Abstract

A technique to measure linear diattenuation and retardance spectra of infrared materials in transmission is described. A sample is rotated between two stationary linear polarizers in the sample compartment of a Fourier transform infrared spectrometer. The intensity modulation that results from the rotation of the sample is Fourier analyzed, and the linear diattenuation and linear retardance of the sample are calculated from the Fourier series coefficients for each wavelength. The advantages of this technique include immunity of the measurement to instrumental polarization, to circular diattenuation, and to circular retardance. The rotating sample polarimeter does not require retarders. Compensation for systematic errors from polarizers with diattenuation less than one is included in the data reduction. This technique is useful for the calibration of retarders and polarizers and hence for the bootstrap calibration of more elaborate polarimeters such as Mueller matrix polarimeters. We present as an example of the technique the caliration spectra 3–14 μm of an infrared quasi-achromatic retarder whose fast axis orientation oscillates with wavelength.

© 1993 Optical Society of America

Full Article  |  PDF Article

Corrections

David B. Chenault and Russell A. Chipman, "Measurements of linear diattenuation and linear retardation spectra with a rotating sample spectropolarimeter: erratum," Appl. Opt. 33, 1145-1145 (1994)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-33-7-1145

References

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  1. C. Warde, U. Efron, “Guest editorial: materials and devices for optical information processing,” Opt. Eng. 25, 197 (1986).
  2. A. A. Ballman, R. L. Byer, D. Eimerl, R. S. Feigelson, B. J. Feldman, L. S. Goldberg, N. Menyuk, C. L. Tang, “Research on nonlinear optical materials: an assessment. V. Inorganic materials for frequency conversion,” Appl. Opt. 26, 224–227 (1987).
    [Crossref] [PubMed]
  3. D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).
  4. D. B. Chenault, R. A. Chipman, “Infrared spectropolarimetry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 254–266 (1989).
  5. D. B. Chenault, R. A. Chipman, K. M. Johnson, D. Doroski, “Infrared linear diattenuation and birefringence spectra of ferroelectric liquid crystals,” Opt. Lett. 17, 447–449 (1992).
    [Crossref] [PubMed]
  6. R. M. A. Azzam, “NIRSE: Normal-incidence rotating-sample ellipsometer,” Opt. Commun. 20, 405–408 (1977).
    [Crossref]
  7. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
    [Crossref] [PubMed]
  8. R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizers and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
    [Crossref]
  9. P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
    [Crossref]
  10. D. E. Aspnes, “Photometric ellipsometer for measuring partially polarized light,” J. Opt. Soc. Am. 65, 1274–1278 (1975).
    [Crossref]
  11. P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” in Proceedings of the Fourth International Conference on Ellipsometry, R. H. Muller, R. M. A. Azzam, D. E. Aspnes, eds. (North-Holland, Amsterdam, 1980).
  12. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  13. D. H. Goldstein, R. A. Chipman, “Error analysis of Mueller matrix polarimeters,” J. Opt. Soc. Am. A 7, 693–700 (1990).
    [Crossref]
  14. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
    [Crossref]
  15. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  16. S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).
  17. D. S. Kliger, J. S. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).
  18. R. A. Chipman, “Polarimetric impulse response and polarimetric transfer function for time-sequential polarimeters,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1317, 223–241 (1990).
  19. R. A. Chipman, D. B. Chenault, “Infrared achromatic retarder,” U.S. Patent4, 961, 634 (9October1990).
  20. I. Filinski, T. Skettrup, “Achromatic optical compensator-modulator,” Appl. Opt. 28, 1720–1726 (1989).
    [Crossref] [PubMed]
  21. V. Chandrasekharan, H. Demany, “Birefringence of sapphire, magnesium fluoride, and quartz in the vacuum ultraviolet, and retardation plates,” Appl. Opt. 7, 939–941 (1968).
    [Crossref] [PubMed]
  22. P. D. Hale, G. W. Day, “Stability of birefringent retarders,” Appl. Opt. 27, 5146–5153 (1988).
    [Crossref] [PubMed]

1992 (1)

1990 (1)

1989 (3)

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

I. Filinski, T. Skettrup, “Achromatic optical compensator-modulator,” Appl. Opt. 28, 1720–1726 (1989).
[Crossref] [PubMed]

1988 (1)

1987 (1)

1986 (1)

C. Warde, U. Efron, “Guest editorial: materials and devices for optical information processing,” Opt. Eng. 25, 197 (1986).

1978 (3)

1977 (1)

R. M. A. Azzam, “NIRSE: Normal-incidence rotating-sample ellipsometer,” Opt. Commun. 20, 405–408 (1977).
[Crossref]

1975 (2)

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[Crossref]

D. E. Aspnes, “Photometric ellipsometer for measuring partially polarized light,” J. Opt. Soc. Am. 65, 1274–1278 (1975).
[Crossref]

1968 (1)

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizers and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[Crossref]

R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2, 148–150 (1978).
[Crossref] [PubMed]

R. M. A. Azzam, “NIRSE: Normal-incidence rotating-sample ellipsometer,” Opt. Commun. 20, 405–408 (1977).
[Crossref]

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

Ballman, A. A.

Bashara, N. M.

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

Byer, R. L.

Chandrasekharan, V.

Chenault, D. B.

D. B. Chenault, R. A. Chipman, K. M. Johnson, D. Doroski, “Infrared linear diattenuation and birefringence spectra of ferroelectric liquid crystals,” Opt. Lett. 17, 447–449 (1992).
[Crossref] [PubMed]

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).

D. B. Chenault, R. A. Chipman, “Infrared spectropolarimetry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 254–266 (1989).

R. A. Chipman, D. B. Chenault, “Infrared achromatic retarder,” U.S. Patent4, 961, 634 (9October1990).

Chipman, R. A.

D. B. Chenault, R. A. Chipman, K. M. Johnson, D. Doroski, “Infrared linear diattenuation and birefringence spectra of ferroelectric liquid crystals,” Opt. Lett. 17, 447–449 (1992).
[Crossref] [PubMed]

D. H. Goldstein, R. A. Chipman, “Error analysis of Mueller matrix polarimeters,” J. Opt. Soc. Am. A 7, 693–700 (1990).
[Crossref]

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

D. B. Chenault, R. A. Chipman, “Infrared spectropolarimetry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 254–266 (1989).

R. A. Chipman, “Polarimetric impulse response and polarimetric transfer function for time-sequential polarimeters,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1317, 223–241 (1990).

R. A. Chipman, D. B. Chenault, “Infrared achromatic retarder,” U.S. Patent4, 961, 634 (9October1990).

Day, G. W.

Demany, H.

Dill, F. H.

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[Crossref]

Doroski, D.

Efron, U.

C. Warde, U. Efron, “Guest editorial: materials and devices for optical information processing,” Opt. Eng. 25, 197 (1986).

Eimerl, D.

Feigelson, R. S.

Feldman, B. J.

Filinski, I.

Goldberg, L. S.

Goldstein, D. H.

D. H. Goldstein, R. A. Chipman, “Error analysis of Mueller matrix polarimeters,” J. Opt. Soc. Am. A 7, 693–700 (1990).
[Crossref]

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).

Hale, P. D.

Hauge, P. S.

P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,” J. Opt. Soc. Am. 68, 1519–1528 (1978).
[Crossref]

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[Crossref]

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” in Proceedings of the Fourth International Conference on Ellipsometry, R. H. Muller, R. M. A. Azzam, D. E. Aspnes, eds. (North-Holland, Amsterdam, 1980).

Johnson, K. M.

Kliger, D. S.

D. S. Kliger, J. S. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Lewis, J. S.

D. S. Kliger, J. S. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Lipson, H.

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

Lipson, S. G.

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

Menyuk, N.

Randall, C. E.

D. S. Kliger, J. S. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Skettrup, T.

Tang, C. L.

Warde, C.

C. Warde, U. Efron, “Guest editorial: materials and devices for optical information processing,” Opt. Eng. 25, 197 (1986).

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

R. M. A. Azzam, “NIRSE: Normal-incidence rotating-sample ellipsometer,” Opt. Commun. 20, 405–408 (1977).
[Crossref]

R. M. A. Azzam, “A simple Fourier photopolarimeter with rotating polarizers and analyzer for measuring Jones and Mueller matrices,” Opt. Commun. 25, 137–140 (1978).
[Crossref]

P. S. Hauge, F. H. Dill, “A rotating-compensator Fourier ellipsometer,” Opt. Commun. 14, 431–437 (1975).
[Crossref]

Opt. Eng. (3)

D. H. Goldstein, R. A. Chipman, D. B. Chenault, “Infrared spectropolarimetry,” Opt. Eng. 28, 120–125 (1989).

C. Warde, U. Efron, “Guest editorial: materials and devices for optical information processing,” Opt. Eng. 25, 197 (1986).

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Opt. Lett. (2)

Other (7)

D. B. Chenault, R. A. Chipman, “Infrared spectropolarimetry,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 254–266 (1989).

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” in Proceedings of the Fourth International Conference on Ellipsometry, R. H. Muller, R. M. A. Azzam, D. E. Aspnes, eds. (North-Holland, Amsterdam, 1980).

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

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

D. S. Kliger, J. S. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

R. A. Chipman, “Polarimetric impulse response and polarimetric transfer function for time-sequential polarimeters,” in Polarimetry: Radar, Infrared, Visible, Ultraviolet, and X-Ray, R. A. Chipman, J. W. Morris, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1317, 223–241 (1990).

R. A. Chipman, D. B. Chenault, “Infrared achromatic retarder,” U.S. Patent4, 961, 634 (9October1990).

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Figures (6)

Fig. 1
Fig. 1

Rotating sample polarimeter configuration. The sample rotates between two fixed linear polarizers.

Fig. 2
Fig. 2

Fourier transform infrared spectropolarimeter. The polarimeter of Fig. 1 is located in the sample compartment.

Fig. 3
Fig. 3

Configuration of the achromatic retarder. The angle between the fast axes of the two plates is ideally 90°.

Fig. 4
Fig. 4

Retardance as a function of wavelength for the multiple-plate achromatic retarder.

Fig. 5
Fig. 5

Diattenuation spectrum of the multiple-plate achromatic retarder.

Fig. 6
Fig. 6

Orientation of the fast axis as a function of wavelength of the achromatic retarder. The fast axes of the two plates are misaligned by approximately 7°.

Tables (1)

Tables Icon

Table 1 Comparison of the Rotating Sample Polarimeter to Rotating Retarder Polarimeters

Equations (11)

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M s = 1 2 ( k 1 + k 2 k 1 k 2 0 0 k 1 k 2 k 1 + k 2 0 0 0 0 2 k 1 k 2 cos δ 2 k 1 k 2 sin δ 0 0 2 k 1 k 2 sin δ 2 k 1 k 2 cos δ ) = τ s ( 1 D 0 0 D 1 0 0 0 0 1 D 2 cos δ 1 D 2 sin δ 0 0 1 D 2 sin δ 1 D 2 cos δ ) ,
D = k 1 k 2 k 1 + k 2 , τ s 1 2 ( k 1 + k 2 )
M sys = M p 2 ( D 2 ) R ( θ ) M s R ( θ ) M p 1 ( D 1 ) = A 2 ( 1 D 2 0 0 D 2 1 0 0 0 0 1 D 2 2 0 0 0 0 1 D 2 2 ) ( 1 0 0 0 0 cos 2 θ sin 2 θ 0 0 sin 2 θ cos 2 θ 0 0 0 0 1 ) × A s ( 1 D 0 0 D 1 0 0 0 0 1 D 2 cos δ 1 D 2 sin δ 0 0 1 D 2 sin δ 1 D 2 cos δ ) × ( 1 0 0 0 0 cos 2 θ sin 2 θ 0 0 sin 2 θ cos 2 θ 0 0 0 0 1 ) A 1 ( 1 D 1 0 0 D 1 1 0 0 0 0 1 D 1 2 0 0 0 0 1 D 1 2 ) ,
S = M sys S inc .
I ( θ ) = τ [ 1 + ½ D 1 D 2 ( 1 + 1 D 2 cos δ ) + D ( D 1 + D 2 ) cos 2 θ + ½ D 1 D 2 ( 1 1 D 2 cos δ ) cos 4 θ ] = τ ( a 0 + a 2 cos 2 θ + a 4 cos 4 θ ) .
D = a 2 a 0 + a 4 ( 1 + D 1 D 2 D 1 + D 2 ) ,
δ = cos 1 { a 0 a 4 ( 1 + 2 D 1 D 2 ) [ ( a 0 + a 4 ) 2 a 2 2 ( 1 + D 1 D 2 D 1 + D 2 ) 2 ] 1 / 2 } .
I ( θ n ) = b 0 2 + k = 1 K ( b k cos k θ n + c k sin k θ n ) = a 0 2 + k = 1 K a k cos ( k θ n k ϕ k ) ,
ϕ k = 1 k arctan ( c k b k ) .
D k 1 × k 2 k 1 + k 2 ,
k 1 k 2 = 1 + D 1 D .

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