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.

1. Atmospheric Turbulence Effects onLaser Beam Propagation

Laser beam at far-field

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

• 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

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

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

• 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

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.

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:

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

-++-

+--+=

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

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

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

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

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

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

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.

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.

Optical Scheme of Kunming 1.2m LR System for Tilt Correction

Thanks