Abstract

With very highly collimated monochromatic light sources, such as optical masers, multiple-beam interference fringes between nearly parallel surfaces are obtained at large separations. Sharp fringes displaying the surface contours have been observed with separations as large as 20 cm. The requirements and limitations of the device are described, as well as some possible applications.

© 1963 Optical Society of America

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References

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  1. S. Tolansky, Surface Microtopography (Interscience, New York, 1960).
  2. S. Tolansky, High Resolution Spectroscopy (Pitman, New York, 1947) p. 141ff.
  3. J. B. Saunders, J. Res. Nat. Bur. Std. 47, 148 (1951).
    [Crossref]
  4. S. Tolansky, Multiple Beam Interferometry (Oxford University Press, London, 1948), Chap. II; J. Brossel, Proc. Phys. Soc. (London) 59, 224 (1947); M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 350ff.
    [Crossref]
  5. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 276–278
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 352.
  7. G. Devlin, J. McKenna, A. May, A. L. Schawlow, Appl. Opt. 1, 11 (1962).
    [Crossref]
  8. L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).
  9. A. D. White, J. D. Rigden, Proc. Inst. Radio Engrs. 50, 1697 (1962).
  10. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [Crossref]
  11. J. Bradley, Proc. Roy. Soc. (London) A262, 529 (1961).

1962 (3)

G. Devlin, J. McKenna, A. May, A. L. Schawlow, Appl. Opt. 1, 11 (1962).
[Crossref]

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

A. D. White, J. D. Rigden, Proc. Inst. Radio Engrs. 50, 1697 (1962).

1961 (1)

J. Bradley, Proc. Roy. Soc. (London) A262, 529 (1961).

1954 (1)

1951 (1)

J. B. Saunders, J. Res. Nat. Bur. Std. 47, 148 (1951).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 352.

Bradley, J.

J. Bradley, Proc. Roy. Soc. (London) A262, 529 (1961).

Devlin, G.

Imbusch, G. F.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

Jacquinot, P.

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 276–278

May, A.

McKenna, J.

Mollenauer, L. F.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

Moos, H. W.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

Rigden, J. D.

A. D. White, J. D. Rigden, Proc. Inst. Radio Engrs. 50, 1697 (1962).

Saunders, J. B.

J. B. Saunders, J. Res. Nat. Bur. Std. 47, 148 (1951).
[Crossref]

Schawlow, A. L.

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

G. Devlin, J. McKenna, A. May, A. L. Schawlow, Appl. Opt. 1, 11 (1962).
[Crossref]

Tolansky, S.

S. Tolansky, Multiple Beam Interferometry (Oxford University Press, London, 1948), Chap. II; J. Brossel, Proc. Phys. Soc. (London) 59, 224 (1947); M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 350ff.
[Crossref]

S. Tolansky, Surface Microtopography (Interscience, New York, 1960).

S. Tolansky, High Resolution Spectroscopy (Pitman, New York, 1947) p. 141ff.

White, A. D.

A. D. White, J. D. Rigden, Proc. Inst. Radio Engrs. 50, 1697 (1962).

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 276–278

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 352.

Appl. Opt. (1)

Bull. Am. Phys. Soc. (1)

L. F. Mollenauer, G. F. Imbusch, H. W. Moos, A. L. Schawlow, Bull. Am. Phys. Soc. 7, 445 (1962).

J. Opt. Soc. Am. (1)

J. Res. Nat. Bur. Std. (1)

J. B. Saunders, J. Res. Nat. Bur. Std. 47, 148 (1951).
[Crossref]

Proc. Inst. Radio Engrs. (1)

A. D. White, J. D. Rigden, Proc. Inst. Radio Engrs. 50, 1697 (1962).

Proc. Roy. Soc. (London) (1)

J. Bradley, Proc. Roy. Soc. (London) A262, 529 (1961).

Other (5)

S. Tolansky, Surface Microtopography (Interscience, New York, 1960).

S. Tolansky, High Resolution Spectroscopy (Pitman, New York, 1947) p. 141ff.

S. Tolansky, Multiple Beam Interferometry (Oxford University Press, London, 1948), Chap. II; J. Brossel, Proc. Phys. Soc. (London) 59, 224 (1947); M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 350ff.
[Crossref]

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 276–278

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 352.

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Figures (7)

Fig. 1
Fig. 1

Optical maser source. The rod was pumped by being placed at the focus of an elliptic cylinder with a linear lamp at the other. Threshold was about 50 J.

Fig. 2
Fig. 2

Two fringes from He–Ne optical maser with output at 6328 Å appear vertically. The interferometer separation was 20 cm. The horizontal cross-hatching is due to reflections from air–glass interfaces.

Fig. 3
Fig. 3

Hg198 4358 Å line at a separation of 6.1 cm. The exposure time was roughly 5 sec on Polaroid type 47 film.

Fig. 4
Fig. 4

Output of optical maser source at (a) 0%, (b) 2%, (c) 8%, and (d) 16% above threshold input power. The composite rod was 3 cm long and silvered on one end. The plate separation was 0.6 cm.

Fig. 5
Fig. 5

Optical maser source fringes near threshold. The etalon spacing was 10.5 cm.

Fig. 6
Fig. 6

Tilted-plate fringes showing the shadow of a wire in a plane parallel to the two plates.

Fig. 7
Fig. 7

The distortion of the fringes by the warming of the wire.

Equations (13)

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d = d 0 + α x ,
n λ = 2 d .
Δ ν ¯ = 1 2 d N ,
N = π R 1 - R .
β n = 2 π λ { 2 d n ( 1 - θ 2 2 ) - 4 3 d α 2 n 3 } .
Δ x θ 0 Δ x = 2 θ 0 2 d 0 λ .
β n = n β 0 - δ n 3 ,
β 0 = 2 π λ 2 d ,
δ = 8 π 3 λ d α 2 .
I = I 0 T 2 | n = 0 Re i n β 0 e - i δ n 3 | 2
e - i δ n 3 1 - i δ n 3 - δ 2 n 6 2 ,
8 π 3 λ d α 2 R n n 3 1 ,
n = 3 1 - R .

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