Abstract

We report on an interferometer designed to provide 110nm/Hz displacement measurement resolution, in the range 0.01Hz to 1Hz, while in low Earth orbit. The interferometer comprises two units, each with its own laser and in separate satellites, which would be in the same orbit separated by approximately 50km. We discuss the requirements on the interferometer subsystem and describe the optical transponder distance measurement, including a phase locking method to generate a heterodyne beat signal between the two lasers. Design, fabrication, and testing of a “flightlike” engineering model interferometer is outlined, and results from environmental and performance tests are reported.

© 2008 Optical Society of America

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References

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  1. 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]
  2. I. Velicogna and J. Wahr, “Measurements of time-variable gravity show mass loss in Antarctica,” Science 311, 1754-1756 (2006).
    [CrossRef] [PubMed]
  3. Committee on Earth Science and Applications from Space: A Community Assessment and Strategy for the Future, National Research Council, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (National Academies Press, 2007).
  4. M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.
  5. S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
    [CrossRef]
  6. P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
    [CrossRef]
  7. The definition of TRL6 is: “TRL 6 System/subsystem model or prototyping demonstration in a relevant end-to-end environment (ground or space): Prototyping implementations on full-scale realistic problems. Partially integrated with existing systems. Limited documentation available. Engineering feasibility fully demonstrated in actual system application.”
  8. Commercial heterodyne metrology interferometers have been available for many years. The primary difference in this work is the use of two entirely separate lasers.
  9. B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
    [CrossRef]
  10. S. A. Webster, M. Oxborrow, and P. Gill, “Subherz-linewidth Nd:YAG laser,” Opt. Lett. 29, 1497 -1499 (2004).
    [CrossRef] [PubMed]
  11. M. Notcutt, L. S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity.” Opt. Lett. 30, 1815-1817 (2005).
    [CrossRef] [PubMed]
  12. “Final technical report (FTR) of the (phase A) study of the Laser Interferometer Space Antenna (Dornier Satellitensysteme GmbH-Matra Marconi Space-Alenia Aerospazio),” ESTEC contract 13631/99/NL/MS, Rep. LI-RP-CD-009ESTEC (April 2000).
  13. M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.
  14. J. Haisma, N. Hattu, J. T. C. M. Pulles, E. Steding, and J. C. G. Vervest, “Direct bonding and beyond,” Appl. Opt. 46, 6793-6803 (2007).
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

I. Velicogna and J. Wahr, “Measurements of time-variable gravity show mass loss in Antarctica,” Science 311, 1754-1756 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (3)

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]

S. A. Webster, M. Oxborrow, and P. Gill, “Subherz-linewidth Nd:YAG laser,” Opt. Lett. 29, 1497 -1499 (2004).
[CrossRef] [PubMed]

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

2003 (1)

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

1999 (1)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

Bender, P.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Bender, P. L.

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

Bergquist, J. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

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]

Chao, B.

M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

Folkner, B.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Folkner, W. M.

M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.

Gill, P.

Haisma, J.

Hall, J. L.

M. Notcutt, L. S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity.” Opt. Lett. 30, 1815-1817 (2005).
[CrossRef] [PubMed]

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

Hattu, N.

Hososkawa, M.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Itano, W. M.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

Kawamura, S.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Klipstein, W. M.

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

Kunimori, H.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Leitch, J.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Loomis, B.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Ma, L. S.

Nagano, S.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Nerem, R. S.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Notcutt, M.

Ohkawa, M.I

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Oxborrow, M.

Pierce, R.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Pulles, J. T. C. M.

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]

Sato, T.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Steding, E.

Stephens, M.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

Tapley, B. D.

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]

M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.

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]

Velicogna, I.

I. Velicogna and J. Wahr, “Measurements of time-variable gravity show mass loss in Antarctica,” Science 311, 1754-1756 (2006).
[CrossRef] [PubMed]

Vervest, J. C. G.

Wahr, J.

I. Velicogna and J. Wahr, “Measurements of time-variable gravity show mass loss in Antarctica,” Science 311, 1754-1756 (2006).
[CrossRef] [PubMed]

Watkins, M.

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

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]

M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.

Webster, S. A.

Ye, J.

M. Notcutt, L. S. Ma, J. Ye, and J. L. Hall, “Simple and compact 1-Hz laser system via an improved mounting configuration of a reference cavity.” Opt. Lett. 30, 1815-1817 (2005).
[CrossRef] [PubMed]

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

Yoshino, T.

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

Appl. Opt. (1)

Meas. Sci. Technol. (1)

S. Nagano, T. Yoshino, H. Kunimori, M. Hososkawa, S. Kawamura, T. Sato, and M.I Ohkawa, “Displacement measuring technique for satellite-to-satellite laser interferometer to determine Earth's gravity field,” Meas. Sci. Technol. 15, 2406-2411 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, “Visible lasers with subhertz linewidths,” Phys. Rev. Lett. 82, 3799-3711 (1999).
[CrossRef]

Science (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]

I. Velicogna and J. Wahr, “Measurements of time-variable gravity show mass loss in Antarctica,” Science 311, 1754-1756 (2006).
[CrossRef] [PubMed]

Space Sci. Rev. (1)

P. L. Bender, J. L. Hall, J. Ye, and W. M. Klipstein, “Satellite-satellite laser links for future gravity missions,” Space Sci. Rev. 108, 377-384 (2003).
[CrossRef]

Other (6)

The definition of TRL6 is: “TRL 6 System/subsystem model or prototyping demonstration in a relevant end-to-end environment (ground or space): Prototyping implementations on full-scale realistic problems. Partially integrated with existing systems. Limited documentation available. Engineering feasibility fully demonstrated in actual system application.”

Commercial heterodyne metrology interferometers have been available for many years. The primary difference in this work is the use of two entirely separate lasers.

Committee on Earth Science and Applications from Space: A Community Assessment and Strategy for the Future, National Research Council, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond (National Academies Press, 2007).

M. M. Watkins, W. M. Folkner, B. Chao, and B. D. Tapley, “EX-5: a laser interferometer mission follow-on to the GRACE mission,” presented at GGG2000, Banff, Canada, 31 July-5 August 2000.

“Final technical report (FTR) of the (phase A) study of the Laser Interferometer Space Antenna (Dornier Satellitensysteme GmbH-Matra Marconi Space-Alenia Aerospazio),” ESTEC contract 13631/99/NL/MS, Rep. LI-RP-CD-009ESTEC (April 2000).

M. Stephens, R. Pierce, J. Leitch, R. S. Nerem, P. Bender, B. Loomis, M. Watkins, and B. Folkner, “Development of an interferometric laser ranging system for a follow-on gravity mission to GRACE,” GRACE Science Team Meeting, San Francisco, California, 8-9 December 2006.

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Figures (12)

Fig. 1
Fig. 1

Schematic representation of the interferometer. M refers to “master” and S to “slave.” The interferometer is used to measure the motion between the two proof mass mirrors. See the text for a complete description.

Fig. 2
Fig. 2

Schematic of the optical phase locked loop as implemented for one channel of the quad cell of the slave laser. The first mixer on the left designates optical heterodyne detection, while the second represents demodulation of the heterodyne signal with a digital mixer using a USO reference.

Fig. 3
Fig. 3

Most prominent expected noise sources. See the text. The graph includes two root-sum-squared curves of all identified noise sources, one with current TRL laser stability, and one with improved laser stability. Laser frequency noise is the dominant noise source over the target frequency range [13].

Fig. 4
Fig. 4

Schematic of the breadboard interferometer layout. The interferometer was constructed using mainly off-the-shelf components on a commercial stainless steel honeycomb breadboard. A single photodiode on the right was used to lock the slave laser. For alignment and heterodyne sensing at the quad cell, a commercial hemispherical x y beam steerer was used.

Fig. 5
Fig. 5

Breadboard optical phase locked loop was constructed of all commercial components, apart from the Blackjack phasemeter. The OPLL used a MiniCircuits mixer referenced to a rubidium standard clock. Two lock-in amplifiers were used as simultaneous phase sensitive detectors for two of the quad cells (QCs).

Fig. 6
Fig. 6

Optics bench schematic showing major components. The bases and telescope block were fabricated from Zerodur. The remaining components, apart from the quartz quarter waveplates, were made of UV grade fused silica.

Fig. 7
Fig. 7

Photo (top) of the two optical benches in their test configuration. The drawing (bottom) shows the approximate location of a flexural pivot for tilt in the x y plane. Another flexure (on the right) was used for translation of the bench. Tilt and translation was monitored using capacitive sensors bonded directly to the Zerodur base.

Fig. 8
Fig. 8

Experiment block diagram for brassboard tests. The OPLL feedback loop is represented by the heavy line, from the slave laser (and one quadrant of the bench IRT#1), to the analog to digital converter (ADC 2), the laser lock FPGA, and back to the slave laser controller. Two channels on the master bench (IRT#2) were demodulated with the phasemeter FPGA. The digital locking, control, and demodulation electronics were supplied by JPL.

Fig. 9
Fig. 9

(Online color) Typical noise spectra comparing the IRT breadboard and brassboard. The laser frequency noise was measured independently by beating the master and slave lasers (apart from the interferometer) immediately following the measurement shown here. The capacitive sensors had a 0.2 nm digitization limit, but did confirm the fixture vibration noise (see the inset) and low frequency drift due to expansion of the fixture’s aluminum base. The limiting noise is labeled on the top for four frequency regions. Note: the short interferometer distance L in the brassboard and breadboard measurements allowed us to use a free-running (nonfrequency stabilized) master laser.

Fig. 10
Fig. 10

Bench tilt was compared using the capacitance sensors and phase recovery on adjacent quad cells on the master bench (IRT#2). Using knowledge of the lever arm h, the capacitance sensor displacements could be compared directly to the phasemeter data using Eq. (13). The direct results (no free parameters) are shown here. The worst discrepancy is about 1 microradian.

Fig. 11
Fig. 11

Representative measurement showing the interferometer phase shift as a result of direct heating near the primary lens of one of the benches. The amount of heat delivered was 145 J in a 20 second duration, far more than would occur with direct solar illumination. The phase shift was about 1 nm / J absorbed.

Fig. 12
Fig. 12

Survival thermal cycle on IRT #2 bench performed prior to vibration.

Tables (2)

Tables Icon

Table 1 Residual Noise Sources for 50 km Satellite Separation a

Tables Icon

Table 2 Typical Vibration Range for the IRT#2 Bench for Each of Three Orthogonal Axes

Equations (14)

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Laser   M :     ω M ( t ) t + ϕ M ( t ) , Laser   S :     ω S ( t ) t + ϕ S ( t ) ,
Master Clock :     Ω M C t + ϕ M C ( t ) , Slave Clock :     Ω S C t + ϕ S C ( t ) .
Φ ( t ) = path k ( z , t ) d z ω ( t ) t = path k ( z , t ) u ( t ) d t ω ( t ) t ,
M S ( L d M + d S ) ( 1 + u / c ) , S M ( L + d M d S ) ( 1 + u / c ) ,
ω S ( t ) = ω M ( t τ ) [ 1 u ( t ) / c ] + Ω S C ,
ϕ S ( t ) = 0 τ ( t ) k M ( z , t ) u ( t ) d t + ϕ M ( t τ ) ϕ S C ( t ) + ϕ OPLL ( t ) ,
Ω D ( t ) = [ ω M ( t 2 τ ) ω M ( t ) ] [ Ω S C Ω M C ] 2 ω M ( t 2 τ ) u ( t ) / c , Φ D ( t ) = 0 2 τ ( t ) k M ( z , t ) u ( t ) d t + [ ϕ M ( t 2 τ ) ϕ M ( t ) ] [ ϕ S C ( t τ ) ϕ M C ( t ) ] + ϕ OPLL ( t ) .
Ω D , ideal ( t ) = 2 ω M u ( t ) / c , Φ D . ideal ( t ) = ( ω M / c ) 0 2 τ ( t ) u ( t ) d t ,
ν L F N ( f ) < ν L ( f ) / L .
L L F N ( f ) = L ν L F N ( f ) ν = L × { 9 × 10 6 1 + 1 / f 10 4 f 0.008 Hz f > 0.008 Hz ( nm / Hz ) ,
L G R S ( f ) = 2 2 × 10 4 1 + 0.005 / f / ( 2 π f ) 2 ( nm / Hz ) ,
Δ k = 2 π λ sin ( M θ ) ,
θ 3 π λ 8 M R Δ Φ .
L ( f ) = ν ( f ) L λ c 2 ( nm / Hz ) ,

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