Abstract

Measurements of the polarization effects in multimirror experiments by using a dual photoelastic modulator are described. The effect of single and multiple mirrors in polarization measurements in two and three dimensions is discussed, and experimental results show how symmetrical placement of mirrors in three-dimensional geometry can eliminate changes in the polarization. Calibration procedures for a dual photoelastic modulator and potential error sources such as misalignment of analyzer, signal dc offset, and neglect of aperture size are presented. Mirror-surface evolution and how it can disturb the polarization measurement are also addressed.

© 2005 Optical Society of America

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References

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  1. J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
    [CrossRef]
  2. F. M. Levinton, “The multichannel motional Stark effect diagnostic on TFTR,” Rev. Sci. Instrum. 63, 5157–5160 (1992).
    [CrossRef]
  3. D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
    [CrossRef]
  4. J. C. Canit, J. Badoz, “New design for a photoelastic modulator,” Appl. Opt. 22, 592–594 (1983).
    [CrossRef] [PubMed]
  5. B. Wang, J. List, R. Rockwell, “Stokes polarimeter using two photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 1–8 (2002).
    [CrossRef]
  6. M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
    [CrossRef]
  7. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 96–108.
  8. N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
    [CrossRef]
  9. PEM-90 Photoelastic Modulator System User Manual (Hinds Instruments, 1993).
  10. O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
    [CrossRef]
  11. D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
    [CrossRef]
  12. T. Oakberg, A. Bryan, “Detectors with photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 98–106 (2002).
    [CrossRef]
  13. B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
    [CrossRef]
  14. A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

2004 (1)

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

2002 (1)

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

1999 (1)

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

1995 (1)

D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
[CrossRef]

1992 (1)

F. M. Levinton, “The multichannel motional Stark effect diagnostic on TFTR,” Rev. Sci. Instrum. 63, 5157–5160 (1992).
[CrossRef]

1989 (1)

O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

1987 (1)

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

1983 (1)

1982 (1)

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Acher, O.

O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Badoz, J.

Bigan, E.

O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Blackler, K.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Bryan, A.

T. Oakberg, A. Bryan, “Detectors with photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 98–106 (2002).
[CrossRef]

Canit, J. C.

D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
[CrossRef]

J. C. Canit, J. Badoz, “New design for a photoelastic modulator,” Appl. Opt. 22, 592–594 (1983).
[CrossRef] [PubMed]

Dalby, J. L.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Drévillion, B.

O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

Drevillon, B.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Gaignebet, E.

D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
[CrossRef]

Hawkes, N.

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

Hawkes, N. C.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Henson, G. D.

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

Kaltchev, M.

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

Kemp, J. C.

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

Kuldkepp, M.

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

Levinton, F. M.

F. M. Levinton, “The multichannel motional Stark effect diagnostic on TFTR,” Rev. Sci. Instrum. 63, 5157–5160 (1992).
[CrossRef]

List, J.

B. Wang, J. List, R. Rockwell, “Stokes polarimeter using two photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 1–8 (2002).
[CrossRef]

Lotte, P.

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

Malaquias, A.

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

Marbot, R.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Migozzi, J. B.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Oakberg, T.

T. Oakberg, A. Bryan, “Detectors with photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 98–106 (2002).
[CrossRef]

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 96–108.

Perrin, J.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Powell, E. R.

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

Rachlew, E.

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

Rockwell, R.

B. Wang, J. List, R. Rockwell, “Stokes polarimeter using two photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 1–8 (2002).
[CrossRef]

Schunke, B.

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

Stacchiola, D.

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

Steiner, C. T.

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

Stratton, B. C.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Thompson, A. W.

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

Tugarinov, S.

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

Tysoe, W.

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

Viaccoz, B.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Violet, A.

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Voitsenya, V. S.

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

von Hellermann, M.

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

Wang, B.

B. Wang, J. List, R. Rockwell, “Stokes polarimeter using two photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 1–8 (2002).
[CrossRef]

Wilson, C. H.

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

Yang, D.

D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
[CrossRef]

Appl. Opt. (1)

J. Opt. (1)

D. Yang, J. C. Canit, E. Gaignebet, “Photoelastic modulator: polarization modulation and phase modulation,” J. Opt. 26, 151–159 (1995).
[CrossRef]

J. Vac. Sci. Technol. A. (1)

D. Stacchiola, A. W. Thompson, M. Kaltchev, W. Tysoe, “Photoelastic modulation-reflection absorption infrared spectroscopy of CO on Pd(111),” J. Vac. Sci. Technol. A. 20, 2101–2105 (2002).
[CrossRef]

Nature (1)

J. C. Kemp, G. D. Henson, C. T. Steiner, E. R. Powell, “The optical polarization of the Sun measured at a sensitivity of parts in ten million,” Nature 326, 270–273 (1987).
[CrossRef]

Rev. Sci. Instrum. (5)

F. M. Levinton, “The multichannel motional Stark effect diagnostic on TFTR,” Rev. Sci. Instrum. 63, 5157–5160 (1992).
[CrossRef]

M. Kuldkepp, E. Rachlew, N. Hawkes, B. Schunke, “First mirror contamination studies for polarimetry MSE measurements for ITER,” Rev. Sci. Instrum. 75, 3446–3448 (2004).
[CrossRef]

N. C. Hawkes, K. Blackler, B. Viaccoz, C. H. Wilson, J. B. Migozzi, B. C. Stratton, “Design of the Joint European Torus motional stark effect diagnostic,” Rev. Sci. Instrum. 70, 894–897 (1999).
[CrossRef]

O. Acher, E. Bigan, B. Drévillion, “Improvements of phase-modulated ellipsometry,” Rev. Sci. Instrum. 60, 65–77 (1989).
[CrossRef]

B. Drevillon, J. Perrin, R. Marbot, A. Violet, J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982).
[CrossRef]

Other (5)

A. Malaquias, M. von Hellermann, P. Lotte, S. Tugarinov, V. S. Voitsenya, “Polarization and reflectivity changes on mirror based viewing systems during long pulse operation,” in Thirtieth European Physical Society Conference on Plasma Physics, Europhysics Conference Abstracts, R. M. Pick, ed. (European Physical Society, 2003), Vol. 27A, O-3.4C.

T. Oakberg, A. Bryan, “Detectors with photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 98–106 (2002).
[CrossRef]

PEM-90 Photoelastic Modulator System User Manual (Hinds Instruments, 1993).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 96–108.

B. Wang, J. List, R. Rockwell, “Stokes polarimeter using two photoelastic modulators,” in Polarization Measurement, Analysis, and Applications V, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE4819, 1–8 (2002).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Response for the -, dc; …, first harmonic; - - -, second harmonic in the detected signal as a function of the operation point.

Fig. 2
Fig. 2

Experimental setup. All parts were fixed on an optical table, and the detector was shielded from background radiation.

Fig. 3
Fig. 3

Misinterpretation of the polarization angle as a function of the polarization angle for three misalignments of the analyzer: —, 0.1°; …, 0.4°; - - -, 0.7°.

Fig. 4
Fig. 4

Misinterpretation of the polarization angle as a function of the polarization angle for three different operation points of the second PEM: —, 2.8 rad; …, 2.9 rad; - - -, 3.0 rad. The first PEM is at operation point 3.05 rad.

Fig. 5
Fig. 5

Direct-current signal monitored when the light is completely blocked at 50 s.

Fig. 6
Fig. 6

Measured and fitted change in linear and circular polarization after a single reflection with an incidence angle of 45°: (a) Au and (b) Rh.

Fig. 7
Fig. 7

Measured input–output polarization difference after two gold mirrors with a 45° incidence angle. The reduction after a symmetry arrangement in three dimensions is clearly displayed.

Fig. 8
Fig. 8

Measurement of the peak angle difference of unexposed single mirrors: ▼, Au; ×, Rh; ■, SS; ●, Ag; ▲, Al.

Fig. 9
Fig. 9

Measurement of the PAD of exposed, ■, Al on stainless steel and, ▼, Al on stainless steel reference.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

S = [ I Q U V ] = [ I I × p × cos ( 2 × γ ) I × p × sin ( 2 × γ ) V ] ,
S = M × S ,
S = M x × M 3 × M 2 × M 1 × S = M tot × S .
M = [ A B 0 0 B A 0 0 0 0 C - D 0 0 D C ] , A = R s + R p 2 ,             B = R s - R p 2 , C = ( R s × R p ) 1 / 2 × cos ( φ p - φ s ) , D = ( R s × R p ) 1 / 2 × sin ( φ p - φ s ) .
I = I 2 + I × p × cos ( 2 × γ ) × cos ( A ) 2 × 2 + I × p × [ cos ( B ) 2 × 2 - sin ( A ) × sin ( B ) 2 × 2 ] × sin ( 2 × γ ) + V × [ cos ( B ) - sin ( A ) + cos ( A ) × sin ( B ) ] 2 × 2 ,
cos [ Z × cos ( ω × t ) ] = J 0 ( Z ) + 2 × n = 1 ( - 1 ) n × J 2 n ( Z ) × cos ( 2 n × ω × t ) , sin [ Z × cos ( ω × t ) ] = 2 × n = 1 ( - 1 ) n - 1 × J 2 n - 1 ( Z ) × cos [ ( 2 n - 1 ) × ω × t ] ,
γ = 1 2 arctan [ V 2 × ω 2 × J 2 ( A 0 ) V 2 × ω 1 × J 2 ( B 0 ) ] ,

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