Abstract

The GRACE Follow-On satellites will use, for the first time, a Laser Ranging Interferometer to measure intersatellite distance changes from which fluctuations in Earth’s geoid can be inferred. We have investigated the beam steering method that is required to maintain the laser link between the satellites. Although developed for the specific needs of the GRACE Follow-On mission, the beam steering method could also be applied to other intersatellite laser ranging applications where major difficulties are common: large spacecraft separation and large spacecraft attitude jitter. The beam steering method simultaneously coaligns local oscillator beam and transmitted beam with the laser beam received from the distant spacecraft using Differential Wavefront Sensing. We demonstrate the operation of the beam steering method on breadboard level using GRACE satellite attitude jitter data to command a hexapod, a six-degree-of-freedom rotation and translation stage. We verify coalignment of local oscillator beam/ transmitted beam and received beam of better than 10 μrad with a stability of 10 μrad/ Hz in the GRACE Follow-On measurement band of 0.002...0.1 Hz. Additionally, important characteristics of the beam steering setup such as Differential Wavefront Sensing signals, heterodyne efficiency, and suppression of rotation-to-pathlength coupling are investigated and compared with analysis results.

© 2014 Optical Society of America

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2014 (3)

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

2013 (2)

E. D. Fitzsimons, J. Bogenstahl, J. Hough, C. J. Killow, M. Perreur-Lloyd, D. I. Robertson, and H. Ward, “Precision absolute positional measurement of laser beams,” Appl. Opt. 52, 2527–2530 (2013).
[Crossref] [PubMed]

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

2012 (2)

T. Bandikova, J. Flury, and U.-D. Ko, “Characteristics and accuracies of the GRACE inter-satellite pointing,” Adv. Space Res. 50, 123–135 (2012).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

2010 (1)

2009 (4)

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

V. M. Tiwari, J. Wahr, and S. Swenson, “Dwindling groundwater resources in northern India, from satellite gravity observations,” Geophys. Res. Lett. 36, L18401 (2009).
[Crossref]

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

2008 (2)

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

B. Wouters, D. Chambers, and E. J. O. Schrama, “GRACE observes small-scale mass loss in Greenland,” Geophys. Res. Lett. 35, L20501 (2008).
[Crossref]

2006 (2)

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state-of-the-art,” EAS Publ. 22, 165–185 (2006).
[Crossref]

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

2004 (2)

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

2003 (2)

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

1999 (2)

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

1994 (1)

1984 (1)

1975 (1)

1958 (1)

Anderson, D. Z.

Bamber, J.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Bandikova, T.

T. Bandikova, J. Flury, and U.-D. Ko, “Characteristics and accuracies of the GRACE inter-satellite pointing,” Adv. Space Res. 50, 123–135 (2012).
[Crossref]

Bar-Sever, Y.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Bertiger, W.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Bettadpur, S.

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

Blundell, M.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Bogenstahl, J.

Braxmaier, C.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Brister, R.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Brown, J.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Burke, J.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Bykov, I.

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

Campbell, H. I.

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state-of-the-art,” EAS Publ. 22, 165–185 (2006).
[Crossref]

Chambers, D.

B. Wouters, D. Chambers, and E. J. O. Schrama, “GRACE observes small-scale mass loss in Greenland,” Geophys. Res. Lett. 35, L20501 (2008).
[Crossref]

Chambers, D. P.

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

Cheng, M.

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

Dahle, C.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Danzmann, K.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Delgado, J. J. E.

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

Desai, S.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Dligatch, S.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Dunn, C.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Elliot, M.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Ettema, J.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Farrant, D.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

Fink, D.

Fitzsimons, E. D.

Flechtner, F.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Fleddermann, R.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Flury, J.

T. Bandikova, J. Flury, and U.-D. Ko, “Characteristics and accuracies of the GRACE inter-satellite pointing,” Adv. Space Res. 50, 123–135 (2012).
[Crossref]

Folkner, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

Foulon, B.

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

Francis, S.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Franklin, G.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

García Marín, A. F.

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

Gerberding, O.

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

Gilles, F.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Green, K.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Greenaway, A. H.

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state-of-the-art,” EAS Publ. 22, 165–185 (2006).
[Crossref]

Haines, B.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Halverson, P. G.

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Harris, I.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Hechenblaikner, G.

Heinzel, G.

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Herding, M.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Hough, J.

Hudson, D.

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

Johann, U.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Josselin, V.

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

Killow, C. J.

Kim, J.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Klipstein, B.

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Klipstein, W.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Klipstein, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

Ko, U.-D.

T. Bandikova, J. Flury, and U.-D. Ko, “Characteristics and accuracies of the GRACE inter-satellite pointing,” Adv. Space Res. 50, 123–135 (2012).
[Crossref]

König, R.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Kruizinga, G.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

Kuang, D.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Kullmann, J.

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

Kusche, J.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Mahrdt, C.

C. Mahrdt, Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute) and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstr. 38, 30167 Hanover, Germany, is preparing a manuscript to be called “Initial line-of-sight calibration for the GRACE follow-on laser ranging interferometer.”

McClelland, D. E.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Meehan, T.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Meers, B. J.

Meyer, U.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Mizuno, J.

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Morrison, E.

Mow-Lowry, C.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Müller, V.

Nandi, S.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Neumayer, K.-H.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Nguyen, D.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Nicklaus, K.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Perreur-Lloyd, M.

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Reigber, C.

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

Ries, J. C.

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

Rignot, E.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Robertson, D. I.

Rogstad, T.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Romans, L.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Rüdiger, A.

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Schilling, R.

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Schmidt, R.

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Schrama, E.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Schrama, E. J. O.

B. Wouters, D. Chambers, and E. J. O. Schrama, “GRACE observes small-scale mass loss in Greenland,” Geophys. Res. Lett. 35, L20501 (2008).
[Crossref]

Schuldt, T.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Schütze, D.

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

Seckold, J.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Shaddock, D. A.

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Sheard, B. S.

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

D. Schütze, V. Müller, G. Stede, B. S. Sheard, G. Heinzel, K. Danzmann, A. J. Sutton, and D. A. Shaddock, “Retroreflector for GRACE follow-on: Vertex vs. point of minimal coupling,” Opt. Express 22, 9324–9333 (2014).
[Crossref] [PubMed]

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

Smith, C.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Spero, R. E.

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Stede, G.

Strain, K.

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Sutton, A. J.

Swenson, S.

V. M. Tiwari, J. Wahr, and S. Swenson, “Dwindling groundwater resources in northern India, from satellite gravity observations,” Geophys. Res. Lett. 36, L18401 (2009).
[Crossref]

Tapley, B. D.

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

Thomas, J. B.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Thompson, P. F.

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

Tien, J.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Tiwari, V. M.

V. M. Tiwari, J. Wahr, and S. Swenson, “Dwindling groundwater resources in northern India, from satellite gravity observations,” Geophys. Res. Lett. 36, L18401 (2009).
[Crossref]

Touboul, P.

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

van de Berg, W. J.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

van den Broeke, M.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

van Meijgaard, E.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Velicogna, I.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

Wahr, J.

V. M. Tiwari, J. Wahr, and S. Swenson, “Dwindling groundwater resources in northern India, from satellite gravity observations,” Geophys. Res. Lett. 36, L18401 (2009).
[Crossref]

Ward, H.

Ward, R. L.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Ware, B.

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Watkins, M.

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Watkins, M. M.

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

Weise, D.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

Willemenot, E.

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

Winkler, W.

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Wouters, B.

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

B. Wouters, D. Chambers, and E. J. O. Schrama, “GRACE observes small-scale mass loss in Greenland,” Geophys. Res. Lett. 35, L20501 (2008).
[Crossref]

Wu, S. C.

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

Wuchenich, D.

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

Yoder, P. R.

Adv. Space Res. (1)

T. Bandikova, J. Flury, and U.-D. Ko, “Characteristics and accuracies of the GRACE inter-satellite pointing,” Adv. Space Res. 50, 123–135 (2012).
[Crossref]

AIP Conf. Proc. (1)

D. A. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Appl. Opt. (4)

B. Geofis. Teor. Appl. (1)

P. Touboul, E. Willemenot, B. Foulon, and V. Josselin, “Accelerometers for CHAMP, GRACE and GOCE space missions: Synergy and evolution,” B. Geofis. Teor. Appl. 40, 321–327 (1999).

Class. Quant. Grav. (3)

R. L. Ward, R. Fleddermann, S. Francis, C. Mow-Lowry, D. Wuchenich, M. Elliot, F. Gilles, M. Herding, K. Nicklaus, J. Brown, J. Burke, S. Dligatch, D. Farrant, K. Green, J. Seckold, M. Blundell, R. Brister, C. Smith, K. Danzmann, G. Heinzel, D. Schütze, B. S. Sheard, W. Klipstein, D. E. McClelland, and D. A. Shaddock, “The design and construction of a prototype lateral-transfer retro-reflector for inter-satellite laser ranging,” Class. Quant. Grav. 31, 095015 (2014).
[Crossref]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quant. Grav. 26, 085008 (2009).
[Crossref]

O. Gerberding, B. S. Sheard, I. Bykov, J. Kullmann, J. J. E. Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Class. Quant. Grav. 30, 235029 (2013).
[Crossref]

EAS Publ. (1)

H. I. Campbell and A. H. Greenaway, “Wavefront sensing: From historical roots to the state-of-the-art,” EAS Publ. 22, 165–185 (2006).
[Crossref]

Geophys. Res. Lett. (4)

B. Wouters, D. Chambers, and E. J. O. Schrama, “GRACE observes small-scale mass loss in Greenland,” Geophys. Res. Lett. 35, L20501 (2008).
[Crossref]

V. M. Tiwari, J. Wahr, and S. Swenson, “Dwindling groundwater resources in northern India, from satellite gravity observations,” Geophys. Res. Lett. 36, L18401 (2009).
[Crossref]

B. D. Tapley, S. Bettadpur, M. Watkins, and C. Reigber, “The gravity recovery and climate experiment: Mission overview and early results,” Geophys. Res. Lett. 31, L09607 (2004).
[Crossref]

B. D. Tapley, D. P. Chambers, S. Bettadpur, and J. C. Ries, “Large scale ocean circulation from the GRACE GGM01 Geoid,” Geophys. Res. Lett. 30, 2163 (2003).
[Crossref]

GPS World (1)

C. Dunn, W. Bertiger, Y. Bar-Sever, S. Desai, B. Haines, D. Kuang, G. Franklin, I. Harris, G. Kruizinga, T. Meehan, S. Nandi, D. Nguyen, T. Rogstad, J. B. Thomas, J. Tien, L. Romans, M. Watkins, S. C. Wu, S. Bettadpur, and J. Kim, “Instrument of GRACE: GPS augments gravity measurements,” GPS World 14, 16–28 (2003).

J. Geod. (1)

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Conf. Ser. (1)

I. Bykov, J. J. E. Delgado, A. F. García Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: Advanced prototyping,” J. Phys. Conf. Ser. 154, 012017 (2009).
[Crossref]

Opt. Commun. (1)

G. Heinzel, A. Rüdiger, R. Schilling, K. Strain, W. Winkler, J. Mizuno, and K. Danzmann, “Automatic beam alignment in the Garching 30-m prototype of a laser-interferometric gravitational wave detector,” Opt. Commun. 160, 321–334 (1999).
[Crossref]

Opt. Express (1)

Rev. Sci. Instrum. (1)

D. Schütze, D. Farrant, D. A. Shaddock, B. S. Sheard, G. Heinzel, and K. Danzmann, “Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset,” Rev. Sci. Instrum. 85, 035103 (2014).
[Crossref] [PubMed]

Science (2)

M. van den Broeke, J. Bamber, J. Ettema, E. Rignot, E. Schrama, W. J. van de Berg, E. van Meijgaard, I. Velicogna, and B. Wouters, “Partitioning recent Greenland mass loss,” Science 326, 984–986 (2009).
[Crossref] [PubMed]

B. D. Tapley, S. Bettadpur, J. C. Ries, P. F. Thompson, and M. M. Watkins, “GRACE measurements of mass variability in the earth system,” Science 305, 503–505 (2004).
[Crossref] [PubMed]

Surv. Geophys. (1)

R. Schmidt, F. Flechtner, U. Meyer, K.-H. Neumayer, C. Dahle, R. König, and J. Kusche, “Hydrological signals observed by the GRACE satellites,” Surv. Geophys. 29, 319–334 (2008).
[Crossref]

Other (4)

B. D. Tapley, S. Bettadpur, M. Cheng, D. Hudson, and G. Kruizinga, “Early results from the gravity recovery and climate experiment,” in Astrodynamics Specialist Conference, J. D. Lafontaine, J. DeLafontaine, J. Treder, M. T. Soyka, and J. A. Sims, eds. (Astrodynamics, 2003), 1899–1911.

C. Mahrdt, Max-Planck-Institute for Gravitational Physics (Albert Einstein Institute) and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstr. 38, 30167 Hanover, Germany, is preparing a manuscript to be called “Initial line-of-sight calibration for the GRACE follow-on laser ranging interferometer.”

Helmholtz Centre Potsdam – GFZ German Research Centre for Geosciences, http://isdc.gfz-potsdam.de .

National Aeronautics and Space Administration (NASA)/ Jet Propulsion Laboratory (JPL), http://podaac.jpl.nasa.gov .

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Figures (9)

Fig. 1
Fig. 1 Sketch of Laser Ranging Interferometer (LRI) on one of the two identical GRACE Follow-On spacecraft (S/C). The Triple Mirror Assembly (TMA) routes the beam around the cold gas tank and the microwave ranging system. The TMA vertex is located at the S/C center-of-mass (CM). On the LRI optical bench, LO beam and RX beam are interfered on a beam splitter (BS) and imaged on a quadrant photo diode (QPD) using a telescope. On the QPD, both integrated phase and relative beam tilt are measured using Differential Wavefront Sensing (DWS). By zeroing the DWS singals in closed-loop, the steering mirror keeps LO beam and RX beam coaligned such that the outgoing TX beam that has been retroreflected by the TMA is sent back to the distant satellite. The compensation plate (CP) cancels linear rotation-to-pathlength coupling that is caused by the beam splitter (BS).
Fig. 2
Fig. 2 Setup to verify the closed-loop beam steering method of the optical bench breadboard model (OBBM) mounted on a hexapod. The slave laser is offset phase-locked to the master laser. LO beam and RX beam are delivered to the setup via optical fibers and interfered on a beam splitter (BS). At one port of BS, the beams (solid lines) are imaged on quadrant photo diode QPD1 with telescope T1. The phases of the four QPD1 segments are recorded using a digital phasemeter. This phasemeter also calculates the Differential Wavefront Sensing (DWS) signals which can be fed back in closed-loop to the steering mirror (SM). At the second port of BS, the reflected LO beam and the transmitted RX beam (dashed lines) pass the compensation plate (CP). After leaving the OBBM, LO beam and RX beam are imaged on QPD2 using telescope T2. The DWS signals obtained from QPD2 give an out-of-loop confirmation of LO beam and RX beam coalignment during SM closed-loop operation. Furthermore, orientation changes of the TX beam (dotted line) can be inferred from two calibrated position-sensitive quadrant photo diodes QPD3 and QPD4. To investigate OBBM rotation-to-pathlength coupling, a part of the RX beam is diverted before entering the OBBM and inferfered with the TX beam (dot-dashed line) on the single-element photo diode PD-REF to obtain an interferometric reference measurement.
Fig. 3
Fig. 3 Schematic overview of the phasemeter (PM) architecture embedded within a field-programmable gate array (FPGA). Shown is the readout of frequency fi, amplitude Ii, and phase φi, i = A1, B1, C1, D1, of the four QPD1 quadrants via digital phase-locked loops (PLLs) and the generation of the DWS signal DWS1hor according to Eq. (1). The DWS signal is then passed on to an integrator which acts as servo controller of the steering mirror loop. The resulting actuator signal is fed to the steering mirror (SM) electronics via digital-to-analogue converters (DACs).
Fig. 4
Fig. 4 Numerically simulated DWS signals DWS1hor (left) for horizontal and DWS1ver (right) for vertical relative beam tilts between LO beam and RX beam on QPD1 under hexapod pitch and yaw rotations.
Fig. 5
Fig. 5 Numerically simulated heterodyne efficiency of LO beam and RX beam on the four segments of QPD1 under hexapod pitch and yaw rotations. For perfectly aligned LO beam and RX beam and the parameters of our setup, the heterodyne efficiency on each QPD1 segment reaches a maximum value of 60%.
Fig. 6
Fig. 6 DWS signals DWS1hor (left) and DWS1ver (right) measured with QPD1, while the hexapod performs calibrated pitch and yaw rotations.
Fig. 7
Fig. 7 Heterodyne efficiencies measured with the four quadrants A1, B1, C1, D1 of QPD1 while the hexapod performs calibrated pitch and yaw rotations.
Fig. 8
Fig. 8 Top: The hexapod performs rotations according to a GRACE satellite attitude jitter dataset, while the steering mirror loop is closed. Shown are hexapod commands, which are executed by the hexapod within ±6 μrad by the manufacturer’s specifications. Bottom: Coalignment of LO beam and RX beam during hexapod rotations obtained from the DWS signals DWS2hor and DWS2ver of the out-of-loop quadrant photo diode QPD2. DWS signals have been converted to relative geometric wavefront tilt angles using the DWS transfer matrix M2 from Tab. 1. Furthermore, orientation changes TXhor, TXver of the TX beam are recorded with the differential position measurement of QPD3, QPD4.
Fig. 9
Fig. 9 Linear power spectral density of coalignment of LO beam and RX beam, while the hexapod performs rotations according to Fig. 8 (top). Both DWS signals DWS2hor and DWS2ver of the out-of-loop quadrant photo diode QPD2 have been converted to relative geometric wavefront tilt angles using the DWS transfer matrix M2 from Tab. 1. Furthermore, orientation changes TXhor, TXver of the TX beam are recorded with the differential position measurement of QPD3, QPD4. For completeness, the DWS measurements DWS1hor and DWS1ver of the in-loop quadrant photo diode QPD1 are also shown, converted to corresponding relative geometric wavefront tilt angles using DWS transfer matrix M1 from Tab. 1. Yet the DWS measurement of QPD1 is inherently small due to the in-loop suppression and does not imply a corresponding beam coalignment.

Tables (1)

Tables Icon

Table 1 Measured DWS transfer matrices M1, M2 for QPD1, QPD2, respectively, which relate relative geometric wavefront tilts between LO beam and RX beam to DWS signals, cf. Eq. (2). Units are rad/rad.

Equations (5)

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DWS 1 hor = 0.5 ( φ A 1 + φ C 1 φ B 1 φ D 1 ) , DWS 1 ver = 0.5 ( φ A 1 + φ B 1 φ C 1 φ D 1 ) .
( DWS 1 hor DWS 1 ver ) = ( M 1 11 M 1 12 M 1 21 M 1 22 ) ( θ yaw θ pitch ) .
γ = c 2 4 ( P LO + P RX ) 2 P LO P RX .
M 1 11 sim = M 1 22 sim = 15 , 600 rad / rad .
γ max sim = 60 % .

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