1. Theoretical Centre-of-mass Corrections for LAGEOS, ETALON and AJISAI Toshimichi OTSUBO Communications Research Laboratory, Kashima, Japan Graham M APPLEBY Natural Environment Research Council, Monks Wood, UK Laser Workshop 2003, Koetzting, 28-31 Oct 2003. See Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

2. Satellite signature effect Multiple reflectors contributing to the satellite response.Multiple reflectors contributing to the satellite response. System-dependent detection timing.System-dependent detection timing. –Single photon –C-SPAD –MCP-PMT Key error factor to achieve accurate GM and TRF scale.Key error factor to achieve accurate GM and TRF scale.

3. LAGEOS(1& 2) US+Italy 1976, 92 Altitude 5900 km Diameter 0.60 m 426 CCRs ETALON(1& 2) USSR 1989 Altitude 19000 km Diameter 1.294 m 2134 CCRs AJISAI Japan 1986 Altitude 1500 km Diameter 2.15 m 1436 CCRs

4. Response from single reflector 3 factors to be considered.3 factors to be considered. –Effective reflection area ( a ) –Reflectance ( e ) –Diffraction How to compute the intensity.How to compute the intensity. … diffraction neglected. ∝ ae … diffraction neglected. … simple diffraction model. ∝ a 2 e … simple diffraction model. [Neubert, 1994; Otsubo, 1999] … this study. ∝ a n e … this study.

5. ← Effective reflection area Reflectance →

6. LAGEOS n=1.1 0.250.24 (m) 251 “Standard”257.6 r - nL 245 3-sigma 242 w/o clipping 245 Ideal S.P. (<0.1 p.e.) 249 1 p.e. 257 100 p.e. 256 10 p.e. 256 1 ps 252 100 ps 248 300 ps 244 1ns 242 3ns FWHM SinglePhoton C-SPAD PMT(LEHM) 250 2-sigma 247 2.5-sigma 247249250252(n=2.0) Centre-of-mass correction 245 Hx Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

7. AJISAI n=1.2 SinglePhoton C-SPAD 1.000.95 (m) 1010 “Standard” 1028 r - nL 976 3-sigma 962 w/o clip 977 Ideal S.P. (<0.1 p.e.) 990 1 p.e. 1023 100 p.e. 1020 10 p.e. 1022 1 ps 1017 100 ps 1009 300 ps 993 1 ns 976 3 ns FWHM 985 2.5-sigma 997 2-sigma PMT(LEHM) 977(n=2.0)9879931002 Centre-of-mass correction 985 Hx Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

8. ETALON n=1.3 SinglePhoton C-SPAD 0.600.55 (m) 576 “Standard”613 r - nL 556 3-sigma 552 w/o clip 558 Ideal S.P. (<0.1 p.e.) 573 1 p.e. 613 100 p.e. 608 10 p.e. 612 1 ps 607 100 ps 598 300 ps 578 1 ns 562 3 ns FWHM 580 2-sigma 564 2.5-sigma PMT(LEHM) 570575582593(n=2.0) Centre-of-mass correction 565 Hx Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

9. Discussions (personal opinions) for mm ranging Avoid the intensity-dependent bias ON-SITE!Avoid the intensity-dependent bias ON-SITE! –Likely to become the elevation-angle-dependent bias, which can significantly degrade the station height determination. C-SPAD does NOT compensate the satellite returns. 1 cm for LAGEOS, 4-5 cm for AJISAI and ETALON.C-SPAD does NOT compensate the satellite returns. 1 cm for LAGEOS, 4-5 cm for AJISAI and ETALON. MCP+CFD seems ok at 1-cm level, but not at 1-mm level.MCP+CFD seems ok at 1-cm level, but not at 1-mm level. –Try the on-site shot-by-shot experiment. –kHz laser? Go for STRICT single photon!

10. Range residuals vs Intensity (Otsubo and Genba, DC Workshop, 2002)

13. Discussions (personal opinions) for mm analysis Better adjust the range bias for a while.Better adjust the range bias for a while. –1-mm accuracy is still a challenge. Impossible to model the CoM correction for multi- photon (esp. MCP+CFD) systems at 1-mm accuracy.Impossible to model the CoM correction for multi- photon (esp. MCP+CFD) systems at 1-mm accuracy. Many other systematic error sources.Many other systematic error sources. –Accept a constant offset bias. Too risky to fix it to 0 mm. –Tight constraints can be applied if necessary. –A different story when all stations do the single photon.

14. Summary Stations,Stations, Eliminate any systematic range errors. Analysts,Analysts, Not assume zero range bias. English speakers,English speakers, Is the word “bias” appropriate? Probably negative impression to non-SLR people.

15. Satellite Signature Effect in GLONASS SLR Data Toshimichi OTSUBO Communications Research Laboratory, Kashima, Japan Graham M APPLEBY Philip GIBBS Natural Environment Research Council, Monks Wood, UK Laser Workshop 2003, Koetzting, 28-31 Oct 2003.

16. GLONASS CCR Array Old type - 396 CCRs. - Until GLO-80. New type (except GLO-88) - 132 CCRs. - Since GLO-84.

20. Effective array size estimation - for 2001. - estimated by concerto ver 3. - bias elevation dependent elevation dependent average ～ (eff array size) x 0.15. average ～ (eff array size) x 0.15. old NEW

21. Effective array size estimation - for 2002. NEW

22. Summary GLONASS CCR DesignGLONASS CCR Design Large flat array is probably not the best idea. It causes the elevation-dependent range error. ~ 2 cm on average. New CCR array at least halved the signature effect. < 1 cm on ave. New CCR array at least halved the signature effect. < 1 cm on ave. Return energy vs signature effectReturn energy vs signature effect Difficult in observing new GLONASSes esp in daytime? What is the best array pattern for such high orbiters? What is the best array pattern for such high orbiters? How about in the GALILEO project? How about in the GALILEO project?