Research Journal of Applied Sciences, Engineering and Technology 4(21): 4492-4496, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: May 04, 2012
Accepted: June 08, 2012
Published: November 01, 2012
The Simulation Research on Capturing Time of Three Scanning Styles in Laser
Tracking System
Leihong Zhang, Liujie Sun, Chunfang Wang and Zhen Liu
School of Communication and Art Design, University of Shanghai for Science and Technology,
Shanghai 200093 China
Abstract: In the optical communication, the choosing scanning style is important for the optical
communication, because the illuminating laser beam is narrow and the communication range is long. In this
study, three typical scanning styles of raster scan, spiral scan and square spiral scan are compared with each
other. The characteristics of the scanning styles are introduced. The numerical simulation model is built.
The capturing time at the same condition is computed. The capturing time is affected by the scanning
interval and the scanning area. In the same scanning area and scanning interval, the capturing time of raster
scan is the biggest one and the capturing time of the square spiral scan is the smallest one.
Keywords: Raster scan, scan, spiral scan, square spiral scan
system was important for the development of the laser
tracking in the optical communication.
INTRODUCTION
In the optical communication, because the
illuminating laser beam is narrow and the
communication range is long, it is difficult to scanning,
capturing and pointing quickly and track successfully.
The illuminating laser beam scans the communication
satellites and the detecting system receives the echo to
track the communication satellites. There are three
typical scanning styles of raster scan, spiral scan and
square spiral scan. The three typical scanning styles of
raster scan, spiral scan and square spiral scan were
compared and simulated in the study (Yu et al., 2002;
Chen et al., 2005; Ma et al., 2005; Chen et al., 2004;
Yu et al., 2003; Feng et al., 2006). The experience
formula of scanning track was obtained by the
simulating result in the process of scanning and
capturing and in an optimization area. The capturing
rate of three typical scanning styles was compared too.
These studies researched on the tracking between two
relative steady satellites in the same orbit. The research
on the tracking between two relative moving satellites
has not been paid much more attention to in a relative
moving orbit.
The scanning and capturing time of three typical
scanning styles were computed in this study. The
characteristics of three typical scanning styles were
obtained by simulation. The experiment simulation was
done between two relative moving satellites in the same
orbit. The merits and demerits of three typical scanning
styles were introduced in this study. The research of
capturing time of three scanning styles in laser tracking
THE TRACK FORMULA OF THE THREE
SCANNING STYLES IN THE SPACE
In the scanning process, the communication
satellite and the tracking system are in the same plane
and orbit. The communication satellite has a relative
speed to the tracking system. The scanning orbit was
shown in the Fig. 1.
The track equation of spiral scan: In the spiral
scanning process, the scanning radius increases as the
scanning area increasing and the scanning angular
velocity is invariable. The scanning track of spiral scan
was shown in the Fig. 2. The track equation is:
ρ =
I0
θ
2π
(1)
ρ: The distance between the scanning point and original
point
θ: The sweeping over angle
I0: The scanning interval in every step
The track equation of square spiral scan: The square
spiral scan has the same dvantages of the spiral scan. Its
scanning radius increased and the angular velocity is
invariable in the scanning process. The scanning track
of square spiral scan is shown in the Fig. 3. The track
equation of square spiral scanning is:
Corresponding Author: Leihong Zhang, School of Communication and Art Design, University of Shanghai for Science and
Technology, Shanghai 200093 China
4492
Res. J. Appl. Sci. Eng. Technol., 4(21): 4492-4496, 2012
scanning area
scanning spot
satellite orbit
scanning track
satellite
satellite
laser
satellite
earth
laser
Fig. 1: Scanning orbit
-1, 0, 1, 2, 2, 2, 2, 2, 1, 0, -1, -2]
n is the scanning step, x and y is the position of
scanning point.
The track equation of raster scan: The raster scan
scans row by row. The tracking system passes an
interval and scans a row after finished a row scanning.
The scanning track of raster scan is shown in the
Fig. 4. The track equation of raster scanning is:
Fig. 2: Scanning track of spiral scan
⎧1 ⎡ 2θ +θ
⎤⎫
LAEL(θV +θH ) = ⎨ ⎢ V U θU +θV − 2θH ⎥⎬
2
I
0
⎦⎭ θ decreases
⎩ ⎣
H
⎧1 ⎡2θ +θ
⎤⎫
LAEL(θV +θH ) = ⎨ ⎢ V U θU +θV +2θH ⎥⎬
⎦⎭
⎩2 ⎣ I0
Fig. 3: Scanning track of square spiral scan
n = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
x = [0, 1, 1, 0, -1, -1, -1, 0, 1, 2, 2,
2, 2, 1, 0, -1, -2, -2, -2, -2, -2]
y = [0, 0, 1, 1, 1, 0, -1, -1, -1,
(2)
θH increases (3)
L is the sweeping over distance, θu is the scanning edge
length, θv is the scanning level position, θH is the
scanning vertical position, I0 is the scanning interval
and the original point is the center point of the scanning
area.
4493 Res. J. Appl. Sci. Eng. Technol., 4(21): 4492-4496, 2012
( θ V, θ H)
0. 5θ
0. 5θ
U
U
Fig. 5: The satellite is on the right half part of the scanning
area
Fig. 4: Track of raster scan
CAPTURING TIME OF THREE
SCANNING STYLES
The satellite on the right half part of the scanning
area: It is supposed that the satellite is on the center
line of the scanning area. The satellite moves to the
right and it is on the right half part of the scanning area.
The position of the satellite is shown in the Fig. 5. The
capturing time of the three scanning styles is:
t=
L−
θU
2
v
+ρ
(4)
L is the distance that between the satellite and the
scanning edge. θu is the scanning edge length, ρ is the
distance between the scanning point and the original
point. v is the moving speed of the satellite, FA is the
scanning bandwidth.
The ρ is:
Spiral scan:
2
θ ⎞
⎛
2
2
2
I 0 FA + (I 0 FA ) + 4πI 0 FA ⎜ L − U ⎟V
2 ⎠
⎝
ρ=
2πV
Square spiral scan:
2
3I 0V + I 0 FA +
ρ=
Fig. 6: The satellite is on the left half part of the scanning area
right and it is on the left half part of the scanning area.
The position of the satellite is shown in the Fig. 6. The
capturing time of the three scanning styles is:
t=
L−
θU
−ρ
2
v
(5)
The ρ is:
Spiral scan:
I 0πV − I 0 FA +
2
(I πV − I
0
ρ=
2
0
⎛ I 2
2
θ
⎛
2
FA − 4πV ⎜⎜ π 0 V − I 0 FA ⎜ L − U
4
2
⎝
⎝
2πV
)
⎞ ⎞⎟
⎟⎟
⎠⎠
Square spiral scan:
(3I V + I
0
2
0
)
2
⎛ 2 ⎛
θ ⎞
2 ⎞
FA + 16⎜⎜ I 0 FA ⎜ L − U ⎟ − I 0 V ⎟⎟V
2 ⎠
⎝
⎝
⎠
8V
(
Rater scan:
θ ⎞ 1 2
1
⎛
2
I 0 FA ⎜ L − U ⎟ − θU V + θU I 0V
2 ⎠ 2
2
⎝
ρ=
2
VθU − I 0 FA
)
2
⎛ 2 ⎛ θ ⎞ 2 ⎞
2
2
− I0V − I0 FA + I0V + I0 FA +16⎜⎜ I0 FA⎜ L − U ⎟ − I0 V ⎟⎟V
2⎠
⎝
⎝
⎠
ρ=
8V
Raster scan:
The satellite is on the left half part of the scanning
area: It is supposed that the satellite is on the center
line of the scanning area. The satellite moves to the
4494 θ ⎞ 1 2
1
⎛
2
I 0 FA ⎜ L − U ⎟ − θ U V + θ U I 0V
2 ⎠ 2
2
⎝
ρ=
2
− Vθ U + I 0 F A
Res. J. Appl. Sci. Eng. Technol., 4(21): 4492-4496, 2012
THE RELATIONSHIP OF THE CAPTURING
TIME, SCANNING INTERVAL AND THE
SCANNING AREA
ఏೆ
600
500
400
, θU is
St
When the satellite speed is low and ܸ ൏
ூబమ ிಲ
Spiral scanning
Square spiral scanning
Raster scanning
Limited capture time
700
between 0 and 872 m, FA is 50 Hz, v is under 3.5 m/s, I0
is between 8 and 10 m/s. It is supposed that the satellite
is on the right half part and the L is 408 m.
The relationship between the capturing time and the
scanning interval: The capturing time was computed
with a certain scanning area and a certain satellite
moving speed. The relationship that between the
capturing time and the scanning interval can be drew in
the Fig. 7. We can obtain the relationship that between
the capturing time and the scanning interval from the
Fig. 7:
300
200
100
0
-100
-200
0
100 200 300 400 500 600 700
θu m
800
900
Fig. 7: The relationship between the capturing time and the
scanning interval
800
Spiral scanning
Square spiral scanning
Raster scanning
700
600
•
The capturing time of spiral scan and the square
spiral scan increased as the increasing of the
scanning interval with a certain scanning area and a
certain satellite moving speed. Because the
scanning circumference perimeter and scanning
time increased as the scanning interval and the
radial scanning interval increased.
The capturing time of raster scan decreased as the
increasing of the scan interval with a certain
scanning area and a certain satellite moving speed.
Because the transverse scanning speed of the raster
scan increased as the scanning interval increased,
the capturing time of raster scan decreased as the
scanning interval increased in the same scanning
area.
The capturing time of raster scan was the biggest
one, the spiral scan and the square spiral scan was
as the fellows. The efficiency of the spiral scan and
the square spiral scan was bigger than the one of
raster scan. The control style of the spiral scan and
the square spiral scan were much more complex
and the scanning track was the most complexity
one. The spiral scan had a blind area and missed
the communication satellite.
The relationship between the capturing time and the
scanning area: The capturing time was computed with
a certain scanning area and a certain satellite moving
speed. The relationship that between the capturing time
and the scanning interval can be drew in the Fig. 8. We
can obtained the relationship that between the capturing
time and the scanning area from the Fig. 8:
St
500
400
300
200
100
0
8.0 8.2 8.4 8.6
8.8 9.0 9.2
I 0m
9.4 9.6 9.8
10
Fig. 8: The relationship between the capturing time and the
scanning area
•
•
•
4495 The capturing time and the scanning edge length of
raster scan increased as the increasing of the
scanning interval with a certain scanning interval
and a certain satellite moving speed. And the
capturing time of spiral scanning and the square
spiral scanning decreased. The capturing time of
the raster scan increased as the scanning area
increased. The distance between the scanning point
and the satellite decreased as the scanning area
increased in the spiral scan and square spiral scan
style.
The scanning edge length must be bigger than 150
m, the raster scan can capture the satellite. Because
the side length and the transverse scanning side
length were small, the distance that the satellite
passed was bigger than the scanning side length. It
couldn’t capture the satellite in one time, we must
scan much more times to capture the satellite.
The capturing time of raster scan is lower than the
one of the spiral scan and the square spiral scan
when the:
θU <
2
I 0 FA
2V
Res. J. Appl. Sci. Eng. Technol., 4(21): 4492-4496, 2012
Because the scanning time of raster scan is lower
than the one of the other scanning styles in the
same scanning area. The capturing time of raster
scan was bigger than the one of the spiral scan and
the square spiral scan, when the:
θU >
2
I 0 FA
2V
CONCLUSION
The characteristics of the three scanning styles are
compared in this study. The simulation model is built,
the capturing time is computed. The laser tracking that
between the tracking system and the communication
satellite is simulated in a small relative speed. The
capturing time of three scanning styles is computed
with a small relative speed and in the same orbit. In the
same scanning area and scanning interval, the capturing
time of raster scan is the biggest one and the capturing
time of the square spiral scan is the smallest one.
ACKNOWLEDGMENT
This study is supported by outstanding young
teacher supporting project in Shanghai City in 2011
(No. slg11033) and the starting project of doctor of
niversity of Shanghai for Science and Technology (No.
1D-11-309-001).
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