Abstract

The fork algorithm for accurately estimating the intensity ratio of binary stars from speckle interferometry data is presented. For brighter stars simulation results suggest that the fork algorithm can attain a signal-to-noise ratio roughly 10 times greater than that of other algorithms, such as triple correlation and shift-and-add. The results of the application of the algorithm to Capella (Alpha Aurigae) data are described.

© 1988 Optical Society of America

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References

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  1. H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
    [CrossRef]
  2. J. C. Dainty, A. H. Greenaway, J. Opt. Soc. Am. 69, 786 (1979).
    [CrossRef]
  3. W. G. Bagnuolo, H. A. McAlister, Publ. Astron. Soc. Pac. 95, 993 (1983).
    [CrossRef]
  4. W. G. Bagnuolo, in International Astronomical Union Colloquium 64, Lowell Observatory Bull. 167 (Lowell Observatory, Flagstaff, Ariz., 1983), p. 180.
  5. R. Barakat, P. Nisensen, J. Opt. Soc. Am. 71, 1390 (1981).
    [CrossRef]
  6. G. P. Weigelt, Opt. Commun. 21, 55 (1977).
    [CrossRef]
  7. R. H. T. Bates, F. Cady, Opt. Commun. 32, 365 (1980).
    [CrossRef]
  8. J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).
  9. W. G. Bagnuolo, J. R. Sowell, “Binary star speckle photometry. I. The colors and spectral types of the Capella stars,” Astron. J. (to be published).

1987 (1)

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

1986 (1)

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

1983 (1)

W. G. Bagnuolo, H. A. McAlister, Publ. Astron. Soc. Pac. 95, 993 (1983).
[CrossRef]

1981 (1)

1980 (1)

R. H. T. Bates, F. Cady, Opt. Commun. 32, 365 (1980).
[CrossRef]

1979 (1)

1977 (1)

G. P. Weigelt, Opt. Commun. 21, 55 (1977).
[CrossRef]

Bagnuolo, W. G.

W. G. Bagnuolo, H. A. McAlister, Publ. Astron. Soc. Pac. 95, 993 (1983).
[CrossRef]

W. G. Bagnuolo, in International Astronomical Union Colloquium 64, Lowell Observatory Bull. 167 (Lowell Observatory, Flagstaff, Ariz., 1983), p. 180.

W. G. Bagnuolo, J. R. Sowell, “Binary star speckle photometry. I. The colors and spectral types of the Capella stars,” Astron. J. (to be published).

Barakat, R.

Bates, R. H. T.

R. H. T. Bates, F. Cady, Opt. Commun. 32, 365 (1980).
[CrossRef]

Cady, F.

R. H. T. Bates, F. Cady, Opt. Commun. 32, 365 (1980).
[CrossRef]

Christou, J.

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

Dainty, J. C.

Franz, O. G.

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

Freeman, J.

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

Greenaway, A. H.

Hartkopf, W. I.

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

Hege, E.

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

Hutter, D. J.

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

McAlister, H. A.

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

W. G. Bagnuolo, H. A. McAlister, Publ. Astron. Soc. Pac. 95, 993 (1983).
[CrossRef]

Nisensen, P.

Ribak, E.

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

Sowell, J. R.

W. G. Bagnuolo, J. R. Sowell, “Binary star speckle photometry. I. The colors and spectral types of the Capella stars,” Astron. J. (to be published).

Weigelt, G. P.

G. P. Weigelt, Opt. Commun. 21, 55 (1977).
[CrossRef]

Astron. J. (1)

H. A. McAlister, W. I. Hartkopf, D. J. Hutter, O. G. Franz, Astron. J. 93, 688 (1987).
[CrossRef]

J. Opt. Eng. (1)

J. Christou, E. Ribak, E. Hege, J. Freeman, J. Opt. Eng. 25, 724 (1986).

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

G. P. Weigelt, Opt. Commun. 21, 55 (1977).
[CrossRef]

R. H. T. Bates, F. Cady, Opt. Commun. 32, 365 (1980).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

W. G. Bagnuolo, H. A. McAlister, Publ. Astron. Soc. Pac. 95, 993 (1983).
[CrossRef]

Other (2)

W. G. Bagnuolo, in International Astronomical Union Colloquium 64, Lowell Observatory Bull. 167 (Lowell Observatory, Flagstaff, Ariz., 1983), p. 180.

W. G. Bagnuolo, J. R. Sowell, “Binary star speckle photometry. I. The colors and spectral types of the Capella stars,” Astron. J. (to be published).

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Figures (3)

Fig. 1
Fig. 1

64 × 64 pixel area of a Capella frame with a 22-level gray scale. A favorable occurrence for the fork algorithm is indicated. The separation is 0.050, the intensity ratio 0.91, and the position angle 203°.

Fig. 2
Fig. 2

Histograms of the intensity fraction f of unweighted (left) and weighted (right) results from simulated data.

Fig. 3
Fig. 3

Observable quantities as a function of the intensity ratio r for five algorithms. Filled squares: triple correlation; bars, weighted shift-and-add; open squares, fork; crosses, shift-and-add; sharps, autocorrelation.

Tables (1)

Tables Icon

Table 1 Algorithm Errors for r = 0.5 Simulations

Equations (12)

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I 1 = i 1 + r i 0 , I 2 = i 2 + r i 1 , I 3 = i 3 + r i 2 , I 4 = i 4 + r i 3 .
Max ( I 2 , I 3 ) > c 1 Max ( I 1 , I 4 ) > c 2 I ¯ ,
p ( i , I ) = exp ( - i 1 ) exp [ - ( I 1 - i 1 ) / r ] = 0             if i 1 > I 1 .
p ( I 1 ) = p ( i 1 , I 1 ) d i = exp ( - I 1 / r ) [ exp ( I Q ) - 1 ] / Q ,
p ( i 1 I 1 ) = Q exp ( i 1 Q ) [ exp ( I 1 Q ) - 1 ] = 0             if i 1 > 1.
i ¯ 1 = I 1 R 1 - 1 / Q ,
R n exp ( I n Q ) exp ( I n Q ) - 1 .
i ¯ 4 = I 4 R 4 - 1 / Q ,             i ¯ 3 = i ¯ 4 / r ,
r ( I 3 - i ¯ 3 ) / ( I 2 - r i ¯ 1 ) b / a .
Δ i 1 2 = I 1 2 ( 1 - R 1 ) R 1 + 1 / Q 2 Δ a 2 / r 2 , Δ i 3 2 = 1 r 2 [ I 4 2 ( 1 - R 4 ) R 4 + 1 / Q 2 ] Δ b 2 ,
Δ f 2 = b 2 Δ a 2 + a 2 Δ b 2 ( a + b ) 4 .
c ( s , t ) = exp ( i ϕ ) exp [ - ( s 2 + t 2 ) / a 1 2 ] , P ( u , v ) = a 2 Re { F [ c ( s , t ) ] } , i ( x , y ) = F [ P ( u , v ) A ( u , v ) ] 2 ,

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