1. Centre-of-mass correction issues: Toward mm-ranging accuracy Toshimichi OTSUBO otsubo@nict.go.jp National Institute of Information and Communications Technology and Graham M APPLEBY gapp@nerc.ac.uk NERC Space Geodesy Facility 10 June 2004, 14 th International Laser Ranging Workshop (San Fernando) ???

2. Difficult challenge: We want to achieve mm accuracy using targets designed for cm accuracy. Very Important: High “accuracy” is NOT equivalent to small single-shot rms.

3. Response function Red: n=1.0 Green: n=2.0 Blue: best-fit LAGEOS AJISAI ETALON Centre-of-mass correction for high energy system … approx. at leading edge for single photon system … approx. at centroid

4. 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

5. 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.

6. 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.

7. The most guilty “error” … intensity-dependent range bias C-SPAD users: “C-” does NOT mean “compensated” for actual targets! Control the return energy (preferably at single-photon). MCP-PMT users: Probably not so serious as C-SPAD, but not sure at 1-mm accurate level. Likely to be elevation-angle-dependent error We should test at each station! cf: following 2 speakers Wilkinson and Appleby (C-SPAD at Herstmonceux) Carman, Noyes and Otsubo (MCP+CFD at Yarragadee)

8. Apr 03 To Feb 04 Residual analysis

9. Apr 03 To Feb 04 Residual analysis

10. Apr 03 To Feb 04 Residual analysis

11. Apr 03 To Feb 04 Residual analysis

12. Apr 03 To Feb 04 Residual analysis

13. Apr 03 To Feb 04 Residual analysis

14. Apr 03 To Feb 04 Residual analysis

15. Apr 03 To Feb 04 Residual analysis

16. Residual analysis “bias vs intensity 2003-04”: summary The intensity dependency is underestimated in this analysis. Intensity-dependent  Elevation-angle-dependent  absorbed in parameter estimation Overall verdicts Single photon systems (Hx, and Zimm also?) behave very good. MCP systems also good, but a few mm trend seen. C-SPAD systems have “the stronger, the shorter” trend. … typically p-p 5 cm for AJISAI, p-p < 1 cm for LAGEOS Graz kHz … difficult to tell  too many “9999” data. Very Important: DO NOT be relieved even if your station looked ok.

17. How guilty of corrupting geodetic result is intensity-dependent range bias? Adding artificial bias to raw LAG1 NP data (50 days: 21 Apr to 9 Jun 03) Station: Yarragadee (7090), Hartebeesthoek (7501) and Graz (7839) Intensity = number of single-shot returns per NP bin StrongWeak 25% 48 shots/bin223 shots/binYarragadee 109 shots/bin322 shots/binHartebeesthoek 65 shots/bin234 shots/binGraz +5 mm - 5 mm

18. How guilty of corrupting geodetic result is intensity-dependent range bias? Orbit determination with Pos+RB estimation, with and w/o introducing artificial bias Difference artificial - original Height +7.4 mm Range bias (orig +5.1 mm) +4.2 mm Height +8.4 mm Range bias (orig +8.9 mm) +4.8 mm Height +6.0 mm Range bias (orig +0.1 mm) +4.9 mm Yarragadee Hartebeesthoek Graz -5 mm +5 mm

19. Conclusions: mm accuracy from cm targets? LAGEOS is a “large” satellite now! Eliminate the intensity-dependent bias! C-SPAD does not fully compensate for satellite returns. MCP systems are more robust, and single-photon systems are the most. Intensity robustness should be TESTED at EVERY station (cf. following 2 speakers) Strong-Weak test for LAGEOS, AJISAI and any LEO with small CCR array. Please report at the future workshops! This bias contaminates the geodetic solutions. Do not go for small single-shot rms. Do not go for many single-shot returns. For the single photon systems, we can calculate the centre-of-mass corrections.