Abstract

Measurements of isoplanatism for speckle interferometry and speckle imaging applications have been made at a 1.57 meter aperture telescope in Hawaii. The measurements were obtained from optically produced spatial power spectra of short-exposure images showing pairs of stars with different angular separations. The result of this process is a sequence of plots of correlation versus spatial frequency in the image for 0.25, 0.5, 1.9, and 4.7 arc sec separation binary stars. Substantial correlation is found to at least 0.6 of the diffraction limit cutoff for the 4.7 arc sec pair.

© 1978 Optical Society of America

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References

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  1. J. C. Dainty, Topics in Applied Physics, edited by J. C. Dainty (Springer-Verlag, New York, 1975), Vol. 9, p. 255.
    [CrossRef]
  2. J. C. Dainty, Mon. Not. R. Astr. Soc. 169, 631 (1974).
  3. J. H. Shapiro, J. Opt. Soc. Am. 66, 469 (1976).
    [CrossRef]
  4. D. Korff, G. Dryden, and R. P. Leavitt, J. Opt. Soc. Am. 65, 1321 (1975).
    [CrossRef]
  5. D. L. Fried, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 20 (1976).
  6. P. Laques, Advances in Electronics and Electron Physics, edited by L. Marton (Academic, New York, 1966), Vol. 22B, p. 755.
    [CrossRef]
  7. H. A. McAllister, “Speckle interferometric measurements of binary stars I,” Astrophys. J. (to be published).
  8. A. M. Schneiderman and D. P. Karo, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).
  9. J. B. Breckinridge and H. A. McAllister, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).
  10. D. Hoffleit, Catalogue of Bright Stars (Yale University Observatory, New Haven, 1964).
  11. R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
    [CrossRef]

1977 (1)

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

1976 (4)

J. H. Shapiro, J. Opt. Soc. Am. 66, 469 (1976).
[CrossRef]

D. L. Fried, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 20 (1976).

A. M. Schneiderman and D. P. Karo, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

J. B. Breckinridge and H. A. McAllister, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

1975 (1)

1974 (1)

J. C. Dainty, Mon. Not. R. Astr. Soc. 169, 631 (1974).

Breckinridge, J. B.

J. B. Breckinridge and H. A. McAllister, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

Dainty, J. C.

J. C. Dainty, Mon. Not. R. Astr. Soc. 169, 631 (1974).

J. C. Dainty, Topics in Applied Physics, edited by J. C. Dainty (Springer-Verlag, New York, 1975), Vol. 9, p. 255.
[CrossRef]

Dryden, G.

Ehn, D. C.

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

Fried, D. L.

D. L. Fried, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 20 (1976).

Hoffleit, D.

D. Hoffleit, Catalogue of Bright Stars (Yale University Observatory, New Haven, 1964).

Hudgin, R. H.

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

Karo, D. P.

A. M. Schneiderman and D. P. Karo, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

Korff, D.

Laques, P.

P. Laques, Advances in Electronics and Electron Physics, edited by L. Marton (Academic, New York, 1966), Vol. 22B, p. 755.
[CrossRef]

Leavitt, R. P.

McAllister, H. A.

J. B. Breckinridge and H. A. McAllister, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

H. A. McAllister, “Speckle interferometric measurements of binary stars I,” Astrophys. J. (to be published).

Nisenson, P.

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

Schirf, V. E.

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

Schneiderman, A. M.

A. M. Schneiderman and D. P. Karo, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

Shapiro, J. H.

Stachnik, R. V.

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

J. Opt. Soc. Am. (4)

J. H. Shapiro, J. Opt. Soc. Am. 66, 469 (1976).
[CrossRef]

D. Korff, G. Dryden, and R. P. Leavitt, J. Opt. Soc. Am. 65, 1321 (1975).
[CrossRef]

A. M. Schneiderman and D. P. Karo, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

J. B. Breckinridge and H. A. McAllister, 1976 Annual Program of the Optical Society of America, J. Opt. Soc. Am. 66, 1077A (1976).

Mon. Not. R. Astr. Soc. (1)

J. C. Dainty, Mon. Not. R. Astr. Soc. 169, 631 (1974).

Nature (1)

R. V. Stachnik, P. Nisenson, D. C. Ehn, R. H. Hudgin, and V. E. Schirf, Nature 266, 149 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. L. Fried, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 20 (1976).

Other (4)

P. Laques, Advances in Electronics and Electron Physics, edited by L. Marton (Academic, New York, 1966), Vol. 22B, p. 755.
[CrossRef]

H. A. McAllister, “Speckle interferometric measurements of binary stars I,” Astrophys. J. (to be published).

J. C. Dainty, Topics in Applied Physics, edited by J. C. Dainty (Springer-Verlag, New York, 1975), Vol. 9, p. 255.
[CrossRef]

D. Hoffleit, Catalogue of Bright Stars (Yale University Observatory, New Haven, 1964).

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Figures (6)

Fig. 1
Fig. 1

Illustration of loss of isoplanatism due to passage of the wave fronts from different angularly separated sources through adjacent sections of the atmosphere. The result in the image plane is a decorrelation of the point spread functions, which occurs first at the higher spatial frequencies. Clearly, the upper levels of turbulence contribute most strongly to loss of isoplanatism.

Fig. 2
Fig. 2

Photograph of 16-mm image intensified speckle camera with fore optics cover removed.

Fig. 3
Fig. 3

Sequence of three images of the nearly equal magnitude 1.9 arc sec separation binary star ζ1 Aqr. The similarity between the changing spread functions is easily seen.

Fig. 4
Fig. 4

Optical spatial power spectra of four binary stars having angular separations in the range 0.2–4.7 arc sec. Single frame transforms are shown in b and e of the same stars for which 200 frame transforms are depicted in a and d.

Fig. 5
Fig. 5

Sample microdensitometer trace of the 200-frame power spectrum of the 4.7 arc sec binary 65 Psc.

Fig. 6
Fig. 6

Correlation (Γ(u,v)) as a function of spatial frequency from measured contrasts of four binary stars. For the 0.25 and 0.5 arc sec binaries, only a single point was measured on each curve. The curve for the 1.9 arc sec pair was measured on three different nights.

Tables (1)

Tables Icon

TABLE I Recording parameters of binary star data.

Equations (13)

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i ( x , y ) = k 1 g 1 ( x + a , y ) + k 2 g 2 ( x - a , y ) ,
g 1 ( x , y ) g 2 ( x , y ) g 1 ( χ + x , ξ + y ) g 2 ( χ , ξ ) d χ d ξ ,
[ i ( x , y ) ] = k 1 G 1 ( u , v ) e - j a u + k 2 G 2 ( u , v ) e + j a u ,
[ i ( x , y ) ] 2 = S ( u , v ) = k 1 2 G 1 ( u , v ) 2 + k 2 2 G 2 ( u , v ) 2 + k 1 k 2 G 1 ( u , v ) G 2 * ( u , v ) e - j 2 a u + k 1 k 2 G 1 * ( u , v ) G 2 ( u , v ) e + j 2 a u .
S ( u , v ) = k 1 2 G 1 ( u , v ) 2 + k 2 2 G 2 ( u , v ) 2 + k 1 k 2 G 1 ( u , v ) G 2 * ( u , v ) e - j 2 a u + k 1 k 2 G 1 * ( u , v ) G 2 ( u , v ) e + j 2 a u ,
G 1 ( u , v ) 2 = G 2 ( u , v ) 2 ,
G 1 ( u , v ) G 2 * ( u , v ) = G 1 * ( u , v ) G 2 ( u , v ) .
S ( u , v ) = ( k 1 2 + k 2 2 ) G 1 ( u , v ) 2 × ( 1 + 2 k 1 k 2 k 1 2 + k 2 2 G 1 ( u , v ) G 2 * ( u , v ) G 1 ( u , v ) 2 cos 2 a u ) .
Γ ( u , v ) = G 1 ( u , v ) G 2 * ( u , v ) G 1 ( u , v ) 2 .
Γ ( u , v ) = 1 ,
Γ ( u , v ) = 0.
m = ( I max / I min ) - 1 ( I max / I min ) + 1 ,
m r = 2 R γ / 2 1 / R γ .