Abstract

The wavefronts are rotated or reversed with respect to each other when a plane mirror is used in one beam and a cube-corner prism or a right-angle prism is used in the second beam of a Twyman–Green interferometer. The purpose of this paper is to explore the conditions under which fringes of equal thickness could be obtained. This is related to the spatial coherence of the collimated beam incident on the beam splitter. Use of a gas laser source is discussed.

© 1964 Optical Society of America

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References

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  1. F. Twyman, Prism and Lens Making (Hilger and Watts Ltd., London, 1957), 2nd ed., 2nd Impression, p. 447.
  2. M. V. R. K. Murty, J. Opt. Soc. Am. 50, 83 (1960).
    [Crossref]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., London, 1959), p. 508.
  4. P. Hariharan and D. Sen, J. Opt. Soc. Am. 51, 1307 (1961).
    [Crossref]

1961 (1)

1960 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., London, 1959), p. 508.

Hariharan, P.

Murty, M. V. R. K.

Sen, D.

Twyman, F.

F. Twyman, Prism and Lens Making (Hilger and Watts Ltd., London, 1957), 2nd ed., 2nd Impression, p. 447.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., London, 1959), p. 508.

J. Opt. Soc. Am. (2)

Other (2)

F. Twyman, Prism and Lens Making (Hilger and Watts Ltd., London, 1957), 2nd ed., 2nd Impression, p. 447.

M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., London, 1959), p. 508.

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Figures (6)

F. 1
F. 1

Schematic diagram for testing a right-angle prism on a Twyman–Green interferometer. S: source; L1: collimating lens; L2: focusing lens; BS: beam splitter; M: plane mirrors; P: right-angle prism; E: eye position. Inset at lower left shows a typical appearance of the fringes when the right angle is in slight error. Inset at upper right shows the method of reversing one beam left to right by the right-angle prism.

F. 2
F. 2

Typical appearance of the fringes in the interferometer when all the angles of the cube-corner are in error by the same amount.

F. 3
F. 3

Illustration of variation and phase reversal of the degree of coherence with a circular source.

F. 4
F. 4

Illustration of variation and phase reversal of the degree of coherence with a slit source. A: the right angle is exact; B: the right angle is in slight error.

F. 5
F. 5

Interference pattern obtained with the scheme shown in Fig. 1 (inset at upper right) using a right-angle prism in one beam. The slit size is so chosen that the first few zeros of the coherence function sinν/ν are within the aperture.

F. 6
F. 6

Schematic diagram showing the method of changing the spatial coherence in the light emerging from a gas laser source. GL:He–Ne visible gas laser; O: microscope objective, movable along the beam to change the degree of spatial coherence; G: ground glass rotating in its own plane.

Equations (7)

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μ = 2 J 1 ( ν ) / ν ,
ν = 4 π α r / λ ¯ .
ν = 4 π α r / λ ¯ = 3.83 ,
2 α = 1.22 ( λ ¯ / 2 r ) .
μ = sin ν / ν ,
ν = 4 π α r / λ ¯ = π ,
2 α = ( λ ¯ / 2 r ) .