig
u
r
e
7
,
we
ca
n
s
ee
th
at
th
e
an
g
le
b
etwe
en
th
e
in
ter
ce
p
ts
+
0
an
d
0
is
180
−
2
.
W
e
d
r
aw
a
lin
e
(
c
)
f
r
o
m
th
e
f
o
cu
s
to
th
e
p
o
in
t
(
0
;
0
)
to
f
o
r
m
a
tr
ian
g
le,
s
ee
Fig
u
r
e
8
.
W
e
f
in
d
th
e
len
g
th
o
f
lin
e
(
c
)
u
s
in
g
th
e
law
o
f
co
s
in
es.
Fig
u
r
e
5
.
A
d
r
awin
g
o
f
a
g
eo
m
etr
ic
p
r
o
p
er
ty
o
f
a
p
a
r
ab
o
la
Fig
u
r
e
6
.
R
ef
r
ac
tio
n
o
f
r
ay
in
c
id
en
t o
n
a
p
ar
ab
o
la
to
war
d
s
th
e
f
o
cu
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Geo
metrica
l d
etermin
a
tio
n
o
f
th
e
fo
ca
l p
o
in
t o
f p
a
r
a
b
o
lic
s
o
la
r
co
n
ce
n
tr
a
to
r
s
(
B
ek
z
o
d
Ma
xmu
d
o
v
)
5061
Fig
u
r
e
7
.
T
h
e
an
g
le
o
f
in
ci
d
en
ce
an
d
r
etu
r
n
o
f
a
r
a
y
to
a
p
o
in
t
0
;
0
o
f
a
p
a
r
ab
o
la
Fig
u
r
e
8
.
A
r
i
g
h
t tr
ian
g
le
is
s
h
o
wn
to
d
eter
m
in
e
th
e
f
o
cu
s
o
f
a
p
ar
ab
o
la
with
a
n
u
n
k
n
o
wn
f
u
n
ctio
n
Acc
o
r
d
in
g
t
o
th
e
th
e
o
r
em
o
f
c
o
s
in
es:
2
=
(
+
0
)
2
+
0
2
−
2
∙
(
+
0
)
∙
0
∙
c
os
(
180
−
2
)
(
2
1
)
Acc
o
r
d
in
g
t
o
th
e
Py
th
a
g
o
r
ea
n
th
eo
r
em
:
2
=
2
+
0
2
(
2
2
)
Fro
m
th
is
,
we
ca
n
wr
ite
th
e
f
o
llo
win
g
:
2
+
0
2
=
(
+
0
)
2
+
0
2
−
2
∙
(
+
0
)
∙
0
∙
c
os
(
180
−
2
)
(
2
3
)
W
e
s
im
p
lify
th
is
eq
u
atio
n
an
d
d
eter
m
in
e
th
e
v
alu
e
o
f
p
:
(
180
−
2
)
=
−
(
2
)
(
2
4
)
2
+
0
2
=
(
+
0
)
2
+
0
2
+
2
∙
(
+
0
)
∙
0
∙
c
os
(
2
)
(
2
5
)
2
+
0
2
=
2
+
2
0
+
2
0
2
+
2
∙
(
+
0
)
∙
0
∙
c
os
(
2
)
(
2
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
5
5
-
5
0
6
6
5062
0
2
=
2
0
+
2
0
2
+
2
∙
(
+
0
)
∙
0
∙
c
os
(
2
)
(
2
7
)
0
2
=
2
0
+
2
0
2
+
2
0
c
os
(
2
)
+
2
0
2
c
os
(
2
)
(
2
8
)
0
2
=
2
0
(
1
+
c
os
(
2
)
)
+
2
0
2
(
1
+
c
os
(
2
)
)
(
2
9
)
2
0
(
1
+
c
os
(
2
)
)
=
0
2
−
2
0
2
(
1
+
c
os
(
2
)
)
(
3
0
)
=
0
2
−
2
0
2
(
1
+
co
s
(
2
)
)
2
0
(
1
+
co
s
(
2
)
)
(
3
1
)
T
h
er
ef
o
r
e,
th
e
p
r
esen
ted
m
et
h
o
d
ca
n
b
e
u
s
ed
to
d
eter
m
in
e
t
h
e
f
o
cu
s
o
f
a
p
a
r
ab
o
lic
s
o
lar
c
o
n
ce
n
tr
ato
r
with
an
u
n
k
n
o
wn
f
u
n
ctio
n
.
T
h
at
is
,
th
e
f
o
ca
l
p
o
i
n
t
o
f
a
p
ar
a
b
o
lic
s
o
l
ar
co
n
ce
n
tr
ato
r
with
an
u
n
k
n
o
wn
f
u
n
ctio
n
ca
n
b
e
d
eter
m
in
ed
(
b
y
k
n
o
win
g
th
e
v
alu
es o
f
0
;
0
,
an
d
α
u
s
in
g
a
r
ec
tan
g
u
lar
en
g
in
ee
r
in
g
r
u
ler
)
.
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
L
et’
s
co
m
p
ar
e
th
e
ex
ac
t
r
esu
lt
s
o
f
th
e
two
m
eth
o
d
s
ab
o
v
e.
I
f
th
e
f
o
ca
l
p
o
i
n
t
o
f
a
p
ar
a
b
o
li
c
f
u
n
ctio
n
s
o
lar
co
n
ce
n
t
r
ato
r
is
th
e
s
am
e
in
b
o
th
m
et
h
o
d
s
,
t
h
en
th
e
m
eth
o
d
s
ar
e
co
n
s
is
ten
t,
co
m
p
atib
le,
an
d
p
r
o
v
id
e
ac
cu
r
ate
r
esu
lts
.
Fo
r
ex
am
p
le,
let's d
eter
m
in
e
th
e
f
o
c
u
s
o
f
th
e
p
ar
ab
o
lic
f
u
n
ctio
n
=
2
8
,
s
ee
Fig
u
r
e
9
.
Fig
u
r
e
9
.
Par
ab
o
lic
f
u
n
ctio
n
=
2
8
Fro
m
m
ath
e
m
atica
l
laws,
we
k
n
o
w
th
at
th
e
p
ar
ab
o
la’
s
f
o
c
u
s
with
th
e
f
u
n
ctio
n
=
2
+
+
eq
u
als
1
4
.
Her
e
=
1
8
,
=
0
,
=
0
.
T
h
e
f
o
cu
s
o
f
th
e
p
ar
a
b
o
lic
f
u
n
ctio
n
=
2
8
is
=
1
4
∗
1
8
=
8
4
=
2
.
I
f
th
e
o
r
ig
in
o
f
th
e
p
ar
a
b
o
lic
f
u
n
cti
o
n
=
2
8
is
at
p
o
in
t
(
0
;
0
)
,
th
en
s
in
ce
th
e
f
o
cu
s
is
at
(
0
;
p
)
,
th
e
f
o
cu
s
is
lo
ca
te
d
at
th
e
p
o
in
t (
0
; 2
)
.
Acc
o
r
d
in
g
to
m
eth
o
d
1
,
b
ased
o
n
f
o
r
m
u
la
(
1
2
)
,
=
4
,
th
at
is
8
4
=
2
.
So
,
in
th
is
m
eth
o
d
,
th
e
f
o
cu
s
is
also
lo
ca
ted
at
th
e
p
o
i
n
t
(
0
;
2
)
.
Acc
o
r
d
in
g
to
m
eth
o
d
2
,
we
wr
ite
th
e
eq
u
atio
n
o
f
a
s
tr
aig
h
t
lin
e
o
f
th
e
p
ar
ab
o
lic
f
u
n
ctio
n
=
2
8
,
f
o
r
ex
am
p
le,
p
ass
in
g
th
r
o
u
g
h
th
e
p
o
in
t
s
(
4
;
2
)
.
Acc
o
r
d
in
g
to
(
2
0
)
,
s
t
r
ai
g
ht
l
i
n
e
=
2
0
s
t
r
ai
g
h
t
l
i
n
e
−
0
2
; f
r
o
m
th
is
we
o
b
tain
th
e
f
o
llo
win
g
.
s
t
r
ai
g
ht
l
i
n
e
=
2
∗
4
8
s
t
r
ai
g
ht
l
i
n
e
−
4
2
8
(
3
2
)
s
t
r
ai
g
ht
l
i
n
e
=
ℎ
l
i
n
e
−
2
(
3
3
)
T
h
e
ar
b
itra
r
y
p
o
in
t
(
4
;
2
)
co
r
r
esp
o
n
d
s
to
b
o
th
th
e
p
ar
a
b
o
lic
f
u
n
ctio
n
=
2
8
an
d
th
e
eq
u
atio
n
o
f
th
e
s
tr
aig
h
t
lin
e
s
t
r
ai
g
h
t
l
i
n
e
=
s
t
r
ai
g
ht
l
i
n
e
−
2
,
s
ee
Fig
u
r
e
1
0
.
0
1
2
3
4
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Geo
metrica
l d
etermin
a
tio
n
o
f
th
e
fo
ca
l p
o
in
t o
f p
a
r
a
b
o
lic
s
o
la
r
co
n
ce
n
tr
a
to
r
s
(
B
ek
z
o
d
Ma
xmu
d
o
v
)
5063
Fig
u
r
e
1
0
.
T
h
e
g
r
ap
h
o
f
th
e
s
tr
aig
h
t
-
lin
e
eq
u
ati
o
n
s
t
r
a
i
g
ht
l
i
n
e
=
s
t
r
ai
g
h
t
l
i
n
e
−
2
,
wh
ich
is
an
attem
p
t to
co
n
v
er
t th
e
p
ar
a
b
o
lic
f
u
n
ctio
n
=
2
8
Acc
o
r
d
in
g
to
(
1
4
)
an
d
(
1
5
)
,
t
h
e
v
alu
e
o
f
is
=
(
)
=
2
=
2
0
.
T
h
e
r
ef
o
r
e,
=
2
∗
4
8
=
1
.
I
t
f
o
llo
ws
th
at
=
45
°
.
As
we
h
av
e
ch
o
s
en
ar
b
itra
r
ily
,
th
e
p
o
in
t
(
4
;
2
)
is
0
;
0
.
T
h
er
ef
o
r
e,
0
=
4
;
0
=
2
;
=
45
°
.
Acc
o
r
d
in
g
ly
,
we
ch
ec
k
m
eth
o
d
2
u
s
in
g
(
3
1
)
.
=
4
2
−
2
∙
2
2
(
1
+
co
s
(
90
°
)
)
2
∙
2
(
1
+
co
s
(
90
°
)
)
=
16
−
8
(
1
+
0
)
4
(
1
+
0
)
=
8
4
=
2
(
3
4
)
As
ca
n
b
e
s
ee
n
f
r
o
m
(
3
4
)
t
h
e
f
o
cu
s
is
lo
ca
ted
at
th
e
p
o
i
n
t
(
0
;
2
)
.
I
t
f
o
llo
ws
th
at,
lik
e
th
e
p
r
ev
io
u
s
m
eth
o
d
s
,
th
e
n
ew
m
eth
o
d
,
w
h
ich
was
in
v
en
ted
u
s
in
g
g
eo
m
etr
ic
s
h
ap
es,
r
u
les,
th
eo
r
em
s
,
an
d
m
ath
em
atica
l
co
n
ce
p
ts
,
is
also
co
r
r
ec
t.
I
t c
a
n
b
e
s
aid
th
at
it h
as ju
s
tifie
d
it
s
elf
.
I
n
o
n
e
o
f
th
e
two
ex
p
er
i
m
en
ts
co
n
d
u
cted
,
t
h
e
f
o
cu
s
o
f
t
h
e
co
n
ce
n
tr
ato
r
was
d
eter
m
in
ed
ex
p
er
im
en
tally
b
y
f
o
cu
s
in
g
t
h
e
laser
b
ea
m
.
I
n
th
e
s
ec
o
n
d
m
eth
o
d
,
it
was
d
eter
m
i
n
ed
u
s
in
g
th
e
m
eth
o
d
we
p
r
o
p
o
s
e
u
s
in
g
(
3
1
)
.
I
n
b
o
th
e
x
p
er
im
en
ts
,
o
n
e
co
n
ce
n
tr
ato
r
was
u
s
ed
.
T
ab
le
1
s
h
o
ws
t
h
e
p
ar
am
eter
s
o
f
t
h
e
co
n
ce
n
tr
ato
r
s
.
T
ab
le
1
.
T
h
e
p
ar
am
ete
r
s
o
f
th
e
co
n
ce
n
tr
ato
r
s
S
u
r
f
a
c
e
Li
g
h
t
r
e
f
l
e
c
t
a
n
c
e
C
o
p
p
e
r
p
i
p
e
d
i
a
m
e
t
e
r
A
i
r
d
r
i
v
e
f
a
n
C
o
n
c
e
n
t
r
a
t
o
r
2
m
2
9
1
%
2
0
m
m
O
W
B
-
4
0
1
1
-
24
T
h
e
ex
p
er
im
en
tal
r
esu
lts
o
f
th
e
f
ir
s
t
m
eth
o
d
o
n
a
laser
-
f
o
cu
s
ed
co
n
ce
n
tr
ato
r
ar
e
p
r
esen
ted
in
T
ab
le
2
.
T
h
e
ex
p
er
im
en
tal
r
es
u
lts
o
f
th
e
s
ec
o
n
d
m
eth
o
d
o
n
a
co
n
ce
n
tr
ato
r
with
a
f
o
cu
s
d
e
ter
m
in
ed
ac
co
r
d
in
g
to
(
3
1
)
ar
e
p
r
esen
ted
in
T
ab
le
3
.
As
ca
n
b
e
s
ee
n
f
r
o
m
th
e
r
es
u
lts
in
T
ab
les
2
an
d
3
,
t
h
e
tem
p
er
atu
r
es
o
f
th
e
air
ex
tr
ac
ted
f
r
o
m
th
e
co
n
ce
n
t
r
ato
r
with
th
e
f
o
ca
l
p
o
in
t
d
ete
r
m
i
n
ed
b
y
th
e
p
r
o
p
o
s
ed
m
eth
o
d
h
av
e
in
cr
ea
s
ed
.
T
h
is
ca
n
b
e
s
ee
n
in
t
h
e
d
iag
r
am
in
Fig
u
r
e
1
1
.
T
ab
le
2
.
T
h
e
ex
p
e
r
im
en
tal
r
es
u
lts
o
f
th
e
f
ir
s
t m
eth
o
d
Ti
mes
o
f
d
a
y
O
u
t
d
o
o
r
t
e
m
p
e
r
a
t
u
r
e
°
C
S
o
l
a
r
i
n
t
e
n
s
i
t
y
w
/
m
2
H
e
a
t
i
n
g
a
i
r
t
e
m
p
e
r
a
t
u
r
e
°
C
9
:
0
0
21
7
3
0
60
1
0
:
0
0
23
7
3
8
70
1
1
:
0
0
26
7
5
5
74
1
2
:
0
0
30
7
7
0
76
1
3
:
0
0
33
7
9
0
79
1
4
:
0
0
31
7
7
5
77
1
5
:
0
0
28
7
6
5
75
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
0
5
5
-
5
0
6
6
5064
T
ab
le
3
.
T
h
e
ex
p
e
r
im
en
tal
r
es
u
lts
o
f
th
e
s
ec
o
n
d
m
eth
o
d
Ti
mes
o
f
d
a
y
O
u
t
d
o
o
r
t
e
m
p
e
r
a
t
u
r
e
°
C
S
o
l
a
r
i
n
t
e
n
s
i
t
y
w
/
m
2
H
e
a
t
i
n
g
a
i
r
t
e
m
p
e
r
a
t
u
r
e
°
C
9
:
0
0
20
7
3
0
61
1
0
:
0
0
23
7
3
8
75
1
1
:
0
0
27
7
5
5
79
1
2
:
0
0
30
7
7
0
81
1
3
:
0
0
33
7
9
0
86
1
4
:
0
0
32
7
7
5
81
1
5
:
0
0
29
7
6
5
78
Fig
u
r
e
1
1
.
Gr
ap
h
ical
r
e
p
r
esen
t
atio
n
o
f
th
e
ad
v
a
n
tag
es o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
I
f
th
er
e
is
a
s
o
lar
co
n
ce
n
tr
at
o
r
with
an
u
n
k
n
o
wn
p
ar
a
b
o
l
ic
f
u
n
ctio
n
,
t
h
e
an
g
le
α
f
o
r
m
ed
b
y
a
n
ar
b
itra
r
y
p
o
i
n
t
0
;
0
o
f
th
e
p
ar
ab
o
l
a
(
co
n
ce
n
tr
ato
r
)
with
th
e
ab
s
ciss
a
ax
is
o
f
th
e
eq
u
atio
n
o
f
th
e
s
tr
aig
h
t
lin
e
d
r
awn
f
r
o
m
t
h
is
p
o
in
t
as
a
n
a
ttem
p
t
to
th
e
p
ar
ab
o
la
ca
n
b
e
d
eter
m
in
ed
u
s
in
g
a
r
ec
tan
g
u
la
r
en
g
in
ee
r
in
g
r
u
ler
as
m
en
tio
n
ed
ab
o
v
e.
B
y
u
s
i
n
g
th
e
r
esu
lts
o
f
th
ese
m
ea
s
u
r
em
en
ts
an
d
t
h
e
p
r
o
p
o
s
ed
m
eth
o
d
2
,
wh
ich
is
ex
p
lain
ed
in
t
h
is
r
esear
ch
wo
r
k
,
it
is
p
o
s
s
ib
le
to
d
eter
m
in
e
its
f
o
ca
l
p
o
in
t.
T
h
is
,
in
t
u
r
n
,
s
er
v
es
to
in
cr
ea
s
e
th
e
u
s
ef
u
l
ef
f
icien
cy
o
f
th
e
s
o
lar
co
n
ce
n
tr
ato
r
.
T
h
is
is
b
ec
au
s
e
th
e
lig
h
t
co
llected
in
th
e
s
o
lar
co
n
ce
n
tr
ato
r
s
is
alwa
y
s
co
n
ce
n
tr
ated
at
th
e
f
o
c
al
p
o
in
t.
Fro
m
t
h
is
p
o
in
t
o
f
v
i
ew,
th
e
im
p
o
r
tan
ce
o
f
k
n
o
win
g
th
e
f
o
ca
l
p
o
in
t
o
f
p
ar
ab
o
lic
s
o
lar
c
o
n
ce
n
tr
at
o
r
s
is
v
er
y
im
p
o
r
tan
t.
4.
CO
NCLU
SI
O
N
T
h
e
s
tu
d
y
s
u
cc
ess
f
u
lly
d
ev
elo
p
ed
an
d
v
alid
ate
d
a
n
ew
m
eth
o
d
f
o
r
ac
c
u
r
ately
d
eter
m
i
n
in
g
th
e
f
o
ca
l
p
o
in
t
o
f
p
ar
a
b
o
lic
s
o
lar
co
n
ce
n
tr
ato
r
s
.
B
y
ap
p
ly
in
g
b
o
th
m
ath
em
atica
l
an
d
g
eo
m
etr
i
c
ap
p
r
o
ac
h
es,
th
e
r
esear
ch
d
em
o
n
s
tr
ated
t
h
at
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
im
p
r
o
v
es
th
e
ac
c
u
r
ac
y
o
f
f
o
ca
l
p
o
in
t
id
e
n
tific
atio
n
,
lead
in
g
to
h
i
g
h
er
e
n
er
g
y
ef
f
ic
ien
cy
an
d
t
h
er
m
al
p
e
r
f
o
r
m
an
c
e.
E
x
p
er
im
e
n
tal
co
m
p
a
r
is
o
n
s
co
n
f
ir
m
e
d
th
at
th
e
co
n
ce
n
tr
ato
r
with
a
f
o
cu
s
d
et
er
m
in
ed
u
s
in
g
th
e
n
ew
m
eth
o
d
ex
h
ib
ited
in
cr
ea
s
ed
h
ea
t
co
llectio
n
ef
f
icien
cy
.
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h
e
f
in
d
in
g
s
s
u
g
g
est
th
at
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atin
g
th
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ap
p
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in
t
o
s
o
lar
co
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ce
n
tr
ato
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d
esig
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an
d
m
an
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f
ac
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in
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p
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o
ce
s
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ca
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if
ican
tly
en
h
an
ce
th
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r
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p
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f
o
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m
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te
m
s
.
Fu
tu
r
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esear
c
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ca
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in
teg
r
atio
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o
f
th
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with
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v
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d
ad
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tical
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esig
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to
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tim
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o
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p
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d
u
tili
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tio
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.
RE
F
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R
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NC
E
S
[
1
]
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.
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1
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4
.
[
2
]
P
.
Tse
k
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C
.
Tz
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p
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c
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v
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”
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p
p
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d
T
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rm
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n
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ri
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,
v
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p
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.
[
3
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H
.
S
.
A
l
-
A
r
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b
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n
a
l
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d
c
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p
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c
t
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w
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p
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s
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f
so
l
a
r
d
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sh
c
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c
e
n
t
r
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t
o
r
s,”
J
o
u
rn
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p
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2
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s1
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y.
[
4
]
L.
L
i
,
Y
.
Z
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.
L
i
,
R
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1
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.
[
5
]
L.
Li
a
n
d
S
.
D
u
b
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y
,
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n
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w
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”
Me
c
h
a
n
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sm
a
n
d
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c
h
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T
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.
4
6
,
p
p
.
1
5
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6
–
1
5
4
8
,
2
0
1
1
.
50
55
60
65
70
75
80
85
90
8
9
10
11
12
13
14
15
16
In
ta
ke a
ir t
e
mp
e
ra
tu
re
0
C
T
im
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If
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s
f
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us
La
se
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f
o
c
us
de
t
e
c
t
i
o
n
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