# Presentation: 674202

## 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.

**Notes:**
I would like to talk about the satellite people are looking for.
Following the general introduction by HK yesterday, my talk is more concentrated on the optical response of the satellite and its satellite signature effect.
This is the newly developed H2A rocket of NASDA.  The LRE satellite was launched for the assessment of the rocket.  The launch was successful on 29 Aug, which was good news, but we haven’t observed it by laser ranging technique. 

## Satellite signature effect

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## 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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Response from single reflector

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## ← Effective reflection area

- ← Effective reflection area

- Reflectance →

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## LAGEOS n=1.1

***0.25***

***0.24 (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

- Single
- Photon

- C-SPAD

- PMT
- (LEHM)

- 250
- 2-sigma

- 247
- 2.5-sigma

- 247

- 249

- 250

- 252

- (n=2.0)

- Centre-of-mass correction

- 245
- Hx

- Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

**Notes:**
For the 5th pilot project, we used a very similar software and a very similar configuration.
Our software concerto was updated to 3.41 for EOPdot estimation.
We threw away some stations’ data if there are less than 30 nps in 28 days.
Although our software concerto can output a sinex file, we needed to slightly amend them for this campaign.

## AJISAI n=1.2

- Single
- Photon

- C-SPAD

***1.00***

***0.95 (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)

- 987

- 993

- 1002

- Centre-of-mass correction

- 985
- Hx

- Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

**Notes:**
For the 5th pilot project, we used a very similar software and a very similar configuration.
Our software concerto was updated to 3.41 for EOPdot estimation.
We threw away some stations’ data if there are less than 30 nps in 28 days.
Although our software concerto can output a sinex file, we needed to slightly amend them for this campaign.

## ETALON n=1.3

- Single
- Photon

- C-SPAD

***0.60***

***0.55 (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)

- 570

- 575

- 582

- 593

- (n=2.0)

- Centre-of-mass correction

- 565
- Hx

- Extracted from Otsubo and Appleby, JGR, 108, B4, 2201, Apr 2003.

**Notes:**
For the 5th pilot project, we used a very similar software and a very similar configuration.
Our software concerto was updated to 3.41 for EOPdot estimation.
We threw away some stations’ data if there are less than 30 nps in 28 days.
Although our software concerto can output a sinex file, we needed to slightly amend them for this campaign.

## Discussions (personal opinions) for mm ranging

- 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.
- 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!

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

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

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

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

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

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

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Discussions (personal opinions) for mm analysis

- 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.
- 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.

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Summary

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

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Satellite Signature Effect in GLONASS SLR Data

- 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.***

**Notes:**
I would like to talk about the satellite people are looking for.
Following the general introduction by HK yesterday, my talk is more concentrated on the optical response of the satellite and its satellite signature effect.
This is the newly developed H2A rocket of NASDA.  The LRE satellite was launched for the assessment of the rocket.  The launch was successful on 29 Aug, which was good news, but we haven’t observed it by laser ranging technique. 

## GLONASS CCR Array

- Old type
- 	- 396 CCRs.
- 	- Until GLO-80.

- New type (except GLO-88)
- 	- 132 CCRs.
- 	- Since GLO-84.

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Slide 17

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Slide 18

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Slide 19

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Effective array size estimation

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

- old

- old

- NEW

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Effective array size estimation

- 	- for 2002.

- NEW

- NEW

- NEW

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.

## Summary

- GLONASS 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.
- Return energy vs signature effect
- 	Difficult in observing new GLONASSes esp in daytime?
-     What is the best array pattern for such high orbiters?
-     How about in the GALILEO project?

**Notes:**
Like AJISAI satellite, the LRE satellite carries both CCRs and mirrors.  CCRs are for laser ranging, and mirrors for the optical and directional observation.
There are two hemispheres, let’s call them N and S although the actual attitude is not North and South.  The N hemisphere has 4 rows, from N4 to N1.
There are only one face on N4 occupied by a CCR holder, 4 faces on N3 occupied by mirrors, 8 faces on N2 and 12 faces on N1.  N1 and N2 have CCR holders and mirrors every other faces.
S1 and S2 are similar to N1 and N2.  And, due to the attachment there are no optical devices below S2.
This is a holder which holds 6 ccrs.