Abstract

To get high accuracy for measuring length, an interferometric measurement is usually used. In this case advancement of the mirror usually accompanies the rotational movement of the mirror, and this affects the proportionality between the advancement of the mirror and fringe displacement. If the rotational movement is small the deviation from proportionality is small, but if the multipass method is used, the angular deviation is also magnified, and the deviation becomes large. The best way to overcome the difficulty is to use a corner cube. A multipass method for a corner cube is described.

© 1973 Optical Society of America

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References

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  1. U.S. Patent 3,584,226 Appl. Opt. 11 No. 2, A28 (1972).
  2. Y. Sakayanagi, J. Fukuda, Sci. Light 21, 17 (1972); the outline is in the Appendix.
  3. F. H. Branin, J. Opt. Soc. Am. 43, 839 (1953).
    [CrossRef]
  4. G. R. Harrison, G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
    [CrossRef]
  5. Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
    [CrossRef]
  6. Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

1972 (2)

U.S. Patent 3,584,226 Appl. Opt. 11 No. 2, A28 (1972).

Y. Sakayanagi, J. Fukuda, Sci. Light 21, 17 (1972); the outline is in the Appendix.

1971 (1)

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

1955 (1)

1953 (1)

1952 (1)

Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

Alston-Garnjost, Mararet

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

Branin, F. H.

Dauber, P. M.

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

Davis, J. W.

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

Fujioka, Y.

Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

Fukuda, J.

Y. Sakayanagi, J. Fukuda, Sci. Light 21, 17 (1972); the outline is in the Appendix.

Harrison, G. R.

Kitayama, T.

Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

Sakayanagi, Y.

Y. Sakayanagi, J. Fukuda, Sci. Light 21, 17 (1972); the outline is in the Appendix.

Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

Smits, R. G.

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

Stroke, G. W.

Appl. Opt. (1)

U.S. Patent 3,584,226 Appl. Opt. 11 No. 2, A28 (1972).

J. Opt. Soc. Am. (2)

Rev. Sci. Instrum. (1)

Mararet Alston-Garnjost, J. W. Davis, P. M. Dauber, R. G. Smits, Rev. Sci. Instrum. 42, 1565 (1971).
[CrossRef]

Sci. Light (2)

Y. Fujioka, Y. Sakayanagi, T. Kitayama, Sci. Light 2, 1 (1952).

Y. Sakayanagi, J. Fukuda, Sci. Light 21, 17 (1972); the outline is in the Appendix.

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Figures (7)

Fig. 1
Fig. 1

Effect of the mirror inclination on the interference distance.

Fig. 2
Fig. 2

Inclination of two mirrors and the deviation of the light beam after n reflections.

Fig. 3
Fig. 3

Schematic arrangement of mirrors.

Fig. 4
Fig. 4

Section of a dihedral mirror. It is composed of two glass blocks by mechanical compression.

Fig. 5
Fig. 5

Mutual positions of a light beam when it is reflected by a corner cube surface. Upper is top view, lower is side view.

Fig. 6
Fig. 6

Scheme of an interferometer. L, laser; S, separator; P, prism; P. T., phototransistor.

Fig. 7
Fig. 7

Side view of the interferometer.

Equations (7)

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O D = L · 2 j
δ = D C = O D j = 2 L · j 2 .
B C = L - δ , A C 2 = ( L - δ ) 2 + O D 2 ,
B C + A C - 2 A O = L - δ + [ ( L - δ ) 2 + ( 2 L · j ) 2 ] 1 / 2 - 2 L = - δ = - 2 L · j 2 .
δ = 2 × 10 - 10 m = 2 Å .
δ = - 10 [ 40 × ( 10 - 5 / 2 ) ] 2 m = - 4 × 10 - 7 m = - 0.4 μ .
6328 × ( 1 / 2 ) × ( 1 / 20 ) = 168 Å .

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