Abstract

An electro-optic modulator applied to a carrier frequency is used to measure the retardation of a wave plate. This method is not only suitable for any wave plate but also can be operated in real time.

© 1993 Optical Society of America

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References

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  1. H. Takasaki, “Photoelectric measurement of polarized light by means of an ADP polarization modulator,” J. Opt. Soc. Am. 51, 461–462 (1961).
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, p. 364.
  3. P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
    [CrossRef]
  4. D. C. Su, L. H. Shyu, “Phase shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
    [CrossRef]
  5. J. H. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 409–437.
  6. M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
    [CrossRef]
  7. H. G. Jerrard, “Optical compensators for measurement of elliptical polarization,” J. Opt. Soc. Am. 38, 35–59 (1948).
    [CrossRef]
  8. H. G. Jerrard, “Transmission of light through birefringent and optically active media: the Poincaré sphere,” J. Opt. Soc. Am. 44, 634–640 (1954).
    [CrossRef]
  9. R. C. Plumb, “Analysis of elliptically polarized light,” J. Opt. Soc. Am. 50, 892–894 (1960).
    [CrossRef]
  10. B. R. Grunstra, H. B. Perkins, “A method for the measurement of optical retardation angles near 90 degrees,” Appl. Opt. 5, 585–587 (1966).
    [CrossRef] [PubMed]
  11. C. M. Mclntyre, S. E. Harris, “Achromatic wave plates for the visible spectrum,” J. Opt. Soc. Am. 58, 1575–1580 (1968).
    [CrossRef]
  12. Y. Lin, Z. Zhou, R. Wang, “Optical heterodyne measurement of the phase retardation of a quarter-wave plate,” Opt. Lett. 13, 553–555 (1988).
    [CrossRef]
  13. H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
    [CrossRef]
  14. R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
    [CrossRef]
  15. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5, p. 121.

1991 (1)

D. C. Su, L. H. Shyu, “Phase shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

1988 (1)

1986 (2)

R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
[CrossRef]

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

1973 (2)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

1968 (1)

1966 (1)

1961 (1)

H. Takasaki, “Photoelectric measurement of polarized light by means of an ADP polarization modulator,” J. Opt. Soc. Am. 51, 461–462 (1961).

1960 (1)

1954 (1)

1948 (1)

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, p. 364.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, p. 364.

Bruning, J. H.

J. H. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 409–437.

Calvani, R.

R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
[CrossRef]

Caponi, R.

R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
[CrossRef]

Cisternino, F.

R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
[CrossRef]

Delisle, C.

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Dill, F. H.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Grunstra, B. R.

Harris, S. E.

Hauge, P. S.

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

Hazebroek, H. F.

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

Holscher, A. A.

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

Jerrard, H. G.

Kothiyal, M. P.

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Lin, Y.

Mclntyre, C. M.

Perkins, H. B.

Plumb, R. C.

Shyu, L. H.

D. C. Su, L. H. Shyu, “Phase shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

Su, D. C.

D. C. Su, L. H. Shyu, “Phase shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

Takasaki, H.

H. Takasaki, “Photoelectric measurement of polarized light by means of an ADP polarization modulator,” J. Opt. Soc. Am. 51, 461–462 (1961).

Wang, R.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5, p. 121.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5, p. 121.

Zhou, Z.

Appl. Opt. (1)

IBM J. Res. Dev. (1)

P. S. Hauge, F. H. Dill, “Design and operation of ETA, an automated ellipsometer,” IBM J. Res. Dev. 17, 472–489 (1973).
[CrossRef]

J. Lightwave Technol. (1)

R. Calvani, R. Caponi, F. Cisternino, “Real-time heterodyne fiber polarimetry with narrow- and broad-band sources,” J. Lightwave Technol. LT-4, 877–883 (1986).
[CrossRef]

J. Mod. Opt. (1)

D. C. Su, L. H. Shyu, “Phase shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Phys. E (1)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

Opt. Acta (1)

M. P. Kothiyal, C. Delisle, “Polarization component phase shifters in phase shifting interferometry: error analysis,” Opt. Acta 33, 787–793 (1986).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5, p. 121.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977), Chap. 5, p. 364.

J. H. Bruning, “Fringe scanning interferometers,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 409–437.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram for measuring the retardation of a wave plate: EO, electro-optic modulator; BS, beam splitter; W, tested wave plate; AN, analyzer; D, photodetector; ESPU, electronic signal processing unit.

Fig. 2
Fig. 2

Recorded signals without the tested quarter-wave plate: upper trace, external modulated signal; middle trace, reference signal; lower trace, test signal.

Fig. 3
Fig. 3

Recorded signals with the tested quarter-wave plate: upper trace, external modulated signal; middle trace, reference signal; lower trace, test signal.

Fig. 4
Fig. 4

Results of 10 points across the tested quarter-wave plate.

Equations (4)

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[ E r x E r y ] = [ 0 0 0 1 ] [ exp ( i ϕ x ) 0 0 exp ( i ϕ y ) ] × [ cos Γ 2 i sin Γ 2 i sin Γ 2 cos Γ 2 ] [ 1 0 ] = [ 0 i exp ( i ϕ y ) sin Γ 2 ] ,
[ E r x E r y ] = a exp ( i α ) [ 0 0 0 1 ] [ cos δ 2 i sin δ 2 i sin δ 2 cos δ 2 ] × [ cos Γ 2 i sin Γ 2 i sin Γ 2 cos Γ 2 ] [ 1 0 ] = a exp ( i α ) [ 0 i sin Γ + δ 2 ] ,
I r = 1 2 ( 1 cos Γ ) ,
I t = 1 2 a 2 [ 1 cos ( Γ + δ ) ] ,

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