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Real-Time Separation ofAtmospheric Tip-Tilt Signal from
Lunar Surface
Xiong Yaoheng Guo Rui
Yunnan Observatory, Chinese Academy of Sciences
14th International Laser Ranging Workshop, San Fernando,Cadiz, Spain
June 8, 2004
Considered:
Ta atmospheric transmission, 0.5, amplitude attenuate
Unconsidered:
1. Atmospheric turbulence effects on laser beampropagation.
2. The distribution of the laser beam
For Kunming station 1.2m laser ranging system on LLR:N =0.17 sub-single photon detection.
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1. Atmospheric Turbulence Effects onLaser Beam Propagation
Laser beam at far-field
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Short-term beam wander:
Short-term beam spread:
Long-term beam spread:
31
35
02
22 22.10
Drk
ZC =Ò·r
20
2
222
22
22 6.17
14
4
rk
Z
F
ZD
Dk
ZL +˜
¯
ˆÁË
Ê -+=Ò·r
56
31
02
02
222
22
22 48.01
6.171
4
4˙˙
˚
˘
ÍÍ
Î
Ș¯
ˆÁË
Ê-+˜¯
ˆÁË
Ê -+=Ò·D
r
rk
Z
F
ZD
Dk
ZSr
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• Here,k wave number, D laser transmitter diameterZ laser propagation axis and coordinateF radius of curvature of laser beamro Fried’s coherence length, 5 ~ 20 cm
• Method:Maxwell wave equation Æ Markovapproximation Æ the second moment and thefour moment (approximation) of the field Æmean square value of above terms
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0 5 10 15 200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Fried's parameter (cm)
arcsec
Long-term beam spreadShort-term beam wanderShort-term beam spread
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2. Returned Laser Photoelectrons Nr for one laser pulse firing:
Depend on turbulence terms to be considered
here: re laser beam radius at target, determined by laser divergence rc short-term beam wander
rs short-term beam spread
( ) ˜¯
ˆÁÁË
Ê
+-
+=
22
2
42222
20 exp
4
se
C
mse
rtarmr R
TTTAAENN
rrr
qqqpha
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• If tilt is removed, the correction factor for thelaser ranging is:
• 1/40 ~ 1/6, depend on the turbulence
For Kunming station 1.2m laser ranging system onLLR:
Nr=0.17¥(1/40 ~ 1/6)
( ) ˜¯
ˆÁÁË
Ê
+-
+=
22
2
22
2
exp4 se
C
se
er
N
N
qqq
qqq
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3. Detection and Computation ofTip-Tilt from Lunar Surface
Goal: to compensate atmospheric tip-tilt effect inreal- time on LLR
Object: the extended light source
Method: When performing the LLR, its telescopewill point the retroreflector array on the moonsurface. Atmospheric tip-tilt signal can only beobtained from a small area of the geomorphologicstructure that is near the moon retroreflector. That isto track geomorphologic structure of the moonsurface through the motion of the successive images.
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A N ¥ N pixels reference image IR(x, y) that iswithin the isoplanatic angle is sampled, and a timeseries I1(x, y)£I2(x, y)£ºº IL(x, y) are sampled aslive images.To determine the displacement between referenceimage and live images by computing the sum of theabsolute difference values of them. For each N ¥ Npixels live image IL(x, y), a M ¥ M pixels window isextracted. This central window of the live image iscompared with the reference image. The absolutedifference values D£®dx, dy£©between them are giventhrough the absolute difference algorithm:
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ÂÂ-
=
-
=
-++=1
0
1
0
),(),(),(M
x
M
yLR yxIyyxxIyxD dddd
The position£®dxmin, dymin£©are obtained where D£®dx, dy£©is minimum. The tilt ( Tx , Ty ) can bedetermined using a parabolic interpolation.
),(2),1(),1(
),1(),1(
2
1
minminminminminmin
minminminminmin yxDyxDyxD
yxDyxDxTx dddddd
ddddd
-++-
+--+=
),(2)1,()1,(
)1,()1,(
2
1
minminminminminmin
minminminminmin yxDyxDyxD
yxDyxDyTy dddddd
ddddd
-++-
+--+=
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4. Experiment Results
Using Kunming SLR station 1.2m telescope
f = 6m128¥128 CCD, 16m ¥ 16m for one pixel
About 0.″55 /pixel Frame rate: 419
Sampling area: near the moon retroreflector array
Apollo 11,Apollo14,Apollo15 and Lunakhod 2
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pixel
pixel
20 40 60 80 100 120
20
40
60
80
100
120
pixel
pixel
20 40 60 80 100 120
20
40
60
80
100
120
pixel
pixel
20 40 60 80 100 120
20
40
60
80
100
120
pixel
pixel
20 40 60 80 100 120
20
40
60
80
100
120
Apollo15¨-------
Apollo11-------Æ
Apollo14¨-------
Lunakhod2-------Æ
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-5
-4
-3
-2
-1
0
1
2
frame
pixel
y component of tip-tilt , 16°¡16pixels Apollo15
y component of tip-tilt
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
frame
pixel
x component of tip-tilt , 16°¡16pixels Apollo15
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
frame
pixel
Õº26 æ¯∂‘≤Ó∑÷À„∑®°¢≤Œøº«¯”Ú32°¡32pixel°¢Y∑ΩœÚµƒ«„–±¡ø(20,80)
y component of tip-tilt , 32°¡32 pixels Apollo15
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0 200 400 600 800 1000 1200 1400 1600 1800 2000-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
frame
pixel
x component of tip-tilt , 32°¡32 pixels Apollo15
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Real-Time:32°¡32 pixels window, take 25 seconds to compute2000 images, fi 12.5ms/one image16°¡16 pixels window, take 6 seconds to compute2000 images, fi 3ms/one image
Conclusion:Detection and separation of atmospheric Tip-Tiltsignal real-time from Lunar surface is within thepresent technique, especially within theatmospheric turbulence scale.
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5. Next Plan
• Apply grant for LLR ( important )
• Combine the LR system and the AO system at1.2m telescope, try to achieve real-time tip-tiltcompensation for the laser beam on the LLR.
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Optical Scheme of Kunming 1.2m LR System for Tilt Correction
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Thanks