Abstract

In this paper a technique is outlined that can be used in an optical interferometer, and that in many applications offers the possibility of eliminating the problem of atmospheric seeing when measuring the phase of the object visibility function.

© 1968 Optical Society of America

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References

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  1. A. A. Michelson, Astrophys. J. 51, 257 (1920).
    [CrossRef]
  2. R. H. Miller, Science 153, 581 (1966).
    [CrossRef] [PubMed]
  3. R. C. Jennison, Monthly Notices Roy. Astron. Soc. 118, 276 (1958).
  4. R. N. Bracewell, Proc. Inst. Radio Eng. 46, 97 (1958).
  5. A. T. Moffet, Astrophys. J. Suppl. No. 67 (1962).
  6. Optical Synthesis, Woods Hole Summer Study, Aug.1967, by the National Academy of Sciences (in preparation).

1966

R. H. Miller, Science 153, 581 (1966).
[CrossRef] [PubMed]

1962

A. T. Moffet, Astrophys. J. Suppl. No. 67 (1962).

1958

R. C. Jennison, Monthly Notices Roy. Astron. Soc. 118, 276 (1958).

R. N. Bracewell, Proc. Inst. Radio Eng. 46, 97 (1958).

1920

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, Proc. Inst. Radio Eng. 46, 97 (1958).

Jennison, R. C.

R. C. Jennison, Monthly Notices Roy. Astron. Soc. 118, 276 (1958).

Michelson, A. A.

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[CrossRef]

Miller, R. H.

R. H. Miller, Science 153, 581 (1966).
[CrossRef] [PubMed]

Moffet, A. T.

A. T. Moffet, Astrophys. J. Suppl. No. 67 (1962).

Astrophys. J.

A. A. Michelson, Astrophys. J. 51, 257 (1920).
[CrossRef]

Astrophys. J. Suppl. No.

A. T. Moffet, Astrophys. J. Suppl. No. 67 (1962).

Monthly Notices Roy. Astron. Soc.

R. C. Jennison, Monthly Notices Roy. Astron. Soc. 118, 276 (1958).

Proc. Inst. Radio Eng.

R. N. Bracewell, Proc. Inst. Radio Eng. 46, 97 (1958).

Science

R. H. Miller, Science 153, 581 (1966).
[CrossRef] [PubMed]

Other

Optical Synthesis, Woods Hole Summer Study, Aug.1967, by the National Academy of Sciences (in preparation).

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Figures (3)

Fig. 1
Fig. 1

Basic interferometer configuration.

Fig. 2
Fig. 2

Three-element interferometer configuration.

Fig. 3
Fig. 3

Possible six-element configuration giving ten simultaneous spacings.

Equations (15)

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V ( u , v ) = object B ( x , y ) exp [ j s · p ] d x d y .
I = I 0 sin ( Ψ 0 ) ,
I A = I 0 sin ( Ψ 0 ) ,
I B = I 0 sin ( Ψ 0 + π / 2 ) = I 0 cos ( Ψ 0 ) ,
I 0 = ( I A 2 + I B 2 ) 1 2 , Ψ 0 = tan - 1 ( I A / I B ) .
I A = I 0 sin ( Ψ 0 + ϕ 0 ) ,
I B = I 0 cos ( Ψ 0 + ϕ 0 ) .
I 1 A = V 1 sin ( ϕ 1 + Ψ 1 ) , I 1 B = V 1 cos ( ϕ 1 + Ψ 1 ) , I 2 A = V 2 sin ( ϕ 2 - ϕ 1 + Ψ 2 ) , I 2 B = V 2 cos ( ϕ 2 - ϕ 1 + Ψ 2 ) , I 3 A = V 3 sin ( ϕ 2 + Ψ 3 ) , I 3 B = V 3 cos ( ϕ 2 + Ψ 3 ) .
R = ( T 1 2 + T 2 2 ) 1 2 = V 1 V 2 V 3 ,
P = tan - 1 ( T 1 / T 2 ) = Ψ 3 - Ψ 1 - Ψ 2 ,
T 1 = ( I 1 B I 2 B - I 1 A I 2 A ) I 3 A - ( I 1 A I 2 B + I 1 B I 2 A ) I 3 B = V 1 V 2 V 3 sin ( Ψ 3 - Ψ 2 - Ψ 1 ) ,
T 2 = ( I 1 B I 2 B - I 1 A I 2 A ) I 3 B + ( I 1 A I 2 B + I 1 B I 2 A ) I 3 A = V 1 V 2 V 3 cos ( Ψ 3 - Ψ 2 - Ψ 1 ) .
P 1 = ϕ 1 + Ψ 1 P 5 = ϕ 4 - ϕ 2 + Ψ 5 P 1 = φ 2 - ϕ 1 + Ψ 1 P 6 = ϕ 4 - ϕ 1 + Ψ 6 P 2 = ϕ 2 + Ψ 2 P 6 = ϕ 5 - ϕ 3 + Ψ 6 P 2 = ϕ 3 - ϕ 2 + Ψ 2 P 7 = ϕ 4 + Ψ 7 P 3 = ϕ 3 - ϕ 1 + Ψ 3 P 8 = ϕ 5 - ϕ 2 + Ψ 8 P 3 = ϕ 4 - ϕ 3 + Ψ 3 P 9 = ϕ 5 - ϕ 1 + Ψ 9 P 3 = ϕ 5 - ϕ 4 + Ψ 3 P 10 = ϕ 5 + Ψ 10 . P 4 = ϕ 3 + Ψ 4
A 2 = P 2 - P 1 - P 1 = Ψ 2 - 2 Ψ 1 A 3 = P 3 - P 2 - P 1 = Ψ 3 - Ψ 2 - Ψ 1 A 4 = P 4 - P 2 - P 2 = Ψ 4 - 2 Ψ 2 A 5 = P 5 - P 3 - P 2 = Ψ 5 - Ψ 3 - Ψ 2 A 6 = P 6 - P 3 - P 3 = Ψ 6 - 2 Ψ 3 A 7 = P 7 - P 3 - P 4 = Ψ 7 - Ψ 3 - Ψ 4 A 8 = P 8 - P 3 - P 5 = Ψ 8 - Ψ 3 - Ψ 5 A 9 = P 9 - P 6 - P 3 = Ψ 9 - Ψ 6 - Ψ 3 A 10 = P 10 - P 6 - P 4 = Ψ 10 - Ψ 6 - Ψ 4 .
Ψ = C ˜ A , where C ˜ = [ 1 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 3 1 1 0 0 0 0 0 0 0 4 1 1 1 0 0 0 0 0 0 5 2 1 0 1 0 0 0 0 0 6 2 2 0 0 1 0 0 0 0 7 2 2 1 0 0 1 0 0 0 8 3 2 0 0 1 0 1 0 0 9 3 3 0 0 1 0 0 1 0 10 3 3 1 0 1 0 0 0 1 ] .

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