Abstract

We describe a method of coinciding the optical center with the center of gravity in an optical element with a corner cube prism. It uses a Michelson interferometer and a rotating table for detection of the discrepancy between the optical center and the center of gravity. Consisting of two procedures: to coincide the optical center with the axis of rotation and to coincide the center of gravity with the axis, this method can adjust the center of gravity close to the axis within 50 μm and the optical center within 1 μm.

© 1988 Optical Society of America

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References

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  1. G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
    [CrossRef]
  2. I. Murata, “A Transportable Apparatus for Absolute Measurement of Gravity,” Bull. Earthquake Res. Inst. 53, 49 (1978).
  3. H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).
  4. M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
    [CrossRef]
  5. G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
    [CrossRef]
  6. A. Sakuma, “Gravitational Acceleration, Mass, and Electrical Quantities,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, Eds., Natl. Bur. Stand. U.S., Spec. Publ. 617, 397 (1984).
  7. H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
    [CrossRef]
  8. E. R. Peck, “Theory of the Corner-Cube Interferometer,” J. Opt. Soc. Am. 38, 1015 (1948).
    [CrossRef] [PubMed]

1987 (1)

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

1983 (1)

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

1982 (1)

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
[CrossRef]

1978 (2)

I. Murata, “A Transportable Apparatus for Absolute Measurement of Gravity,” Bull. Earthquake Res. Inst. 53, 49 (1978).

H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).

1973 (1)

G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
[CrossRef]

1948 (1)

Arnautov, G. P.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Bell, G. A.

G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
[CrossRef]

Boulanger, Yu. D.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Faller, J. E.

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
[CrossRef]

Gibbings, D. L. H.

G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
[CrossRef]

Hanada, H.

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).

Kalish, E. N.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Koronkevitch, V. P.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Murata, I.

H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).

I. Murata, “A Transportable Apparatus for Absolute Measurement of Gravity,” Bull. Earthquake Res. Inst. 53, 49 (1978).

Patterson, J. B.

G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
[CrossRef]

Peck, E. R.

Rinker, R. L.

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
[CrossRef]

Sakuma, A.

A. Sakuma, “Gravitational Acceleration, Mass, and Electrical Quantities,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, Eds., Natl. Bur. Stand. U.S., Spec. Publ. 617, 397 (1984).

Stus, Yu. F.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Takano, S.

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

Tarasyuk, V. G.

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Tsubokawa, T.

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

Tsuruta, S.

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

Yanagisawa, M.

H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).

Zumberge, M. A.

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
[CrossRef]

Bull. Earthquake Res. Inst. (1)

I. Murata, “A Transportable Apparatus for Absolute Measurement of Gravity,” Bull. Earthquake Res. Inst. 53, 49 (1978).

J. Geod. Soc. Jpn. (1)

H. Hanada, M. Yanagisawa, I. Murata, “An Experiment on Non-Rotating Free Fall Method for the Absolute Gravimetry,” J. Geod. Soc. Jpn. 24, 191 (1978).

J. Opt. Soc. Am. (1)

Metrologia (3)

G. A. Bell, D. L. H. Gibbings, J. B. Patterson, “An Absolute Determination of the Gravitational Accelerationat Sydney, Australia,” Metrologia 9, 47 (1973).
[CrossRef]

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A Portable Apparatus for Absolute Measurements of the Earth’s Gravity,” Metrologia 18, 145 (1982).
[CrossRef]

G. P. Arnautov, Yu. D. Boulanger, E. N. Kalish, V. P. Koronkevitch, Yu. F. Stus, V. G. Tarasyuk, “Gabl, an Absolute Free-Fall Laser Gravimeter,” Metrologia 19, 49 (1983).
[CrossRef]

Rev. Sci. Instrum. (1)

H. Hanada, T. Tsubokawa, S. Takano, S. Tsuruta, “New Design of Absolute Gravimeter for Continuous Observations,” Rev. Sci. Instrum. 58, 669 (1987).
[CrossRef]

Other (1)

A. Sakuma, “Gravitational Acceleration, Mass, and Electrical Quantities,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, Eds., Natl. Bur. Stand. U.S., Spec. Publ. 617, 397 (1984).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the device for coinciding the optical center with the center of gravity: 1, laser; 2, corner cube prism; 3, beam splitter; 4, photodetector; 5, optical element with a corner cube prism; 6, horizontally adjustable table; 7, rotating table.

Fig. 2
Fig. 2

Optical element on the rotating table.

Fig. 3
Fig. 3

Relationship between the centrifugal force and the distance of the center of gravity from the axis of rotation using the revolution rate of the rotating table as a parameter.

Fig. 4
Fig. 4

Examples of the interference fringes produced during one revolution of the table: upper, the optical center is sufficiently close to the axis of rotation; lower, the optical center is more than 0.3 mm away from the axis.

Fig. 5
Fig. 5

Geometry of the corner cube prism; G is the center of gravity.

Fig. 6
Fig. 6

Relationship between the change of the optical path length for a range of 10° and the distance of the optical center from the axis of rotation. The thickness of the corner cube prism is assumed to be 20 mm.

Fig. 7
Fig. 7

Relationship between the angular velocity of the optical element and the distance of the optical center from the center of gravity, which meets the absolute gravity measurements of 10−9 accuracy.

Equations (4)

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F c = m d ω 2 ,
F f = m g λ ,
λ < d ω 2 / g .
δ = 2 l + 2 ( d - h ) cos α - 2 d sec γ cos ( α - γ ) + 2 μ d sec γ = 2 l + 2 μ d cos γ - 2 h cos α = 2 l + 2 μ d 1 - sin 2 α / μ 2 - 2 h cos α ,

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