Abstract

High resolution interferometry of the solar disk and measurements of the solar angular diameter are presented utilizing a small aperture lensless interferometer based on the Talbot self-imaging effect.

© 1990 Optical Society of America

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References

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  1. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).
  2. J. M. Cowley, A. F. Moodie, “Fourier Images IV: The Phase Grating,” Proc. Phys. Soc. 76, 378–384 (1960).
    [CrossRef]
  3. D. E. Silva, Appl. Opt. 10, “A Simple Interferometric Method of Beam Collimation,” 1980–1982 (1971).
    [CrossRef]
  4. J. M. Cowley, Diffraction Physics (North-Holland, New York, 1984).
  5. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  6. E. J. Seykora, “A Spatial Coherence Interferometer Utilizing a Grating and Its Possible Use for Solar Limb Investigations,” Bull. Am. Astron. Soc. 18, No. 2, 703 (1986).
  7. H. A. Hill, R. T. Stebbins, “The Intrinsic Visual Oblateness of the Sun,” Astrophys. J. 200, 471–483 (1975)
    [CrossRef]
  8. H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
    [CrossRef]
  9. The Astronomical Almanac for the Year 1989 (U.S. GPO, Washington, DC, 1988).

1987 (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1986 (1)

E. J. Seykora, “A Spatial Coherence Interferometer Utilizing a Grating and Its Possible Use for Solar Limb Investigations,” Bull. Am. Astron. Soc. 18, No. 2, 703 (1986).

1975 (2)

H. A. Hill, R. T. Stebbins, “The Intrinsic Visual Oblateness of the Sun,” Astrophys. J. 200, 471–483 (1975)
[CrossRef]

H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
[CrossRef]

1971 (1)

1960 (1)

J. M. Cowley, A. F. Moodie, “Fourier Images IV: The Phase Grating,” Proc. Phys. Soc. 76, 378–384 (1960).
[CrossRef]

1836 (1)

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Cowley, J. M.

J. M. Cowley, A. F. Moodie, “Fourier Images IV: The Phase Grating,” Proc. Phys. Soc. 76, 378–384 (1960).
[CrossRef]

J. M. Cowley, Diffraction Physics (North-Holland, New York, 1984).

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Hill, H. A.

H. A. Hill, R. T. Stebbins, “The Intrinsic Visual Oblateness of the Sun,” Astrophys. J. 200, 471–483 (1975)
[CrossRef]

H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Moodie, A. F.

J. M. Cowley, A. F. Moodie, “Fourier Images IV: The Phase Grating,” Proc. Phys. Soc. 76, 378–384 (1960).
[CrossRef]

Oleson, R. J.

H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
[CrossRef]

Seykora, E. J.

E. J. Seykora, “A Spatial Coherence Interferometer Utilizing a Grating and Its Possible Use for Solar Limb Investigations,” Bull. Am. Astron. Soc. 18, No. 2, 703 (1986).

Silva, D. E.

Stebbins, R. T.

H. A. Hill, R. T. Stebbins, “The Intrinsic Visual Oblateness of the Sun,” Astrophys. J. 200, 471–483 (1975)
[CrossRef]

H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
[CrossRef]

Talbot, F.

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Appl. Opt. (1)

Astrophys. J (1)

H. A. Hill, R. T. Stebbins, R. J. Oleson, “The Finite Fourier Transform Definition of an Edge on the Solar Disk,” Astrophys. J 200, 484–498 (1975).
[CrossRef]

Astrophys. J. (1)

H. A. Hill, R. T. Stebbins, “The Intrinsic Visual Oblateness of the Sun,” Astrophys. J. 200, 471–483 (1975)
[CrossRef]

Bull. Am. Astron. Soc. (1)

E. J. Seykora, “A Spatial Coherence Interferometer Utilizing a Grating and Its Possible Use for Solar Limb Investigations,” Bull. Am. Astron. Soc. 18, No. 2, 703 (1986).

Philos. Mag. (1)

F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proc. Phys. Soc. (1)

J. M. Cowley, A. F. Moodie, “Fourier Images IV: The Phase Grating,” Proc. Phys. Soc. 76, 378–384 (1960).
[CrossRef]

Other (2)

The Astronomical Almanac for the Year 1989 (U.S. GPO, Washington, DC, 1988).

J. M. Cowley, Diffraction Physics (North-Holland, New York, 1984).

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Figures (3)

Fig. 1
Fig. 1

Optical and electronic configuration used to measure the visibility of the Talbot self-image as a function of rn, the distance between rulings G1 and G2. The light of wavelength λ illuminated ruling G1, which was vibrated at 80 Hz by speaker drive S. The visibility of self-images of ruling G1 at field stop F and ruling G2 were detected at detector D using a phase-locked amplifier system which operated coherently with the speaker drive frequency. Output ADC 1 is proportional to Io, the illumination intensity, whereas ADC 2 and ADC 3 are proportional to the sin and cos components of ΔI, the self-image visibility.

Fig. 2
Fig. 2

Normalized intensity or visibility of the Talbot self-images as a function of interferometer order n for a He–Ne laser beam. Each plot is in multiples of d2/λ = 1.13 cm. The upper plot was recorded using a well collimated beam, whereas the lower was uncollimated, representing the beam’s divergence.

Fig. 3
Fig. 3

Lock-in amplifier outputs with the interferometer at the r5 = 5.95-cm position while tracking and not tracking the sun. Tracking was stopped at T = 25 s. Each oscillation period in the nontracking region represents a solar angular displacement of 293 arcsec.

Equations (6)

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r n = n d 2 / λ ,
r max = D d / 2 λ ,
V = 2 | J 1 ( π n d θ λ ) ( π n d θ λ ) | ,
V = 2 ( I max - I max ) I max + I max = Δ I I o
θ = 3.83 λ π n d 1 m rad .
V 1 V 2 = Δ I 1 Δ I 2 = n 2 n 1 | J 1 ( π n 1 d θ λ ) J 1 ( π n 2 d θ λ ) | ,

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