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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 6, Iss. 10 — Oct. 1, 1989
  • pp: 1513–1521

Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements

R. M. A. Azzam and Ali G. Lopez  »View Author Affiliations

JOSA A, Vol. 6, Issue 10, pp. 1513-1521 (1989)

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The first three columns of the instrument matrix A of the four-detector photopolarimeter (FDP) are determined by Fourier analysis of the output current vector I(P) as a function of the azimuth angle P of the incident linearly polarized light. Therefore 12 of the 16 elements of A are measured free of the imperfections of the (absent) quarter-wave retarder (QWR). The effect of angular beam deviation by the polarizer is compensated for by taking the average, (1/2) [I(P) + I(P + 180°)], of the FDP output at 180°-apart, optically equivalent, angular positions of the polarizer. The remaining fourth column of A is determined by the FDP’s response to the right- and left-handed circular polarization states. Because these states are impossible to generate with an imperfect QWR, a novel procedure is developed. In particular, the response of the FDP to the unattainable right- or left-handed circular polarization state is found by taking the average of the responses of the FDP to an elliptical near-circular state and that state rotated in azimuth by 90°. This calibration scheme is applied to measure A of our prototype FDP of four Si detectors at λ = 632.8 nm. A is determined, in external and internal reference frames, free of imperfections in the polarizing optical elements. The FDP, with its uncontaminated A matrix, is used subsequently to evaluate the imperfections of the QWR with the help of an appropriate model.

© 1989 Optical Society of America

Original Manuscript: February 8, 1989
Manuscript Accepted: April 11, 1989
Published: October 1, 1989

R. M. A. Azzam and Ali G. Lopez, "Accurate calibration of the four-detector photopolarimeter with imperfect polarizing optical elements," J. Opt. Soc. Am. A 6, 1513-1521 (1989)

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  1. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985); U.S. Patent4,681,450 (July21, 1987). [CrossRef] [PubMed]
  2. R. M. A. Azzam, E. Masetti, I. M. Elminyawi, F. G. Grosz, “Construction, calibration, and testing of a four-detector photopolarimeter,” Rev. Sci. Instrum. 59, 84–88 (1988). [CrossRef]
  3. 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]
  4. See, for example, M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), p. 554.
  5. The FDP has also been calibrated and operated at several other wavelengths in the visible spectrum by using a filtered continuum light source. See A. G. Lopez, R. M. A. Azzam, “Four-detector photopolarimeter (FDP): precision analysis and low-light-level measurements,” in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), p. 181.
  6. R. M. A. Azzam, “Stationary property of normal-incidence reflection from isotropic surfaces,”J. Opt. Soc. Am. 72, 1187–1189 (1982). [CrossRef]
  7. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  8. The effect of angular beam derivation of the QWR and by the polarizer is also compensated for by taking the average of four readings of the output current vector I of the FDP corresponding to four optically equivalent settings of the two elements. These settings are obtained by rotating each element by 180° from a given position, so that I= (1/4)[I(P, C) + I(P+ 180°, C) + I(P, C+ 180°) + I(P+ 180°, C+ 180°)]. This average is a generalization of that indicated by Eq. (9) for the case in which the polarizer alone is used.
  9. R. M. A. Azzam, N. M. Bashara, “Ellipsometry with imperfect components including incoherent effects,”J. Opt. Soc. Am. 61, 1380–1391 (1971). [CrossRef]
  10. P. S. Hauge, “Mueller-matrix ellipsometry with imperfect compensators,”J. Opt. Soc. Am. 68, 1519–1528 (1978). [CrossRef]
  11. 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); “Beam splitters for the division-of-amplitude photopolarimeter (DOAP),” Opt. Acta 32, 767–777 (1985). [CrossRef]

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