Abstract

A type of shearing interferometry is presented in which a constant shear is introduced in the radial direction. For small shear, the interferogram displays the radial phase derivative of the wave front under test. The interferometer can be realized with axicon or circular-grating arrangements and seems useful for studying objects with cylindrical or circular geometry.

© 1971 Optical Society of America

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References

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  1. W. H. Steel, Interferometry (Cambridge University Press, Cambridge, England, 1967).
  2. O. Bryngdahl in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 37.
    [Crossref]
  3. P. Hariharan and D. Sen, J. Sci. Instr. 38, 428 (1961).
    [Crossref]
  4. J. H. McLeod, J. Opt. Soc. Am. 44, 592 (1954).
    [Crossref]
  5. W. N. Peters and A. M. Ledger, Appl. Opt. 9, 1435 (1970).
    [Crossref] [PubMed]
  6. O. Bryngdahl, J. Opt. Soc. Am. 60, 915 (1970).
    [Crossref]
  7. J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).
  8. O. Bryngdahl, J. Opt. Soc. Am. 58, 865 (1968).
    [Crossref]

1970 (2)

1968 (1)

1961 (1)

P. Hariharan and D. Sen, J. Sci. Instr. 38, 428 (1961).
[Crossref]

1958 (1)

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

1954 (1)

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Am. 60, 915 (1970).
[Crossref]

O. Bryngdahl, J. Opt. Soc. Am. 58, 865 (1968).
[Crossref]

O. Bryngdahl in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 37.
[Crossref]

Dyson, J.

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

Hariharan, P.

P. Hariharan and D. Sen, J. Sci. Instr. 38, 428 (1961).
[Crossref]

Ledger, A. M.

McLeod, J. H.

Peters, W. N.

Sen, D.

P. Hariharan and D. Sen, J. Sci. Instr. 38, 428 (1961).
[Crossref]

Steel, W. H.

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, England, 1967).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Sci. Instr. (1)

P. Hariharan and D. Sen, J. Sci. Instr. 38, 428 (1961).
[Crossref]

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

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

Other (2)

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, England, 1967).

O. Bryngdahl in Progress in Optics IV, edited by E. Wolf (North-Holland, Amsterdam, 1965), p. 37.
[Crossref]

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Figures (5)

F. 1
F. 1

Axicon configurations that introduce a variable (a) and a fixed (b) radial displacement in a wave front.

F. 2
F. 2

Circular-grating arrangement that splits up a wave front into two radially displaced wave fronts. The first diffraction order is separated from the zeroth order by internal reflection.

F. 3
F. 3

Circular-grating arrangement that splits up a wave front into two radially displaced wave fronts. The first diffraction order is separated from the zeroth order by blocking in a diffraction plane. Observe that in case the gratings are conventional ones, a lateral shearing interferometer is obtained.

F. 4
F. 4

Interferogram made by use of a shearing interferometer with a constant radial displacement between the wave fronts. Defects appear, owing to insufficient quality of the axicons used, especially at the center and the periphery. Ideally the background would consist of straight parallel fringes.

F. 5
F. 5

A conventional Mach–Zehnder-type interferogram of the same object as used in Fig. 4.

Equations (4)

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I = 1 16 | u ( r , φ ) + u ( r + Δ , φ ) | 2 .
I | exp { i ϕ ( r , φ ) } + exp { i ϕ ( r + Δ , φ ) } | 2 = 4 cos 2 1 2 { ϕ ( r + Δ , φ ) ϕ ( r , φ ) } .
ϕ ( r + Δ , φ ) ϕ ( r , φ ) = ( 2 p + 1 ) π ,
ϕ ( r + Δ , φ ) ϕ ( r , φ ) = Δ { d ϕ ( r , φ ) d r + θ 1 Δ d 2 ( r + θ 2 Δ , φ ) d r 2 } ,