Abstract

A brief review of radial shearing interferometers as well as a logical development of various types of these interferometers is presented. The discussion considers two types of interferometers. One type essentially introduces a radial shear in collimated light while in the other type a radial shear is introduced in converging light. Finally, a compact interferometer is described. This interferometer uses the Snell’s law of refraction for obtaining radial shear and consists of two identical prisms which make up a pentaprism. In one of the prisms, a hemispherical depression is made, and this is the basic element that introduces radial shear.

© 1964 Optical Society of America

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References

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  1. W. J. Bates, Proc. Phys. Soc. (London) B59, 940 (1947).
    [CrossRef]
  2. L. R. Baker, Proc. Phys. Soc. (London) B68, 871 (1955).
  3. D. S. Brown, Proc. Phys. Soc. (London) B67, 232 (1954).
  4. R. L. Drew, Proc. Phys. Soc. (London) B64, 1005 (1951).
  5. M. V. R. K. Murty, Appl. Opt. 3, 531(1964).
    [CrossRef]
  6. J. B. Saunders, J. Opt. Soc. Am. 52, 1314 (1962), Abstract WD 11.
  7. D. S. Brown, Interferometry, Symposium No. 11 at National Physical Laboratory, London, England, 1959 (Her Majesty’s Stationery Office, London, 1960), p. 253.
  8. P. Hariharan, D. Sen, Opt. Acta 9, 159 (1962).
    [CrossRef]

1964 (1)

1962 (2)

J. B. Saunders, J. Opt. Soc. Am. 52, 1314 (1962), Abstract WD 11.

P. Hariharan, D. Sen, Opt. Acta 9, 159 (1962).
[CrossRef]

1955 (1)

L. R. Baker, Proc. Phys. Soc. (London) B68, 871 (1955).

1954 (1)

D. S. Brown, Proc. Phys. Soc. (London) B67, 232 (1954).

1951 (1)

R. L. Drew, Proc. Phys. Soc. (London) B64, 1005 (1951).

1947 (1)

W. J. Bates, Proc. Phys. Soc. (London) B59, 940 (1947).
[CrossRef]

Baker, L. R.

L. R. Baker, Proc. Phys. Soc. (London) B68, 871 (1955).

Bates, W. J.

W. J. Bates, Proc. Phys. Soc. (London) B59, 940 (1947).
[CrossRef]

Brown, D. S.

D. S. Brown, Proc. Phys. Soc. (London) B67, 232 (1954).

D. S. Brown, Interferometry, Symposium No. 11 at National Physical Laboratory, London, England, 1959 (Her Majesty’s Stationery Office, London, 1960), p. 253.

Drew, R. L.

R. L. Drew, Proc. Phys. Soc. (London) B64, 1005 (1951).

Hariharan, P.

P. Hariharan, D. Sen, Opt. Acta 9, 159 (1962).
[CrossRef]

Murty, M. V. R. K.

Saunders, J. B.

J. B. Saunders, J. Opt. Soc. Am. 52, 1314 (1962), Abstract WD 11.

Sen, D.

P. Hariharan, D. Sen, Opt. Acta 9, 159 (1962).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. B. Saunders, J. Opt. Soc. Am. 52, 1314 (1962), Abstract WD 11.

Opt. Acta (1)

P. Hariharan, D. Sen, Opt. Acta 9, 159 (1962).
[CrossRef]

Proc. Phys. Soc. (London) (4)

W. J. Bates, Proc. Phys. Soc. (London) B59, 940 (1947).
[CrossRef]

L. R. Baker, Proc. Phys. Soc. (London) B68, 871 (1955).

D. S. Brown, Proc. Phys. Soc. (London) B67, 232 (1954).

R. L. Drew, Proc. Phys. Soc. (London) B64, 1005 (1951).

Other (1)

D. S. Brown, Interferometry, Symposium No. 11 at National Physical Laboratory, London, England, 1959 (Her Majesty’s Stationery Office, London, 1960), p. 253.

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Figures (12)

Fig. 1
Fig. 1

Diagram showing the difference between the lateral and radial shearing of a wavefront.

Fig. 2
Fig. 2

Schematic block diagram showing the two situations of radial shearing interferometry in collimated and divergent light.

Fig. 3
Fig. 3

Schematic diagram showing the use of two identical telescopic systems in a Mach-Zehnder interferometer to obtain radial shear in collimated light.

Fig. 4
Fig. 4

Schematic diagram showing the use of a telescopic system in a cyclical interferometer to obtain radial shear in collimated light.

Fig. 5
Fig. 5

Schematic diagram showing the use of two identical positive lenses in a Mach-Zehnder interferometer to obtain radial shear in divergent light.

Fig. 6
Fig. 6

Schematic diagram showing the use of two positive lenses in a cyclical interferometer to obtain radial shear in divergent light.

Fig. 7
Fig. 7

Diagram showing the contracting and the expanding of the numerical aperture of a spherical wavefront by a hemispherical lens.

Fig. 8
Fig. 8

Schematic diagram showing the use of two identical hemispherical lenses in a Mach-Zehnder interferometer to obtain radial shear in divergent light.

Fig. 9
Fig. 9

Schematic diagram showing the use of a single hemispherical lens in a cyclical interferometer to obtain radial shear in divergent light.

Fig. 10
Fig. 10

Schematic diagram showing the solid version of Fig. 9. The interferometer consists of two half pentaprisms in one of which a hemispherical depression is made.

Fig. 11
Fig. 11

A photograph of fringe system obtained when a good lens is tested using the interferometer shown in Fig. 10. A slight tilt is included between the interfering wavefronts to obtain straight fringes.

Fig. 12
Fig. 12

A photograph of the fringe system obtained with the lens off-axis in the interferometer shown in Fig. 10. The presence of coma is easily seen in the interferogram.

Equations (7)

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W ( x + Δ x , y + Δ y ) W ( x , y ) Δ x W x + Δ y W y = n λ,
W ( R , ϕ ) = A R i cos j ϕ .
W e = A ( r S e r max ) i cos j ϕ ,
W c = A ( r S c r max ) i cos j ϕ .
W c W e = A cos j ϕ [ ( r S c r max ) i ( r S e r max ) i ] .
r = R r max S c ,
W c W e = A ( 1 S c i S e i ) R i cos j ϕ .

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