Abstract

A corner-cube retroreflector has the property that the optical path length for a reflected laser beam is insensitive to rotations about a mathematical point called its optical center (OC). This property is exploited in ballistic absolute gravity meters in which a proof mass containing a corner-cube retroreflector is dropped in a vacuum, and its position is accurately determined with a laser interferometer. In order to avoid vertical position errors when the proof mass rotates during free fall, it is important to collocate its center of mass (COM) with the OC of the retroreflector. This is commonly done using a mechanical scale-based balancing procedure, which has limited accuracy due to the difficulty in finding the exact position of the COM and the OC. This paper describes a novel way to achieve the collocation by incorporating the proof mass into a pendulum and using a quadrature interferometer to interrogate its apparent translation in its twist mode. The mismatch between the COM and OC generates a signal in a quiet part of the spectrum where no mechanical resonance exists. This allows us to tune the position of the COM relative to the OC to an accuracy of about 1 μm in all three axes. This provides a way to directly demonstrate that a rotation of the proof mass by several degrees causes an apparent translation in the direction of the laser beam of less than 1 nm. This technique allows an order of magnitude improvement over traditional methods of balancing.

© 2015 Optical Society of America

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References

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  1. T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
    [Crossref]
  2. C. H. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
    [Crossref]
  3. E. R. Peck, “Theory of the corner-cube interferometer,” J. Opt. Soc. Am. 38, 1015–1024 (1948).
    [Crossref]
  4. H. Hanada, “Coinciding the OC with the center of gravity in a corner cube prism: a method,” Appl. Opt. 27, 3530–3533 (1988).
    [Crossref]
  5. A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
    [Crossref]
  6. C. Rothleitner, “Ultra-high precision, absolute, Earth gravity measurements,” Thesis (University Erlangen-Nuremberg, 2008).
  7. A. Vitouchkine and J. Faller, “A direct and sensitive method for positioning the centre of mass of a dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters,” Metrologia 41, L19–L21 (2004).
    [Crossref]
  8. F. Gray, “Pulse code communication,” U.S. patent2,632,058 (17March1953).

2010 (1)

C. H. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[Crossref]

2004 (1)

A. Vitouchkine and J. Faller, “A direct and sensitive method for positioning the centre of mass of a dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters,” Metrologia 41, L19–L21 (2004).
[Crossref]

2002 (1)

A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
[Crossref]

1995 (1)

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

1988 (1)

1948 (1)

Desogus, S.

A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
[Crossref]

Faller, J.

A. Vitouchkine and J. Faller, “A direct and sensitive method for positioning the centre of mass of a dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters,” Metrologia 41, L19–L21 (2004).
[Crossref]

Faller, J. E.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Francis, O.

C. H. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[Crossref]

Germak, A.

A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
[Crossref]

Gray, F.

F. Gray, “Pulse code communication,” U.S. patent2,632,058 (17March1953).

Hanada, H.

Hilt, R.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Klopping, F.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Niebauer, T. M.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Origlia, C.

A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
[Crossref]

Peck, E. R.

Rothleitner, C.

C. Rothleitner, “Ultra-high precision, absolute, Earth gravity measurements,” Thesis (University Erlangen-Nuremberg, 2008).

Rothleitner, C. H.

C. H. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[Crossref]

Sasagawa, G. S.

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

Vitouchkine, A.

A. Vitouchkine and J. Faller, “A direct and sensitive method for positioning the centre of mass of a dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters,” Metrologia 41, L19–L21 (2004).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Metrologia (4)

A. Vitouchkine and J. Faller, “A direct and sensitive method for positioning the centre of mass of a dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters,” Metrologia 41, L19–L21 (2004).
[Crossref]

A. Germak, S. Desogus, and C. Origlia, “Interferometer for the IMGC rise-and-fall absolute gravimeter,” Metrologia 39, 471–475 (2002).
[Crossref]

T. M. Niebauer, G. S. Sasagawa, J. E. Faller, R. Hilt, and F. Klopping, “A new generation of absolute gravimeters,” Metrologia 32, 159–180 (1995).
[Crossref]

C. H. Rothleitner and O. Francis, “On the influence of the rotation of a corner cube reflector in absolute gravimetry,” Metrologia 47, 567–574 (2010).
[Crossref]

Other (2)

C. Rothleitner, “Ultra-high precision, absolute, Earth gravity measurements,” Thesis (University Erlangen-Nuremberg, 2008).

F. Gray, “Pulse code communication,” U.S. patent2,632,058 (17March1953).

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Figures (6)

Fig. 1.
Fig. 1. Simple ballistic gravity interferometer.
Fig. 2.
Fig. 2. Two cases for offset between OC and COM of the pendulum proof mass.
Fig. 3.
Fig. 3. Proof mass pendulum setup.
Fig. 4.
Fig. 4. Quadrature interferometer: beam path diagram.
Fig. 5.
Fig. 5. Quadrature interferometer signals.
Fig. 6.
Fig. 6. Spectrum of pendulum motion (20 min record).

Equations (3)

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d z δ x θ + δ z ( 1 1 2 θ 2 ) .
θ ( t ) = θ 0 e t τ sin ( w t ) ,
d z δ z 1 4 δ z θ 0 2 e 2 t τ + δ x θ 0 e t τ sin ( ω t ) + 1 4 δ z θ 0 2 e 2 t τ cos ( 2 ω t ) .

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