Abstract

The Mark III interferometer is a phase-coherent stellar interferometer designed for astrometry. Operating through the turbulent atmosphere, the instrument is also a sensitive detector of atmospheric phase fluctuations. The effect of phase fluctuations on astrometric accuracy is reviewed, and phase measurements obtained with the instrument at Mt. Wilson using a 12-m base line are presented. These measurements agree well with the predictions of a simple Kolmogorov spatial spectrum over the frequency range of 0.001–100 Hz. From these measurements, the outer scale of turbulence for propagation through the entire atmosphere is estimated to be >2 km. The standard deviation for an absolute astrometric measurement estimated from these measurements is ∼0.14T−1/6 sec of arc for long integration times for conditions of 0.5-sec of arc seeing. For star-switched relative measurements, this error should decrease as the square root of the number of switching cycles.

© 1987 Optical Society of America

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References

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  1. M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
    [Crossref]
  2. M. Shao et al., “The Mark III Stellar Interferometer,” submitted to Astron. Astrophys. (1987).
  3. M. M. Colavita, M. Shao, D. H. Staelin, “The Two-Color Method for Optical Astrometry: Theory and Preliminary Measurements with the Mark III Stellar Interferometer,” Appl. Opt.26, in press (1987), this issue.
    [Crossref] [PubMed]
  4. D. L. Fried, “Statistics of a Geometric Representation of Wave-front Distortion,” J. Opt. Soc. Am. 55, 1427 (1965).
    [Crossref]
  5. W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 239 (1980).
    [Crossref]
  6. D. P. Greenwood, D. L. Fried, “Power Spectra Requirements for Wave-Front-Compensative Systems,” J. Opt. Soc. Am. 66, 193 (1976).
    [Crossref]
  7. A. Ishimaru, Wave Propagation and Scattering in a Random Media, Vol. 2 (Academic, New York, 1978).
  8. M. M. Colavita, “Atmospheric Limitations of a Two-Color Astrometric Interferometer,” Ph.D. Thesis, MIT, Cambridge, MA (1985).
  9. R. S. Lawrence, J. W. Strohbehn, “A Survey of Clear-Air Propagation Effects Relevant to Optical Communications,” Proc. IEEE 58, 1523 (1970).
    [Crossref]
  10. L. Lindegren, “Atmospheric Limitations of Narrow-Field Optical Astrometry,” Astron. Astrophys. 89, 41 (1980).
  11. R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE. 63, 1669 (1975).
    [Crossref]
  12. G. W. Reinhardt, S. A. Collins, “Outer-Scale Effects in Turbulence-Degraded Light-Beam Spectra,” J. Opt. Soc. Am. 62, 1526 (1972).
    [Crossref]
  13. D. P. Greenwood, D. O. Tarazano, “A Proposed Form for the Atmospheric Microtemperature Spatial Spectrum in the Input Range,” RADC Tech. Rep. RADG-TR-74-19 (1974).
  14. C. S. Gardner, “Effects of Random Path Fluctuations on the Accuracy of Laser Ranging Systems,” Appl. Opt. 15, 2539 (1976).
    [Crossref] [PubMed]
  15. A. F. Dravskikh, A. M. Finkelstein, “Tropospheric Limitations in Phase and Frequency Coordinate Measurements in Astronomy,” Astrophys. Space Sci. 60, 251 (1979).
    [Crossref]
  16. J. W. Armstrong, R. A. Sramek, “Observations of Tropospheric Phase Scintillations at 5 GHz on Vertical Paths,” Radio Sci. 17, 1579 (1982).
    [Crossref]
  17. D. Mozurkewich et al., “Preliminary Measurements of Star Positions with the Mark III Stellar Interferometer,” submitted to Astron. J. (1987).
  18. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, M. H. Ackley, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
    [Crossref]
  19. H. Matsumoto, K. Tsukahara, “Effects of the Atmospheric Phase Fluctuation on Long-Distance Measurement,” Appl. Opt. 23, 3388 (1984).
    [Crossref] [PubMed]

1987 (1)

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

1984 (1)

1982 (1)

J. W. Armstrong, R. A. Sramek, “Observations of Tropospheric Phase Scintillations at 5 GHz on Vertical Paths,” Radio Sci. 17, 1579 (1982).
[Crossref]

1980 (2)

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 239 (1980).
[Crossref]

L. Lindegren, “Atmospheric Limitations of Narrow-Field Optical Astrometry,” Astron. Astrophys. 89, 41 (1980).

1979 (1)

A. F. Dravskikh, A. M. Finkelstein, “Tropospheric Limitations in Phase and Frequency Coordinate Measurements in Astronomy,” Astrophys. Space Sci. 60, 251 (1979).
[Crossref]

1976 (2)

1975 (1)

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE. 63, 1669 (1975).
[Crossref]

1972 (1)

1971 (1)

1970 (1)

R. S. Lawrence, J. W. Strohbehn, “A Survey of Clear-Air Propagation Effects Relevant to Optical Communications,” Proc. IEEE 58, 1523 (1970).
[Crossref]

1965 (1)

Ackley, M. H.

Armstrong, J. W.

J. W. Armstrong, R. A. Sramek, “Observations of Tropospheric Phase Scintillations at 5 GHz on Vertical Paths,” Radio Sci. 17, 1579 (1982).
[Crossref]

Bouricius, G. M. B.

Clifford, S. F.

Colavita, M. M.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

M. M. Colavita, M. Shao, D. H. Staelin, “The Two-Color Method for Optical Astrometry: Theory and Preliminary Measurements with the Mark III Stellar Interferometer,” Appl. Opt.26, in press (1987), this issue.
[Crossref] [PubMed]

M. M. Colavita, “Atmospheric Limitations of a Two-Color Astrometric Interferometer,” Ph.D. Thesis, MIT, Cambridge, MA (1985).

Collins, S. A.

Dravskikh, A. F.

A. F. Dravskikh, A. M. Finkelstein, “Tropospheric Limitations in Phase and Frequency Coordinate Measurements in Astronomy,” Astrophys. Space Sci. 60, 251 (1979).
[Crossref]

Fante, R. L.

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE. 63, 1669 (1975).
[Crossref]

Finkelstein, A. M.

A. F. Dravskikh, A. M. Finkelstein, “Tropospheric Limitations in Phase and Frequency Coordinate Measurements in Astronomy,” Astrophys. Space Sci. 60, 251 (1979).
[Crossref]

Fried, D. L.

Gardner, C. S.

Greenwood, D. P.

D. P. Greenwood, D. L. Fried, “Power Spectra Requirements for Wave-Front-Compensative Systems,” J. Opt. Soc. Am. 66, 193 (1976).
[Crossref]

D. P. Greenwood, D. O. Tarazano, “A Proposed Form for the Atmospheric Microtemperature Spatial Spectrum in the Input Range,” RADC Tech. Rep. RADG-TR-74-19 (1974).

Hershey, J. L.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

Hughes, J. A.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in a Random Media, Vol. 2 (Academic, New York, 1978).

Johnston, K. J.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

Lawrence, R. S.

R. S. Lawrence, J. W. Strohbehn, “A Survey of Clear-Air Propagation Effects Relevant to Optical Communications,” Proc. IEEE 58, 1523 (1970).
[Crossref]

Lindegren, L.

L. Lindegren, “Atmospheric Limitations of Narrow-Field Optical Astrometry,” Astron. Astrophys. 89, 41 (1980).

Matsumoto, H.

Mozurkewich, D.

D. Mozurkewich et al., “Preliminary Measurements of Star Positions with the Mark III Stellar Interferometer,” submitted to Astron. J. (1987).

Ochs, G. R.

Reinhardt, G. W.

Shao, M.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

M. Shao et al., “The Mark III Stellar Interferometer,” submitted to Astron. Astrophys. (1987).

M. M. Colavita, M. Shao, D. H. Staelin, “The Two-Color Method for Optical Astrometry: Theory and Preliminary Measurements with the Mark III Stellar Interferometer,” Appl. Opt.26, in press (1987), this issue.
[Crossref] [PubMed]

Simon, R. S.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

Sramek, R. A.

J. W. Armstrong, R. A. Sramek, “Observations of Tropospheric Phase Scintillations at 5 GHz on Vertical Paths,” Radio Sci. 17, 1579 (1982).
[Crossref]

Staelin, D. H.

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

M. M. Colavita, M. Shao, D. H. Staelin, “The Two-Color Method for Optical Astrometry: Theory and Preliminary Measurements with the Mark III Stellar Interferometer,” Appl. Opt.26, in press (1987), this issue.
[Crossref] [PubMed]

Strohbehn, J. W.

R. S. Lawrence, J. W. Strohbehn, “A Survey of Clear-Air Propagation Effects Relevant to Optical Communications,” Proc. IEEE 58, 1523 (1970).
[Crossref]

Tango, W. J.

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 239 (1980).
[Crossref]

Tarazano, D. O.

D. P. Greenwood, D. O. Tarazano, “A Proposed Form for the Atmospheric Microtemperature Spatial Spectrum in the Input Range,” RADC Tech. Rep. RADG-TR-74-19 (1974).

Tsukahara, K.

Twiss, R. Q.

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 239 (1980).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (1)

L. Lindegren, “Atmospheric Limitations of Narrow-Field Optical Astrometry,” Astron. Astrophys. 89, 41 (1980).

Astron. J. (1)

M. Shao, M. M. Colavita, D. H. Staelin, K. J. Johnston, R. S. Simon, J. A. Hughes, J. L. Hershey, “The Application of Interferometry to Optical Astrometry,” Astron. J. 93, 1280 (1987).
[Crossref]

Astrophys. Space Sci. (1)

A. F. Dravskikh, A. M. Finkelstein, “Tropospheric Limitations in Phase and Frequency Coordinate Measurements in Astronomy,” Astrophys. Space Sci. 60, 251 (1979).
[Crossref]

J. Opt. Soc. Am. (4)

Proc. IEEE (2)

R. L. Fante, “Electromagnetic Beam Propagation in Turbulent Media,” Proc. IEEE. 63, 1669 (1975).
[Crossref]

R. S. Lawrence, J. W. Strohbehn, “A Survey of Clear-Air Propagation Effects Relevant to Optical Communications,” Proc. IEEE 58, 1523 (1970).
[Crossref]

Prog. Opt. (1)

W. J. Tango, R. Q. Twiss, “Michelson Stellar Interferometry,” Prog. Opt. 17, 239 (1980).
[Crossref]

Radio Sci. (1)

J. W. Armstrong, R. A. Sramek, “Observations of Tropospheric Phase Scintillations at 5 GHz on Vertical Paths,” Radio Sci. 17, 1579 (1982).
[Crossref]

Other (6)

D. Mozurkewich et al., “Preliminary Measurements of Star Positions with the Mark III Stellar Interferometer,” submitted to Astron. J. (1987).

D. P. Greenwood, D. O. Tarazano, “A Proposed Form for the Atmospheric Microtemperature Spatial Spectrum in the Input Range,” RADC Tech. Rep. RADG-TR-74-19 (1974).

M. Shao et al., “The Mark III Stellar Interferometer,” submitted to Astron. Astrophys. (1987).

M. M. Colavita, M. Shao, D. H. Staelin, “The Two-Color Method for Optical Astrometry: Theory and Preliminary Measurements with the Mark III Stellar Interferometer,” Appl. Opt.26, in press (1987), this issue.
[Crossref] [PubMed]

A. Ishimaru, Wave Propagation and Scattering in a Random Media, Vol. 2 (Academic, New York, 1978).

M. M. Colavita, “Atmospheric Limitations of a Two-Color Astrometric Interferometer,” Ph.D. Thesis, MIT, Cambridge, MA (1985).

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Figures (8)

Fig. 1
Fig. 1

Site of the Mark III stellar interferometer at Mt. Wilson.

Fig. 2
Fig. 2

Approximately to-scale schematic diagram of the Mark III stellar interferometer.

Fig. 3
Fig. 3

Fringe position for α Aql, 6 Nov. 1986.

Fig. 4
Fig. 4

Fringe servo error for α Aql, 6 Nov. 1986.

Fig. 5
Fig. 5

Power spectra of fringe position and servo error for α Aql, 6 Nov. 1986.

Fig. 6
Fig. 6

Power spectrum of fringe position for β Cas, 25 Nov. 1986.

Fig. 7
Fig. 7

Power spectrum of fringe position for β Gem, 30 Nov. 1986.

Fig. 8
Fig. 8

Composite power spectrum of fringe position obtained with the Mark II interferometer, Aug. and Sept. 1983.

Equations (16)

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r 0 = 1.68 [ k 2 0 dh C n 2 ( h ) ] 3 / 5 ,
T 0 = 1.36 [ k 2 0 dh C n 2 ( h ) V 5 / 3 ( h ) ] 3 / 5 = 0.81 ( r 0 / V ) , V ( h ) = V ,
W α ( f ) = 16 π 2 B 2 0 dh V 1 0 du × Φ ( [ u 2 + ( ω / V ) 2 ] 1 / 2 ) g ( u , ω ) ,
W α ( f ) = 0.0654 B 2 0 dh C n 2 V 5 / 3 [ 1 cos ( 2 π f B / V ) ] f 8 / 3 ,
W α ( f ) = 5 4 1.29 0 dh C n 2 V 1 / 3 f 2 / 3 , f 0.20 V / B ,
W α ( f ) = 0.0654 B 2 0 dh C n 2 V 5 / 3 f 8 / 3 , f 0.20 V / B .
σ α 2 = 0 df W α ( f ) sinc 2 ( π f T ) ,
σ α 2 = 5 4 2.92 ( 0 dh C n 2 V 1 / 3 ) T 1 / 3 , T B / V .
σ α 0.25 T 1 / 6 sec of arc , T B / V .
W α ( f ) = 1.29 0 dh C n 2 V 1 / 3 f 2 / 3 × [ 1 + ( V / 2 π f L 0 ) 2 ] 4 / 3 , f 0.23 V / B .
W α ( f ) = 6.6 0 dh C n 2 V 1 × [ L 0 2 + ( 2 π f / V ) 2 ] 1 / 3 , f 0.18 V / B ; B L 0
W α ( f ) = 6.6 0 dh C n 2 V 1 ( 4 3 ) B 2 × [ L 0 2 + ( 2 π f / V ) 2 ] 4 / 3 ; B L 0 .
W α ( f ) = 3.3 0 dh C n 2 V 1 L 0 2 / 3 , f V / 2 π L 0 ; B L 0 ,
W α ( f ) = 3.3 0 dh C n 2 V 1 ( 4 3 ) ( L 0 / B ) 2 L 0 2 / 3 , f V / 2 π L 0 ; B L 0 .
x ( t ) = L ( t ) + ϕ ( t ) / k ,
σ x 2 = 6.88 k 2 ( B / r 0 ) 5 / 3 .

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