1. Range Bias vs Intensity 2005 Toshimichi Otsubo Kashima Space Research Center National Institute of Information and Communications Technology ILRS Fall 2005 Workshop, 5 Oct 2005

2. Satelllite signature Transmitted pulse NOT equal to Return pulse –Multiple CCRs contributing to the return. –Where is the detection timing? –Key error factor for TRF scale, GM, etc.

3. System-type-dependent centre-of-mass correction LAGEOS From Otsubo and Appleby, JGR, 2003. 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) 245 Hx

4. System-type-dependent centre-of-mass correction AJISAI 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 985 Hx From Otsubo and Appleby, JGR, 2003.

5. Intensity-dependent Bias Are CoM corrections constant in the real world? –Big challenge for “mm accuracy” Systematic error  harmful in the analysis stage –Likely to be elevation-angle-dependent –Directly contaminates station heights (Otsubo, 2004). –Short pulse: fully compensated by C-SPAD / CFD. –Long pulse: target signature (STRL < LAG < AJI) –The stronger, the shorter? Not so simple?

6. Bias vs Intensity: Analysis Procedure Use of “Returns per NP bin” as intensity parameter –Strong signal  High return rate –Weak signal  Low return rate (Extreme: single photon) Orbit determination –Period: Jan 2004 to Jul 2005 (210 days) –Satellites: LAG1+LAG2, AJISAI, STARLETTE+STELLA –‘ concerto v4 ’ solved for orbits, station position & range bias –Stations: Top 20 in Quarterly Performance Card (Thanks Mark!) –Post-fit residuals sorted by “returns per NP bin”

7. Riga 1884: PMT

8. McDonald 7080: PMT

9. Yarragadee 7090: PMT

10. Greenbelt 7105: PMT

11. Monument Peak 7110: PMT

12. Changchun 7237: APD

13. Beijing 7249: APD

14. Hartebeestoek 7501: PMT

15. Zimmerwald 7810 (423 nm): APD

16. Zimmerwald 7810 (846 nm): APD

17. Borowiec 7811: PMT

18. San Fernando 7824: PMT

19. Mt Stromlo 7825: APD

20. Riyadh 7832: SPAD? (No SCI Log)

21. Grasse 7835: APD

22. Shanghai 7837: APD

23. Simosato 7838: PMT

24. Graz 7839: APD

25. Herstmonceux 7840: APD

26. Potsdam 7841: PMT

27. Matera 7941: PMT? (No SCI Log)

28. Wettzell 8834: PMT+APD (?)

29. Discussions: 1 mm accuracy? Still things to do! “Bias vs Intensity”: overall summary –Up to +/- 5 mm for LAG1+LAG2 and STRL+STEL. –Up to +/- 10-15 mm for AJI. –Single photon systems behave superbly. –The result is most likely to be underestimated. –It has already affected TRFs for a long time. Necessity to eliminate the intensity dependence –Accurate vertical component is our strength! –Think “accuracy” instead of “single shot rms” or “# of returns.” –Let us see “High-Low Experiments” !!

31. System-type-dependent centre-of-mass correction ETALON 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) 565 Hx From Otsubo and Appleby, JGR, 2003.