design of laser retro-reflector array and laser … · 2004. 8. 12. · •the china’s fourth...
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DESIGN OF LASER RETRO-REFLECTOR ARRAY
AND LASER RANGING EXPERIMENT
FOR SHENZHOU-IV SATELLITE
Yang Fumin, Chen Wanzhen, Zhang Zhongping,Chen Juping, Wang Yuanming
Shanghai Astronomical ObservatoryChinese Academy of Sciences
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• The China’s fourth unmanned spacecraft “Shenzhou IV”
was launched on December 30, 2002
• One module of the spacecraft returned to earth on
January 6, 2003
• The other part, the orbital module, remained in the orbit
and carried on some scientific experiment.
• One of the instruments on board was the microwave
altimeter for sea level measurement
• A laser retro-reflector array and a GPS receiver onboard
for precise orbit determination.
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Diameter: 20cm
Corner cubes: 9
Material: Fused quartz
Weight: 850g
Configuration of LRA
“Shenzhou IV”Laser Reflector Array
LRA was designed andmanufactured by theShanghai Observatory
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Mechanical Drawing
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Calculation of Effective Reflection Area
of Shenzhou IV Satellite
1. Calculation for the incidence angle of laser
beam with respect to the retro-reflector that
has an inclination angle with the normal plane
pointing to the Earth’s center
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Effective area of the retro-reflector The relation between the incidence angle and the
relative effective area is given by:
( ) 01 cos2sin
2itgir ⋅⋅⋅-⋅= - mm
ph
where , ,
¶« is relative effective geometric area,
i0 is incidence angle of laser beam,
ir is refraction angle of laser beam,
is index of refraction for retro-reflector, usually the
retro-reflector is made of fused quartz (n=1.445).
While i0=0, then ¶« =1.
( ) 2/1221 ritg-=m ˜¯
ˆÁË
Ê= -
n
iir
01 sinsin
n
n
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E
eX
eY
OX
OY
SYSX
O
OZ
e
el
az
S
SZ?
r
Three coordinate systems
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The unity length vector of the laser beam both instation coordinate system and in geocentric coordinatesystem is the same:
In geocentric system, the unity length vector of thesatellite position is:
˙˙˙
˚
˘
ÍÍÍ
Î
È
=
)sin(
)sin()cos(
)cos()cos(
el
azel
azel
L
˙˙˙
˚
˘
ÍÍÍ
Î
È
=
)cos(
)sin()sin(
)cos()sin(
e
aze
aze
S
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Here, e is geocentric angle of satellite and can
be gotten by :
Where
is the slant distance from the station to the
satellite.
is geocentric distance of the satellite.
SEO–
)]cos(arcsin[ elr
es
*=r
r
sr
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˙˙˙
˚
˘
ÍÍÍ
Î
È
=˙˙˙
˚
˘
ÍÍÍ
Î
È
=
ab
b
ab
coscos
sin
sincos
z
y
x
n
n
n
n
The transformation from satellite coordinate systemto geocentric coordinate system is as follows:
˙˙˙
˚
˘
ÍÍÍ
Î
È
˙˙˙
˚
˘
ÍÍÍ
Î
È -
˙˙˙
˚
˘
ÍÍÍ
Î
È
-˙˙˙
˚
˘
ÍÍÍ
Î
È -
=
˙˙˙
˚
˘
ÍÍÍ
Î
È
s
s
s
e
e
e
z
y
x
cc
cc
ee
ee
azaz
azaz
z
y
x
100
0)cos()sin(
0)sin()cos(
)cos(0)sin(
010
)sin(0)cos(
100
0)cos()sin(
0)sin()cos(
Where )]cos()(arctan[tan eazc *-=
In satellite coordinate system, the normal vector ofretro-reflector is:
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In geocentric coordinate system, the unity lengthvector of the normal of the retro-reflector is:
The incidence angle of laser beam to the reflector isgiven by:
˙˙˙
˚
˘
ÍÍÍ
Î
È
˙˙˙
˚
˘
ÍÍÍ
Î
È -
˙˙˙
˚
˘
ÍÍÍ
Î
È
-˙˙˙
˚
˘
ÍÍÍ
Î
È -
=
˙˙˙
˚
˘
ÍÍÍ
Î
È
z
y
x
z
y
x
n
n
n
cc
cc
ee
ee
azaz
azaz
N
N
N
100
0)cos()sin(
0)sin()cos(
)cos(0)sin(
010
)sin(0)cos(
100
0)cos()sin(
0)sin()cos(
N
N
)arccos( NLi ⋅=
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2. Calculation result of distribution of effective
reflection area on Shenzhou-IV LRA
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3-D distribution pattern of effective reflection area of LRA
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Optical Tests of LRA
1. Test of the surface flatness and divergence of LRA are
with ZYGO Interferometer.
Divergence of reflectors are 10-16 arcsec.
2. Relative Reflection Area Measurement
3. Optical Reflectivity Measurement
4. Far Field Diffraction Pattern Measurement
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Relative Reflection Area Measurement
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5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 55° 60°0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RELATIVE AREA
INCIDENCE ANGLE - DEGREES
THEORETICAL CURVE ?= 0∞ ?= 30∞ ?= 60∞
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Optical Reflectivity Measurement
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0 1 2 3 4 5 6 7 8 9 100.9
0.905
0.91
0.915
0.92
0.925
0.93
0.935
0.94
0.945
REFLECTIVITY
Optical Reflectivity Measurement of LRA
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Far Field Diffraction Pattern Measurement
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Far Field Diffraction Patterns
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Laser Ranging Campaign of Shenzhou IV in China
• Since January 7, 2003, the Beijing, Shanghai, Changchun,
Wuhan and BeijingA (Argentina) stations started to track
the orbital module at an altitude of 350 KM
• Supported by the USB (United S-Band Ranging and Range
Rate) system, and pass by pass precise orbit prediction
provided by the Xi’an Mission Control Center, the 5 stations
can track the module even in the earth shadow
• 82 passes experimental ranging data were obtained during
January-March, 2003.
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ÖD?ú?¤?âÍø
ÉϺ£
Î人
CTLRS
?¤´º
±±?©
À¥Ã÷
TROSÁ÷¶¯?µ
Chinese SLR Network
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Real Time Display of Shenzhou IV Tracking at Shanghai
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The First Pass at Beijing Station on Jan.7, 2003
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Beijing Station on Mar.21, 2003
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Changchun Station on Jan.31, 2003
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Changchun Station on Feb.3, 2003
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Shanghai Station on Jan.7, 2003
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Shanghai Station on Feb.24, 2003
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