Abstract

The development of sharpened fringes in long path length interferometers (like the Twyman-Green, Mach-Zehnder, and series) by intensity and by multiple reflection is described. The cause of the extreme localization of some of the multiple-reflection fringe patterns is discussed.

© 1958 Optical Society of America

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References

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  1. S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, New York, 1948), p. 3.
  2. F. Twyman, Prism and Lens Making (Hilger & Watts Ltd., London, 1952), second edition p. 484.
  3. J. W. T. Walsh, Photometry (Constable and Company, London, 1953), second edition p. 62.
  4. G. Hansen, Physik. Z. 43, 15 (1942).
  5. D. Post, doctoral thesis, University of Illinois, Urbana, 1957. Also J. Opt. Soc. Am., (to be published).
  6. J. B. Saunders, J. Opt. Soc. Am. 44, 241 (1954); D. Post, J. Opt. Soc. Am. 44, 243 (1954).
    [CrossRef]
  7. J. Guild, Phys. Soc. (London) 33, 35 (1920).
  8. J. Brossel, Phys. Soc. (London) 59, 224 (1947).
    [CrossRef]
  9. Reference 1, Chap. 9.

1954 (1)

1947 (1)

J. Brossel, Phys. Soc. (London) 59, 224 (1947).
[CrossRef]

1942 (1)

G. Hansen, Physik. Z. 43, 15 (1942).

1920 (1)

J. Guild, Phys. Soc. (London) 33, 35 (1920).

Brossel, J.

J. Brossel, Phys. Soc. (London) 59, 224 (1947).
[CrossRef]

Guild, J.

J. Guild, Phys. Soc. (London) 33, 35 (1920).

Hansen, G.

G. Hansen, Physik. Z. 43, 15 (1942).

Post, D.

D. Post, doctoral thesis, University of Illinois, Urbana, 1957. Also J. Opt. Soc. Am., (to be published).

Saunders, J. B.

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, New York, 1948), p. 3.

Twyman, F.

F. Twyman, Prism and Lens Making (Hilger & Watts Ltd., London, 1952), second edition p. 484.

Walsh, J. W. T.

J. W. T. Walsh, Photometry (Constable and Company, London, 1953), second edition p. 62.

J. Opt. Soc. Am. (1)

Phys. Soc. (London) (2)

J. Guild, Phys. Soc. (London) 33, 35 (1920).

J. Brossel, Phys. Soc. (London) 59, 224 (1947).
[CrossRef]

Physik. Z. (1)

G. Hansen, Physik. Z. 43, 15 (1942).

Other (5)

D. Post, doctoral thesis, University of Illinois, Urbana, 1957. Also J. Opt. Soc. Am., (to be published).

S. Tolansky, Multiple-Beam Interferometry (Oxford University Press, New York, 1948), p. 3.

F. Twyman, Prism and Lens Making (Hilger & Watts Ltd., London, 1952), second edition p. 484.

J. W. T. Walsh, Photometry (Constable and Company, London, 1953), second edition p. 62.

Reference 1, Chap. 9.

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Figures (3)

Fig. 1
Fig. 1

Visual brightness of “cos2ϕ fringes” of three physical luminances [lower to upper: ( 4 / 3 ) L 0 1 2 = 0.1, 10, 100] adjusted by a factor to make the visual brightness at ϕ=0 the same.

Fig. 2
Fig. 2

The series interferometer.

Fig. 3
Fig. 3

Multiple reflection arrangement of the Mach-Zehnder (A), the fully compensated Twyman-Green (B), and the uncompensated Twyman-Green (C) interferometers; (a) totally reflecting mirror, (b) dielectric coated dividing plate, (c) compensating plate, (d) highly reflecting partially transmitting mirror.

Equations (10)

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Δ L / L = 0.02 [ ( 1 + 0.75 ( L ) 1 2 ]
0.02 Δ B = Δ L / L [ 1 + 0.75 ( L ) 1 2 ] ,
B = 10 2 ln [ 4 / 3 ( L ) 1 2 + 1 ] .
L = L 0 cos 2 ϕ ,
B = 10 2 ln [ 4 / 3 ( L 0 cos 2 ϕ ) 1 2 + 1 ] .
X = ( Δ T / Δ θ ) sin i .
δ = 2 ( n t 1 + T 1 ) cos i - 2 ( n t 2 + T 2 ) cos i ,
δ / i = - 2 Δ T sin i + 2 [ ( T 1 - T 2 ) / i ] cos i .
T 1 - T 2 = y 1 ( 1 + y 1 θ 1 tan i ) - y 2 ( 1 + y 2 θ 2 tan i ) ( T 1 - T 2 ) / i = ( y 1 2 θ 1 - y 2 2 θ 2 ) sec 2 i ,
δ / i = - 2 Δ T sin i + 2 ( y 1 2 θ 1 - y 2 2 θ 2 ) / cos i .