Abstract

An achromatic two-grating interferometer is used for imaging through inhomogeneities. Theoretical and experimental results for a two-point object are presented.

© 1992 Optical Society of America

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References

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  1. A. Labeyrie, “High resolution techniques in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, pp. 48–87.
  2. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  3. D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
    [CrossRef]
  4. R. Hanbury Brown, R. Q. Twiss, “Interferometry of the intensity fluctuations in light III. Application to astronomy,” Proc. R. Soc. London Ser. A 248, 199–221 (1958).
    [CrossRef]
  5. W. S. Finsen, “Interferometer observation of binary stars,” Astron. J. 69, 319–324 (1964).
    [CrossRef]
  6. A. A. Michelson, F. G. Pease, “Measurement of the diameter of α orionis with the interferometer,” Astrophys. J. 53, 249–256 (1922).
    [CrossRef]
  7. D. H. Rogstad, “Technique for measuring visibility phase with an optical interferometer in the presence of atmospheric seeing,” Appl. Opt. 7, 585–588 (1968).
    [CrossRef] [PubMed]
  8. W. T. Rhodes, J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,” J. Opt. Soc. Am. 63, 647–657 (1973).
    [CrossRef]
  9. E. N. Leith, Hsuan Chen, Y. S. Cheng, “Diffraction-limited imaging through a phase-distorting medium,” Opt. Lett. 6, 4–6 (1981).
    [CrossRef] [PubMed]
  10. D. W. Cutter, A. Lohmann, “Achromatic stellar interferometry,” Opt. Commun. 12, 220–222 (1974).
    [CrossRef]

1981

1974

D. W. Cutter, A. Lohmann, “Achromatic stellar interferometry,” Opt. Commun. 12, 220–222 (1974).
[CrossRef]

D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
[CrossRef]

1973

1970

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1968

1964

W. S. Finsen, “Interferometer observation of binary stars,” Astron. J. 69, 319–324 (1964).
[CrossRef]

1958

R. Hanbury Brown, R. Q. Twiss, “Interferometry of the intensity fluctuations in light III. Application to astronomy,” Proc. R. Soc. London Ser. A 248, 199–221 (1958).
[CrossRef]

1922

A. A. Michelson, F. G. Pease, “Measurement of the diameter of α orionis with the interferometer,” Astrophys. J. 53, 249–256 (1922).
[CrossRef]

Chen, Hsuan

Cheng, Y. S.

Currie, D. G.

D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
[CrossRef]

Cutter, D. W.

D. W. Cutter, A. Lohmann, “Achromatic stellar interferometry,” Opt. Commun. 12, 220–222 (1974).
[CrossRef]

Finsen, W. S.

W. S. Finsen, “Interferometer observation of binary stars,” Astron. J. 69, 319–324 (1964).
[CrossRef]

Goodman, J. W.

Hanbury Brown, R.

R. Hanbury Brown, R. Q. Twiss, “Interferometry of the intensity fluctuations in light III. Application to astronomy,” Proc. R. Soc. London Ser. A 248, 199–221 (1958).
[CrossRef]

Knapp, S. L.

D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
[CrossRef]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

A. Labeyrie, “High resolution techniques in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, pp. 48–87.

Leith, E. N.

Liewer, K. M.

D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
[CrossRef]

Lohmann, A.

D. W. Cutter, A. Lohmann, “Achromatic stellar interferometry,” Opt. Commun. 12, 220–222 (1974).
[CrossRef]

Michelson, A. A.

A. A. Michelson, F. G. Pease, “Measurement of the diameter of α orionis with the interferometer,” Astrophys. J. 53, 249–256 (1922).
[CrossRef]

Pease, F. G.

A. A. Michelson, F. G. Pease, “Measurement of the diameter of α orionis with the interferometer,” Astrophys. J. 53, 249–256 (1922).
[CrossRef]

Rhodes, W. T.

Rogstad, D. H.

Twiss, R. Q.

R. Hanbury Brown, R. Q. Twiss, “Interferometry of the intensity fluctuations in light III. Application to astronomy,” Proc. R. Soc. London Ser. A 248, 199–221 (1958).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Astron. J.

W. S. Finsen, “Interferometer observation of binary stars,” Astron. J. 69, 319–324 (1964).
[CrossRef]

Astrophys. J.

A. A. Michelson, F. G. Pease, “Measurement of the diameter of α orionis with the interferometer,” Astrophys. J. 53, 249–256 (1922).
[CrossRef]

D. G. Currie, S. L. Knapp, K. M. Liewer, “Four stellar-diameter measurements by a new technique: amplitude interferometry,” Astrophys. J. 187, 131–134 (1974).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

D. W. Cutter, A. Lohmann, “Achromatic stellar interferometry,” Opt. Commun. 12, 220–222 (1974).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London Ser. A

R. Hanbury Brown, R. Q. Twiss, “Interferometry of the intensity fluctuations in light III. Application to astronomy,” Proc. R. Soc. London Ser. A 248, 199–221 (1958).
[CrossRef]

Other

A. Labeyrie, “High resolution techniques in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. XIV, pp. 48–87.

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Figures (4)

Fig. 1
Fig. 1

The basic grating interferometer.

Fig. 2
Fig. 2

Sampling scheme for source intensity measurement of a binary star system. The irradiance is measured at P1, … P8.

Fig. 3
Fig. 3

Experimental arrangement.

Fig. 4
Fig. 4

Experimentais result showing the true ratio of object point irradiances on the horizontal axis and the measured ratios on the vertical axis. If the measurement values were error free, the experimental points would lie on the straight line.

Equations (18)

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I ( x , z ) = 0 . 5 + 0 . 5 cos [ 4 π f 1 ( x θ z ) ] .
I ( x , z ) = 0 . 5 ( S 1 + S 2 ) + 0 . 5 S 1 cos [ 4 π f 1 ( x z θ 1 ) ] + 0 . 5 S 2 cos [ 4 π f 1 ( x z θ 2 ) ] = 0 . 5 [ S 1 + S 2 + S 0 cos ( 4 π f 1 x δ ) ] .
I ( x , y ) = S 1 [ | n ( x + α z ) | 2 + | n ( x α z ) | 2 ] + S 2 [ | n ( x 2 θ d + α z ) | 2 + | n ( x 2 θ d α z ) | 2 ] + 2 Re { [ S 1 n * ( x + α z ) n ( x α z ) + S 2 n * ( x 2 θ d + α z ) n ( x 2 θ d α z ) ] exp ( j 4 π f 1 x ) } ,
u 1 = I 1 = S 1 | A 1 | 2 + S 2 | A 2 | 2 ,
u 2 = I 2 = S 1 | A 2 | 2 + S 2 | A 3 | 2 ,
u 3 = I 3 = S 1 | A 3 | 2 + S 2 | A 4 | 2 ,
u 4 = I 4 + j I 5 = S 1 A 1 A 2 * + S 2 A 2 A 3 * ,
u 5 = I 6 + j I 7 = S 1 A 2 A 3 * + S 2 A 3 A 4 * ,
u 6 = I 8 + j I 9 = S 1 A 3 A 4 * + S 2 A 4 A 5 * ,
u 7 = I 10 + j I 11 = S 1 A 1 A 3 * + S 2 A 2 A 4 * ,
u 8 = I 12 + j I 13 = S 1 A 2 A 4 * + S 2 A 3 A 5 * ,
det C = 0 ,
[ S ( I 4 + I 6 ) I 6 ] c 2 S ( I 2 + I 10 ) a c S I 11 b c = ( I 10 I 4 + I 11 I 5 ) ,
[ S ( I 5 + I 7 ) I 7 ] c 2 S I 11 a c S ( I 2 I 10 ) b c = ( I 11 I 4 I 10 I 5 ) ,
[ S I 8 S 2 ( I 6 + I 8 ) ] c 2 + S 2 ( I 3 + I 12 ) a c + S 2 I 13 b c = S ( I 3 I 4 + I 4 I 12 + I 5 I 13 + I 6 I 12 + I 7 I 13 I 2 I 6 I 2 I 8 ) + I 2 I 8 I 6 I 12 I 7 I 13 ,
[ S I 9 S 2 ( I 7 + I 9 ) ] c 2 + S 2 I 13 a c + S 2 ( I 3 I 12 ) b c = S ( I 3 I 5 + I 4 I 13 + I 6 I 13 I 5 I 12 I 7 I 12 I 2 I 7 I 2 I 9 ) + I 2 I 9 I 6 I 13 I 7 I 12 .
det C = 0 ,
C 11 = S ( I 4 + I 6 ) I 6 , C 12 = I 2 I 10 , C 13 = I 11 , C 14 = I 10 I 4 + I 11 I 5 , C 21 = S ( I 6 + I 7 ) I 7 C 22 = I 11 , C 23 = I 2 + I 10 , C 24 = I 11 I 4 I 10 I 5 , C 31 = S [ S ( I 8 + I 6 ) + I 8 ] , C 32 = S ( I 3 + I 12 ) , C 33 = S I 13 , C 34 = S ( I 2 I 6 + I 2 I 8 I 3 I 4 I 4 I 12 I 5 I 13 I 6 I 12 I 7 I 13 ) I 2 I 8 + I 6 I 12 + I 7 I 13 , C 41 = S [ S ( I 7 + I 9 ) + I 9 ] , C 42 = S I 13 , C 43 = S ( I 3 I 12 ) , C 44 = S ( I 2 I 7 + I 2 I 9 I 3 I 5 + I 5 I 12 I 4 I 13 I 6 I 13 + I 7 I 12 ) I 2 I 9 + I 6 I 13 I 7 I 12 .

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