Abstract

In the application of the Michelson interferometer for measurement of length by photoelectric methods there is a choice of either plane mirrors or cube corners as the end reflectors. In the present paper it is shown that the guide on which the moving cube corner moves needs to be only of moderate accuracy whereas it is known that the guide must be made very accurately when plane mirrors are used.

© 1960 Optical Society of America

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References

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  1. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927).
  2. W. F. Meggers, J. Opt. Soc. Am. 38, 7 (1948).
    [CrossRef] [PubMed]
  3. J. Terrien and J. Hamon, Compt. rend. 239, 586 (1954).
  4. W. F. Meggers and F. O. Westfall, J. Research Natl. Bur. Standards 44, 447 (1950).
    [CrossRef]
  5. G. R. Harrison, Phys. Today 3, 6 (1950).
    [CrossRef]
  6. G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
    [CrossRef]
  7. Harrison, Sturgis, Baker, and Stroke, J. Opt. Soc. Am. 47, 15 (1957).
    [CrossRef]
  8. Harrison, Sturgis, Davis, and Yamada, J. Opt. Soc. Am. 49, 205 (1959).
    [CrossRef]
  9. E. R. Peck and S. W. Obetz, J. Opt. Soc. Am. 43, 505 (1953).
    [CrossRef] [PubMed]
  10. G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957).
    [CrossRef]
  11. E. R. Peck, J. Opt. Soc. Am. 38, 1015 (1948).
    [CrossRef] [PubMed]
  12. E. R. Peck, J. Opt. Soc. Am. 45, 931 (1955).
    [CrossRef]
  13. E. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 53, 233 (1885).
  14. Rayleigh, Phil. Mag. 31, 87 (1891).
  15. C. F. Bruce, Australian J. Phys. 8, 224 (1955).
    [CrossRef]
  16. B. S. Thornton, Australian J. Phys. 8, 241 (1955).
    [CrossRef]
  17. M. V. R. K. Murty, “Simulation of primary aberrations of a lens using Michelson interferometer,” Ph.D. thesis (University of Rochester, Rochester, New York, 1959).
  18. E. H. Linfoot, Recent Advances in Optics (Oxford University Press, New York, 1955), pp. 37, 38.
  19. P. Connes, Rev. opt. 35, 37 (1956).

1959 (1)

1957 (2)

1956 (1)

P. Connes, Rev. opt. 35, 37 (1956).

1955 (4)

C. F. Bruce, Australian J. Phys. 8, 224 (1955).
[CrossRef]

B. S. Thornton, Australian J. Phys. 8, 241 (1955).
[CrossRef]

G. R. Harrison and G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
[CrossRef]

E. R. Peck, J. Opt. Soc. Am. 45, 931 (1955).
[CrossRef]

1954 (1)

J. Terrien and J. Hamon, Compt. rend. 239, 586 (1954).

1953 (1)

1950 (2)

W. F. Meggers and F. O. Westfall, J. Research Natl. Bur. Standards 44, 447 (1950).
[CrossRef]

G. R. Harrison, Phys. Today 3, 6 (1950).
[CrossRef]

1948 (2)

1891 (1)

Rayleigh, Phil. Mag. 31, 87 (1891).

1885 (1)

E. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 53, 233 (1885).

Baker,

Bruce, C. F.

C. F. Bruce, Australian J. Phys. 8, 224 (1955).
[CrossRef]

Connes, P.

P. Connes, Rev. opt. 35, 37 (1956).

Davis,

Hamon, J.

J. Terrien and J. Hamon, Compt. rend. 239, 586 (1954).

Harrison,

Harrison, G. R.

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Oxford University Press, New York, 1955), pp. 37, 38.

Lommel, E.

E. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 53, 233 (1885).

Meggers, W. F.

W. F. Meggers and F. O. Westfall, J. Research Natl. Bur. Standards 44, 447 (1950).
[CrossRef]

W. F. Meggers, J. Opt. Soc. Am. 38, 7 (1948).
[CrossRef] [PubMed]

Michelson, A. A.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927).

Murty, M. V. R. K.

M. V. R. K. Murty, “Simulation of primary aberrations of a lens using Michelson interferometer,” Ph.D. thesis (University of Rochester, Rochester, New York, 1959).

Obetz, S. W.

Peck, E. R.

Rayleigh,

Rayleigh, Phil. Mag. 31, 87 (1891).

Stroke,

Stroke, G. W.

Sturgis,

Terrien, J.

J. Terrien and J. Hamon, Compt. rend. 239, 586 (1954).

Thornton, B. S.

B. S. Thornton, Australian J. Phys. 8, 241 (1955).
[CrossRef]

Westfall, F. O.

W. F. Meggers and F. O. Westfall, J. Research Natl. Bur. Standards 44, 447 (1950).
[CrossRef]

Yamada,

Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. (1)

E. Lommel, Abhandl. bayer. Akad. Wiss. Math.-Naturw. Kl. 53, 233 (1885).

Australian J. Phys. (2)

C. F. Bruce, Australian J. Phys. 8, 224 (1955).
[CrossRef]

B. S. Thornton, Australian J. Phys. 8, 241 (1955).
[CrossRef]

Compt. rend. (1)

J. Terrien and J. Hamon, Compt. rend. 239, 586 (1954).

J. Opt. Soc. Am. (8)

J. Research Natl. Bur. Standards (1)

W. F. Meggers and F. O. Westfall, J. Research Natl. Bur. Standards 44, 447 (1950).
[CrossRef]

Phil. Mag. (1)

Rayleigh, Phil. Mag. 31, 87 (1891).

Phys. Today (1)

G. R. Harrison, Phys. Today 3, 6 (1950).
[CrossRef]

Rev. opt. (1)

P. Connes, Rev. opt. 35, 37 (1956).

Other (3)

M. V. R. K. Murty, “Simulation of primary aberrations of a lens using Michelson interferometer,” Ph.D. thesis (University of Rochester, Rochester, New York, 1959).

E. H. Linfoot, Recent Advances in Optics (Oxford University Press, New York, 1955), pp. 37, 38.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the Michelson interferometer with cube corners showing the position of the moving cube corner with respect to the stationary cube corner. S.P.—source plane; F.P.—fringe plane; C.L.—collimating lens; F.L.—focusing lens; B.S.—beam-splitter; Cs—stationary cube corner; Cs′—virtual image of Cs as reflected in B.S.; Cm—moving cube corner with no lateral shift; Cm′—moving cube corner with a small lateral shift; CmCs′=t; CmCm′=.

Fig. 2
Fig. 2

Photographs of the fringes at infinity illustrating the effect of lateral shift of the moving cube corner.

Fig. 3
Fig. 3

Plot of the fringe signal modulation m versus the parameter p for three values of the parameter q, viz., 0, 0.91, and 2.22.

Equations (15)

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N λ = 2 t cos θ ,
N λ = 2 t - t θ 2 .
N λ = 2 t - t r 2 .
N λ = 2 t + 2 r cos ϕ - t r 2 .
I = ( 1 + cos 2 π N ) .
I = ( 1 + cos k δ ) ,
δ = 2 t + 2 r cos ϕ - t r 2 k = 2 π / λ .
F = 0 R 0 2 π ( 1 + cos k δ ) r d r d ϕ .
F = π R 2 [ 1 + m cos ( 2 k t - ψ ) ] ,
m = ( 2 / p ) ( U 1 2 + U 2 2 ) 1 2 ,             for             | p q | < 1 ; m = 2 p [ 1 + V 0 2 + V 1 2 - 2 V 0 cos ( p 2 + q 2 2 p ) - 2 V 1 sin ( p 2 + q 2 2 p ) ] 1 2 ,             for             | p q | > 1 ;
ψ = [ ( p / 2 ) - tan - 1 ( U 2 / U 1 ) ] ± n π ,             for             | p q | < 1 , ψ = ( p 2 + tan - 1 { V 0 - cos ( p 2 + q 2 2 p ) V 1 - sin ( p 2 + q 2 2 p ) } ) ± n π ,             for             | p q | > 1.
U n = j = 0 ( - 1 ) j ( p q ) 2 j + n J 2 j + n ( q ) V n = j = 0 ( - 1 ) j ( q p ) 2 j + n J 2 j + n ( q ) .
p = 2 k t R 2 ;             q = 2 k R .
m = ( F max - F min ) / ( F max + F min ) .
m ( 0 , q ) = [ 2 J 1 ( q ) q ] m ( p , 0 ) = ( sin ( p / 4 ) p / 4 ) .