Abstract

A robust one-beam interferometer with external phase-delay control is described. The device resembles a Mach–Zehnder interferometer in which the two arms are together in one collimated beam. However, the proposed device is not an amplitude-division interferometer but a wave-front division one. The phase-delay control occurs at the interferometer output with the help of two polarizing beam splitters, a quarter-wave plate, a Faraday rotator, and a polarizer. An additional phase delay is introduced by application of an electrical current to the Faraday rotator or by rotation of the polarizer (the latter is of topological origin), which permits the use of techniques of phase-stepping interferometry.

© 1999 Optical Society of America

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References

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  1. H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
    [CrossRef] [PubMed]
  2. E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
    [CrossRef]
  3. K. Creath, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
    [CrossRef]
  4. E. Greivenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  5. G. N. Ramachandran and S. Ramaseshan, in Handbuch der Physik, S. Ramaseshan, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 7–11.
  6. M. V. Berry, Proc. Soc. London Ser. A 329, 45 (1984); J. Mod. Opt. 34, 1401 (1987).
    [CrossRef]
  7. G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
    [CrossRef]

1998 (1)

E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
[CrossRef]

1994 (1)

G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
[CrossRef]

1993 (1)

H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
[CrossRef] [PubMed]

1984 (1)

M. V. Berry, Proc. Soc. London Ser. A 329, 45 (1984); J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

Bao, N.

G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
[CrossRef]

Berry, M. V.

M. V. Berry, Proc. Soc. London Ser. A 329, 45 (1984); J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

Bruning, J. H.

E. Greivenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Chung, P. S.

G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
[CrossRef]

Creath, K.

K. Creath, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

Dultz, W.

E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
[CrossRef]

H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
[CrossRef] [PubMed]

Ferrari, J. A.

E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
[CrossRef]

Frins, E. M.

E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
[CrossRef]

Greivenkamp, E.

E. Greivenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

Jin, G.

G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
[CrossRef]

Klein, S.

H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
[CrossRef] [PubMed]

Ramachandran, G. N.

G. N. Ramachandran and S. Ramaseshan, in Handbuch der Physik, S. Ramaseshan, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 7–11.

Ramaseshan, S.

G. N. Ramachandran and S. Ramaseshan, in Handbuch der Physik, S. Ramaseshan, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 7–11.

Schmitzer, H.

H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
[CrossRef] [PubMed]

Opt. Eng. (1)

G. Jin, N. Bao, and P. S. Chung, Opt. Eng. 33, 2733 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

H. Schmitzer, S. Klein, and W. Dultz, Phys. Rev. Lett. 71, 1530 (1993).
[CrossRef] [PubMed]

Proc. Soc. London Ser. A (1)

M. V. Berry, Proc. Soc. London Ser. A 329, 45 (1984); J. Mod. Opt. 34, 1401 (1987).
[CrossRef]

Pure Appl. Opt. (1)

E. M. Frins, W. Dultz, and J. A. Ferrari, Pure Appl. Opt. 7, 53 (1998).
[CrossRef]

Other (3)

K. Creath, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
[CrossRef]

E. Greivenkamp and J. H. Bruning, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.

G. N. Ramachandran and S. Ramaseshan, in Handbuch der Physik, S. Ramaseshan, ed. (Springer-Verlag, Berlin, 1961), Vol. XXV/1, pp. 7–11.

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Figures (3)

Fig. 1
Fig. 1

One-beam interferometer: L, polarized He–Ne laser; SF, spatial filter; L1, collimating lens; PO, phase object; PBS’s, polarizing cube beam splitters; QW, λ/4-wave plate with its fast axis at 45° with respect to the polarization directions; FR, Faraday rotator; P, polarizer with its transmission direction at θ with respect to the fast axis of the λ/4-wave plate; CS, electrical current source; L2, lens that images PO onto output plane C (where the CCD camera is placed).

Fig. 2
Fig. 2

Experimental results: interferograms of butane gas flowing through a tube acquired with the polarizer at (a) θ=0°, (b) θ=45°, and (c) θ=90°. Clearly, the bright fringes of interferograms (a) and (c) are π (rad) shifted in phase.

Fig. 3
Fig. 3

Three-dimensional plot of phase profile of the gas flow, calculated with a three-frame algorithm.

Equations (2)

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Ix,y=I0x,y1+Vx,ycosϕx,y+ϕR+2θ,
ϕx,y=tan-1I2x,y-I3x,yI1x,y-I2x,y-π/4,

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