Abstract

The realization of a standard device for measuring phase retardance has been retarded by the lack of a simple underlying physical concept that can be formulated in a simple mathematical expression to provide quick, direct, and accurate results. A proposed device that meets these requirements and simple formulas for retardance measurements are presented.

© 2000 Optical Society of America

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References

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  1. H. G. Jerrard, “The calibration of quarter-wave plates,” J. Opt. Soc. Am. 42, 159–165 (1952).
    [CrossRef]
  2. J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), Chap. 10, pp. 129–140.
  3. W. G. Oldham, “Ellipsometry using a retardation plate as compensator,” J. Opt. Soc. Am. 57, 617–624 (1967).
    [CrossRef]
  4. F. L. McCrackin, “Analyses and corrections of instrumental errors in ellipsometry,” J. Opt. Soc. Am. 60, 57–63 (1970).
    [CrossRef]
  5. Kh. K. Aben, “Phase plates in the measurement of phase difference,” Opt. Spectrosc. (USSR) 14, 124–127 (1963).
  6. D. A. Holmes, D. L. Feucht, “Formulas for using wave plates in ellipsometry,” J. Opt. Soc. Am. 57, 466–472 (1967).
    [CrossRef] [PubMed]
  7. J. A. Johnson, N. M. Bashara, “General equations of symmetrical ellipsometer arrangements,” J. Opt. Soc. Am. 60, 221–224 (1970).
    [CrossRef]
  8. W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), pp. 165–170.
  9. M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
    [CrossRef]
  10. K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” (National Institute of Standards and Technology, Boulder, Colo., 1996).

1998 (1)

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

1970 (2)

1967 (2)

1963 (1)

Kh. K. Aben, “Phase plates in the measurement of phase difference,” Opt. Spectrosc. (USSR) 14, 124–127 (1963).

1952 (1)

Aben, Kh. K.

Kh. K. Aben, “Phase plates in the measurement of phase difference,” Opt. Spectrosc. (USSR) 14, 124–127 (1963).

Bashara, N. M.

Bennett, H. E.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), Chap. 10, pp. 129–140.

Bennett, J. M.

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), Chap. 10, pp. 129–140.

El-Bahrawi, M. S.

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

Feucht, D. L.

Holmes, D. A.

Jerrard, H. G.

Johnson, J. A.

Khodier, S. A.

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

McCrackin, F. L.

Nagib, N. N.

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

Oldham, W. G.

Rochford, K. B.

K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” (National Institute of Standards and Technology, Boulder, Colo., 1996).

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), pp. 165–170.

Sidki, H. M.

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

Wang, C. M.

K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” (National Institute of Standards and Technology, Boulder, Colo., 1996).

J. Opt. Soc. Am. (5)

Opt. Laser Technol. (1)

M. S. El-Bahrawi, N. N. Nagib, S. A. Khodier, H. M. Sidki, “Birefringence of muscovite mica,” Opt. Laser Technol. 30, 411–415 (1998).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

Kh. K. Aben, “Phase plates in the measurement of phase difference,” Opt. Spectrosc. (USSR) 14, 124–127 (1963).

Other (3)

W. A. Shurcliff, Polarized Light (Harvard U. Press, Cambridge, Mass., 1962), pp. 165–170.

K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” (National Institute of Standards and Technology, Boulder, Colo., 1996).

J. M. Bennett, H. E. Bennett, “Polarization,” in Handbook of Optics, W. G. Driscoll, ed. (McGraw-Hill, New York, 1978), Chap. 10, pp. 129–140.

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Figures (1)

Fig. 1
Fig. 1

Orientations of the optical elements.

Equations (21)

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ExEy=1/210 0exp-iδ2×1+exp-iδ11-exp-iδ11-exp-iδ11+exp-iδ1cos psin p,
Ex=1/2cos p+sin p+cos p-sin pexp-iδ1,
Ey=1/2cos p+sin p-cos p-sin pexp-iδ1exp-iδ2.
-tan ae=cos pe+sin pe+cos pe-sin peexp-iδ1expiδ2/cos pe+sin pe-cos pe-sin peexp-iδ1=tanpe+45+exp-iδ1expiδ2/tanpe+45-exp-iδ1.
exp-2iδ1+tanp1+45-tanp2+45tan a2+tan a1/tan a2-tan a1exp-iδ1-tanp1+45tanp2+45=0.
exp2iδ2+tan a1-tan a2tanp1+45+tanp2+45/tanp1+45-tanp2+45expiδ2-tan a1 tan a2=0.
tanp1+45tanp2+45=-1,
tan a1 tan a2=-1,
cos δ1=-1/2tanp1+45-tanp2+45tan a2+tan a1/tan a2-tan a1=-cos 2a1/cos 2p1
=-cos 2a2/cos 2p2,
cos δ2=-1/2tan a1-tan a2tanp1+45+tanp2+45/tanp1+45-tanp2+45=-sin 2p1/sin 2a1
=-sin 2p2/sin 2a2.
-π/2pπ/2, -π/2aπ/2.
cotp1+45exp-iδ1=tan a1 exp-iδ2+1/tan a1 exp-iδ2-1.
tan δ1=tan 2a1 sin δ2
=tan 2a2 sin δ2.
tan δ2=cot 2p1 sin δ1
=cot 2p2 sin δ1.
p0=45-p1,p0=45-p2.
δ2=cos-1-sin 2p1/sin 2a1,
δ2=2π-cos-1-sin 2p1/sin 2a1.

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