Abstract

The design, the construction, and the testing of a division-of-amplitude photopolarimeter (DOAP) introduced by Azzam [ Opt. Acta 29, 685 ( 1982); Opt. Acta 32, 767 ( 1985)] are described. The DOAP can perform time-resolved measurements of all four Stokes parameters of arbitrarily polarized light. The instrument was calibrated and tested at 632.8- and 1523-nm laser wavelengths. The mean deviations of the measured Stokes vectors from ideal polarization-state generator curves were less than 1% at 632.8 nm and less than 4% at 1523 nm. The larger deviations at 1523 nm resulted from larger imperfections in the quarter-wave plate used in the polarization-state generator. The results of instrument calibration methods introduced by Azzam et al. [ Rev. Sci. Instrum. 59, 84 ( 1988); J. Opt. Soc. Am. A 6, 1513 ( 1989)] are presented and discussed. The DOAP has been used to study light scattering by rough surfaces and to carry out conventional, generalized, and Mueller matrix ellipsometry.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
    [CrossRef]
  2. P. S. Hauge, “Techniques of measurement of the polarization-altering properties of linear optical systems,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 2–10 (1977).
    [CrossRef]
  3. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
    [CrossRef] [PubMed]
  4. R. M. A. Azzam, I. M. Elminyawi, A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
    [CrossRef]
  5. R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
    [CrossRef]
  6. R. M. A. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” Opt. Acta 32, 767–777 (1985).
    [CrossRef]
  7. M. R. Latta, S. L. Heesacker, “Measurement of polarization components using a four detector polarimeter,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 207–219 (1990).
    [CrossRef]
  8. K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
    [CrossRef]
  9. P. S. Hauge, “Survey of methods for the complete determination of the state of polarization,” in Polarized Light: Instruments, Devices, Applications, W. L. Hyde, R. M. A. Azzam, eds., Proc. Soc. Photo-Opt. Instrum. Eng.88, 3–10 (1976).
    [CrossRef]
  10. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chaps. 1–3.
  11. R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
    [CrossRef]
  12. R. M. A. Azzam, A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing elements,” J. Opt. Soc. Am. A 6, 1513–1521 (1989).
    [CrossRef]
  13. P. S. Hauge, “Mueller matrix ellipsometry with imperfect compensators,”J. Opt. Soc. Am. 68, 1519–1528 (1978).
    [CrossRef]
  14. R. M. A. Azzam, “Instrument matrix of the four-detector photopolarimeter: physical meaning of its rows and columns and constraints on its elements,” J. Opt. Soc. Am. A 7, 87–91 (1990).
    [CrossRef]
  15. D. F. Edwards, in Handbook of the Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), p. 565.
  16. D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
    [CrossRef]
  17. K. Vedam, S. S. So, “Characterization of real surfaces by ellipsometry,” Surf. Sci. 29, 379–395 (1972).
    [CrossRef]
  18. S. Krishnan, “Thermophysical and optical properties of electromagnetically levitated liquid metals,” Ph.D. dissertation (Rice University, Houston, Tex., 1988).
  19. S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).
  20. S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).
  21. S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
    [CrossRef]
  22. G. P. Hansen, S. Krishnan, R. H. Hauge, J. L. Margrave, “Ellipsometric method for the measurement of temperature and optical constants of incandescent transition metals,” Appl. Opt. 28, 1885–1896 (1989).
    [CrossRef] [PubMed]

1991 (2)

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

1990 (3)

R. M. A. Azzam, “Instrument matrix of the four-detector photopolarimeter: physical meaning of its rows and columns and constraints on its elements,” J. Opt. Soc. Am. A 7, 87–91 (1990).
[CrossRef]

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

1989 (2)

1988 (2)

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

R. M. A. Azzam, I. M. Elminyawi, A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[CrossRef]

1985 (2)

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” Opt. Acta 32, 767–777 (1985).
[CrossRef]

1982 (2)

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

1980 (1)

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

1978 (1)

1972 (1)

K. Vedam, S. S. So, “Characterization of real surfaces by ellipsometry,” Surf. Sci. 29, 379–395 (1972).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Instrument matrix of the four-detector photopolarimeter: physical meaning of its rows and columns and constraints on its elements,” J. Opt. Soc. Am. A 7, 87–91 (1990).
[CrossRef]

R. M. A. Azzam, A. G. Lopez, “Accurate calibration of the four-detector photopolarimeter with imperfect polarizing elements,” J. Opt. Soc. Am. A 6, 1513–1521 (1989).
[CrossRef]

R. M. A. Azzam, I. M. Elminyawi, A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[CrossRef]

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” Opt. Acta 32, 767–777 (1985).
[CrossRef]

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chaps. 1–3.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chaps. 1–3.

Brudzewski, K.

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

Edwards, D. F.

D. F. Edwards, in Handbook of the Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), p. 565.

Elminyawi, I. M.

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

R. M. A. Azzam, I. M. Elminyawi, A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[CrossRef]

El-Saba, A. M.

R. M. A. Azzam, I. M. Elminyawi, A. M. El-Saba, “General analysis and optimization of the four-detector photopolarimeter,” J. Opt. Soc. Am. A 5, 681–689 (1988).
[CrossRef]

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Hansen, G. P.

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

G. P. Hansen, S. Krishnan, R. H. Hauge, J. L. Margrave, “Ellipsometric method for the measurement of temperature and optical constants of incandescent transition metals,” Appl. Opt. 28, 1885–1896 (1989).
[CrossRef] [PubMed]

Hauge, P. S.

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

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

P. S. Hauge, “Techniques of measurement of the polarization-altering properties of linear optical systems,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 2–10 (1977).
[CrossRef]

P. S. Hauge, “Survey of methods for the complete determination of the state of polarization,” in Polarized Light: Instruments, Devices, Applications, W. L. Hyde, R. M. A. Azzam, eds., Proc. Soc. Photo-Opt. Instrum. Eng.88, 3–10 (1976).
[CrossRef]

Hauge, R. H.

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

G. P. Hansen, S. Krishnan, R. H. Hauge, J. L. Margrave, “Ellipsometric method for the measurement of temperature and optical constants of incandescent transition metals,” Appl. Opt. 28, 1885–1896 (1989).
[CrossRef] [PubMed]

Heesacker, S. L.

M. R. Latta, S. L. Heesacker, “Measurement of polarization components using a four detector polarimeter,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 207–219 (1990).
[CrossRef]

Krishnan, S.

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

G. P. Hansen, S. Krishnan, R. H. Hauge, J. L. Margrave, “Ellipsometric method for the measurement of temperature and optical constants of incandescent transition metals,” Appl. Opt. 28, 1885–1896 (1989).
[CrossRef] [PubMed]

S. Krishnan, “Thermophysical and optical properties of electromagnetically levitated liquid metals,” Ph.D. dissertation (Rice University, Houston, Tex., 1988).

Latta, M. R.

M. R. Latta, S. L. Heesacker, “Measurement of polarization components using a four detector polarimeter,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 207–219 (1990).
[CrossRef]

Lopez, A. G.

Margrave, J. L.

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

G. P. Hansen, S. Krishnan, R. H. Hauge, J. L. Margrave, “Ellipsometric method for the measurement of temperature and optical constants of incandescent transition metals,” Appl. Opt. 28, 1885–1896 (1989).
[CrossRef] [PubMed]

Masetti, E.

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Nordine, P. C.

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

Reed, R. A.

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

Schiffman, R. A.

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

So, S. S.

K. Vedam, S. S. So, “Characterization of real surfaces by ellipsometry,” Surf. Sci. 29, 379–395 (1972).
[CrossRef]

Vedam, K.

K. Vedam, S. S. So, “Characterization of real surfaces by ellipsometry,” Surf. Sci. 29, 379–395 (1972).
[CrossRef]

Weber, J. K. R.

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

Appl. Opt. (1)

High Temp. Sci. (2)

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical properties of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 29, 17–51 (1990).

S. Krishnan, G. P. Hansen, R. H. Hauge, J. L. Margrave, “Spectral emissivities and optical constants of electromagnetically levitated liquid metals as functions of temperature and wavelength,” High Temp. Sci. 26, 143–163 (1990).

J. Am. Ceram. Soc. (1)

S. Krishnan, J. K. R. Weber, R. A. Schiffman, P. C. Nordine, R. A. Reed, “Refractive index of liquid aluminum oxide at 0.6328 μm,”J. Am. Ceram. Soc. 74, 881–883 (1991).
[CrossRef]

J. Mod. Opt. (1)

K. Brudzewski, “Static Stokes ellipsometer: general analysis and optimization,” J. Mod. Opt. 38, 889–896 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Acta (2)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[CrossRef]

R. M. A. Azzam, “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” Opt. Acta 32, 767–777 (1985).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

R. M. A. Azzam, E. Masetti, I. M. Elminyawi, A. M. El-Saba, “Construction, calibration, and testing for a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988).
[CrossRef]

Surf. Sci. (2)

K. Vedam, S. S. So, “Characterization of real surfaces by ellipsometry,” Surf. Sci. 29, 379–395 (1972).
[CrossRef]

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[CrossRef]

Thin Solid Films (1)

D. E. Aspnes, “Optical properties of thin films,” Thin Solid Films 89, 249–262 (1982).
[CrossRef]

Other (6)

S. Krishnan, “Thermophysical and optical properties of electromagnetically levitated liquid metals,” Ph.D. dissertation (Rice University, Houston, Tex., 1988).

D. F. Edwards, in Handbook of the Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), p. 565.

P. S. Hauge, “Techniques of measurement of the polarization-altering properties of linear optical systems,” in Optical Polarimetry: Instrumentation and Applications, R. M. A. Azzam, D. L. Coffeen, eds., Proc. Soc. Photo-Opt. Instrum. Eng.112, 2–10 (1977).
[CrossRef]

P. S. Hauge, “Survey of methods for the complete determination of the state of polarization,” in Polarized Light: Instruments, Devices, Applications, W. L. Hyde, R. M. A. Azzam, eds., Proc. Soc. Photo-Opt. Instrum. Eng.88, 3–10 (1976).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chaps. 1–3.

M. R. Latta, S. L. Heesacker, “Measurement of polarization components using a four detector polarimeter,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1166, 207–219 (1990).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic of the DOAP instrument showing the various elements of the PSG, the PSD, and the electronics and computer interfaces.

Fig. 2
Fig. 2

Normalized Stokes parameters (a) S1, (b) S2, and (c) S3 measured by the DOAP (squares) and predicted for an ideal PSG (curves) shown as a function of the retarder fast axis. In these measurements the polarizer is fixed at P = 0, and the QWR fast axis is varied through 360° of azimuth. The calibration matrix of the DOAP was derived by using the 4P method. The measurements were carried out at a wavelength of 632.8 nm.

Fig. 3
Fig. 3

Normalized Stokes parameters (a) S1, (b) S2, and (c) S3 measured by the DOAP (squares) and predicted for an ideal PSG (curves) shown as a function of the retarder fast axis. In these measurements the polarizer is fixed at P = 0, and the QWR fast axis is varied through 360° of azimuth. The calibration matrix of the DOAP was derived by using the more accurate E–P method. The measurements were carried out at a wavelength of 632.8 nm.

Fig. 4
Fig. 4

Normalized Stokes parameters (a) S1 (b) S2, and (c) S3 measured by the DOAP (squares) and predicted for an ideal PSG (curves) shown as a function of the retarder fast axis. In these measurements the polarizer is fixed at P = 0, and the QWR fast axis is varied through 360° of azimuth. The calibration matrix of the DOAP was derived by using the more accurate E–P method. The measurements were carried out at a wavelength of 1523 nm.

Tables (2)

Tables Icon

Table 1 Lengths of the NPV’s for the DOAP

Tables Icon

Table 2 Deviations from Ideal PSG Curves at 632.8 and 1523 nm

Equations (20)

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

S 0 = I ,
S 1 = S 0 p cos ( 2 χ ) cos ( 2 α ) ,
S 2 = S 0 p cos ( 2 χ ) sin ( 2 α ) ,
S 3 = S 0 p sin ( 2 χ ) .
p = ( S 1 2 + S 2 2 + S 3 2 ) 1 / 2 S 0 ,
α = 1 2 tan - 1 ( S 2 S 1 ) ,
χ = 1 2 tan - 1 [ S 3 ( S 1 2 + S 2 2 ) 1 / 2 ] .
I = MS ,
S = M - 1 I .
S 0 = 1 ,
S 1 = ½ cos ( 2 P ) + ½ cos ( 4 C - 2 P ) ,
S 2 = ½ sin ( 2 P ) + ½ sin ( 4 C - 2 P ) ,
S 3 = sin ( 2 C - 2 P ) ,
I m = M S m ,
M = I m S m - 1 .
M 4 P = [ 1.0000 - 0.8123 - 0.2640 0.4034 0.8920 - 0.7109 0.2279 - 0.3198 0.7481 0.4966 - 0.5466 - 0.1160 0.7823 0.4889 0.5747 0.0879 ] .
M E - P = [ 1.0000 - 0.8132 - 0.2614 0.3857 0.8975 - 0.7183 0.2456 - 0.3342 0.7506 0.4841 - 0.5586 - 0.0953 0.7722 0.4735 0.5735 0.0859 ] .
M 1.523 μ m = [ 1.0000 - 0.6023 - 0.3785 0.5404 1.0438 - 0.6024 0.4108 - 0.5549 2.4882 1.3451 - 2.0779 - 0.1256 2.5428 1.2647 2.1810 0.1482 ] .
M n = ( M n 1 M n 0 , M n 2 M n 0 , M n 3 M n 0 )             for n = 0 , 1 , 2 , 3 ,
( M n 1 2 + M n 2 2 + M n 3 2 ) 1 / 2 M n 0             for n = 0 , 1 , 2 , 3.

Metrics