Abstract

We present two figures of merit based on singular value decomposition, which can be used to assess the noise immunity of a complete Stokes polarimeter. These are used to optimize a polarimeter featuring a rotatable retarder and a fixed polarizer. A retardance of 132° (approximately three-eighths wave) and retarder orientation angles of ±51.7° and ±15.1° are found to be optimal when four measurements are used. Use of this retardance affords a factor-of-1.5 improvement in signal-to-noise ratio over systems employing a quarter-wave plate. A geometric means of visualizing the optimization process is discussed, and the advantages of the use of additional measurements are investigated. No advantage of using retarder orientation angles spaced uniformly through 360° is found over repeated measurements made at the four retarder orientation angles.

© 2000 Optical Society of America

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References

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  1. R. M. A. Azzam, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 27.
  2. J. A. Shaw, Appl. Opt. 38, 3157 (1999).
    [CrossRef]
  3. R. A. Chipman, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.
  4. See, e.g., G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).
  5. R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, J. Opt. Soc. Am. A 5, 681 (1988).
    [CrossRef]
  6. A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651 (1995).
    [CrossRef]
  7. A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, Appl. Opt. 38, 2829 (1999).
    [CrossRef]
  8. K. Brudzewski, J. Mod. Opt. 38, 889 (1991).
    [CrossRef]
  9. Z. Sekera, J. Opt. Soc. Am. 47, 484 (1957).
  10. H. G. Berry, G. Gabrielse, and A. E. Livingston, Appl. Opt. 16, 3200 (1977).
    [CrossRef] [PubMed]
  11. R. M. A. Azzam, Opt. Lett 2, 148 (1978).
    [CrossRef]
  12. M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
    [CrossRef]
  13. Mathematica 4 (Wolfram Research, Champaign, Ill., 1999).
  14. A. Ambirajan and D. C. Look, Opt. Eng. 34, 1656 (1995).
    [CrossRef]
  15. See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

1999

J. A. Shaw, Appl. Opt. 38, 3157 (1999).
[CrossRef]

A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, Appl. Opt. 38, 2829 (1999).
[CrossRef]

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

1995

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1656 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651 (1995).
[CrossRef]

1991

K. Brudzewski, J. Mod. Opt. 38, 889 (1991).
[CrossRef]

1988

1978

R. M. A. Azzam, Opt. Lett 2, 148 (1978).
[CrossRef]

1977

1957

Abushagur, M. A. G.

Ambirajan, A.

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1656 (1995).
[CrossRef]

Ax, G. R.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Azzam, R. M. A.

A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, Appl. Opt. 38, 2829 (1999).
[CrossRef]

R. M. A. Azzam, I. M. Elminyawi, and A. M. El-Saba, J. Opt. Soc. Am. A 5, 681 (1988).
[CrossRef]

R. M. A. Azzam, Opt. Lett 2, 148 (1978).
[CrossRef]

R. M. A. Azzam, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 27.

Berry, H. G.

Born, M.

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Brudzewski, K.

K. Brudzewski, J. Mod. Opt. 38, 889 (1991).
[CrossRef]

Chipman, R. A.

R. A. Chipman, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.

Elminyawi, I. M.

El-Saba, A. M.

Gabrielse, G.

Golub, G. H.

See, e.g., G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

Howe, J. D.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Livingston, A. E.

Look, D. C.

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1656 (1995).
[CrossRef]

Miller, M. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Petty, T. E.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Sekera, Z.

Shaw, J. A.

Smith, M. H.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Sornsin, E. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Van Loan, C. F.

See, e.g., G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

Wolf, E.

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Woodruff, J. B.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

K. Brudzewski, J. Mod. Opt. 38, 889 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1651 (1995).
[CrossRef]

A. Ambirajan and D. C. Look, Opt. Eng. 34, 1656 (1995).
[CrossRef]

Opt. Lett

R. M. A. Azzam, Opt. Lett 2, 148 (1978).
[CrossRef]

Proc. SPIE

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, and E. A. Sornsin, Proc. SPIE 3754, 137 (1999).
[CrossRef]

Other

Mathematica 4 (Wolfram Research, Champaign, Ill., 1999).

R. A. Chipman, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 22.

See, e.g., G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

See, e.g., M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

R. M. A. Azzam, in Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995), Chap. 27.

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Figures (3)

Fig. 1
Fig. 1

Each trajectory is the locus of points on the Poincaré sphere that can be selected by choice of retarder orientation θ for a given retardence.

Fig. 2
Fig. 2

Curves for retardances of 90° and 132°, showing an inscribed regular tetrahedron in the curve for 132°. The tetrahedron vertices correspond to retarder angles of ±51.7° and ±15.1°.

Fig. 3
Fig. 3

Comparison of multiple measurement techniques, showing values of the EWV figure of merit as a function of the number N of measurements for cases (1)–(3) described in text. Missing points at N=4,6, 8 in the data for cases (1) and (2) are due to singularities in the measurement matrices. A single data point is also shown for a four-measurement procedure using a quarter-wave plate.

Equations (6)

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

=W+n,
RAD=j=0R-11/μj.
vj=k=0N-1W+j,k2uk.
vj/u=k=0N-1W+j,k2
EWV=j=03k=0N-1W+j,k2=TrW+TW+=j=0R-11/μj2.
1, cos22θk+cos δ sin22θk,sin2δ/2sin4θk,-sin δ sin2θkT.

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