Abstract

A two-polarization Michelson interferometer with a low-retardance beam splitter and digital signal processing is used to measure the retardance of optical devices. Error analysis of the improved optical system and data processing shows that the measurement has an uncertainty of 0.039° for measurements of nominally 90° retarders. Retardance variations arising from coherent reflections in the retarder used for intercomparison add an uncertainty of from 0.005° to 0.03°, increasing the combined measurement uncertainty to as much as 0.049°.

© 1997 Optical Society of America

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References

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  1. K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
    [CrossRef]
  2. K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
    [CrossRef]
  3. H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
    [CrossRef]
  4. H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654–661 (1983).
    [CrossRef]
  5. D. Gabor, “Theory of communication. Part I. The analysis of information,” J. Inst. Elec. Eng. 93, 429–441 (1946).
  6. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw–Hill, New York, 1986), pp. 267–271.
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Vol. 6, pp. 619.
  8. R. A. Paquin, “Properties of metals,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. 2 p. 35.22.
  9. A. L. Fymat, “Jones’ matrix representation of optical instruments. I: Beam splitters,” Appl. Opt. 10, 2499–2505 (1971).
    [CrossRef] [PubMed]
  10. F. J. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 6, 51–83 (1978).
    [CrossRef]
  11. B. N. Taylor, C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurementsNational Institute of Standards Technology Technical Note 1297, 1993 (U.S. Government Printing Office, Washington D.C.), pp. 2–5.
  12. P. A. Williams, A. H. Rose, C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
    [CrossRef]
  13. K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” , 1996 (National Institute of Standards and Technology, Gaithersburg, Md.).
  14. E. Hecht, A. Zajak, Optics (Addison–Wesley, Reading, Mass, 1974), pp. 301–305.

1997 (2)

1983 (1)

H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654–661 (1983).
[CrossRef]

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 6, 51–83 (1978).
[CrossRef]

1973 (1)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

1971 (1)

1946 (1)

D. Gabor, “Theory of communication. Part I. The analysis of information,” J. Inst. Elec. Eng. 93, 429–441 (1946).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Vol. 6, pp. 619.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw–Hill, New York, 1986), pp. 267–271.

Clarke, I. G.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Day, G. W.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Fymat, A. L.

Gabor, D.

D. Gabor, “Theory of communication. Part I. The analysis of information,” J. Inst. Elec. Eng. 93, 429–441 (1946).

Hale, P. D.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 6, 51–83 (1978).
[CrossRef]

Hazebroek, H. F.

H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654–661 (1983).
[CrossRef]

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajak, Optics (Addison–Wesley, Reading, Mass, 1974), pp. 301–305.

Holscher, A. A.

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurementsNational Institute of Standards Technology Technical Note 1297, 1993 (U.S. Government Printing Office, Washington D.C.), pp. 2–5.

Paquin, R. A.

R. A. Paquin, “Properties of metals,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. 2 p. 35.22.

Rochford, K. B.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” , 1996 (National Institute of Standards and Technology, Gaithersburg, Md.).

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Rose, A. H.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

P. A. Williams, A. H. Rose, C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
[CrossRef]

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurementsNational Institute of Standards Technology Technical Note 1297, 1993 (U.S. Government Printing Office, Washington D.C.), pp. 2–5.

Visser, W. M.

H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654–661 (1983).
[CrossRef]

Wang, C. M.

Williams, P. A.

K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
[CrossRef]

P. A. Williams, A. H. Rose, C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
[CrossRef]

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Vol. 6, pp. 619.

Zajak, A.

E. Hecht, A. Zajak, Optics (Addison–Wesley, Reading, Mass, 1974), pp. 301–305.

Appl. Opt. (3)

J. Inst. Elec. Eng. (1)

D. Gabor, “Theory of communication. Part I. The analysis of information,” J. Inst. Elec. Eng. 93, 429–441 (1946).

J. Phys. E (2)

H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973).
[CrossRef]

H. F. Hazebroek, W. M. Visser, “Automated laser interferometric ellipsometry and precision reflectometry,” J. Phys. E 16, 654–661 (1983).
[CrossRef]

Proc. IEEE (1)

F. J. Harris, “On the use of windows for harmonic analysis with discrete Fourier transform,” Proc. IEEE 6, 51–83 (1978).
[CrossRef]

Other (7)

B. N. Taylor, C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurementsNational Institute of Standards Technology Technical Note 1297, 1993 (U.S. Government Printing Office, Washington D.C.), pp. 2–5.

K. B. Rochford, C. M. Wang, “Uncertainty in null polarimeter measurements,” , 1996 (National Institute of Standards and Technology, Gaithersburg, Md.).

E. Hecht, A. Zajak, Optics (Addison–Wesley, Reading, Mass, 1974), pp. 301–305.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw–Hill, New York, 1986), pp. 267–271.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Vol. 6, pp. 619.

R. A. Paquin, “Properties of metals,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. 2 p. 35.22.

K. B. Rochford, P. A. Williams, A. H. Rose, I. G. Clarke, P. D. Hale, G. W. Day, “Standard polarization components: progress toward an optical retardance standard,” in Polarization Analysis and Measurement II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE2265, 2–8 (1994).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental layout for interferometric retardance measurement. Components include mirror, M; beam splitter, BS; polarizing beam splitter, PBS; retarder, R; analog-to-digital converter, AID; two detectors, D.

Fig. 2
Fig. 2

Retardance error resulting from finite polarizer extinction ϵ.

Fig. 3
Fig. 3

Retardance error arising from polarizer misalignmentΔα and Δβ.

Fig. 4
Fig. 4

Typical fringe data from interferometer.

Tables (3)

Tables Icon

Table 1 Worst-Case and Measured Variation Caused by Coherent Reflections

Tables Icon

Table 2 Uncertainty Caused by Twist in Rhomb

Tables Icon

Table 3 Retardance Measurements and Measurement Uncertainty

Equations (7)

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

ϕ = 1 N   i = 1 N   ϕ 1 t i - ϕ 2 t i .
s H t = - iS f sgn f ,
z t = 0 f < 0 = 2 S f f > 0
δ m = tan - 1 tan δ 0 2 F 1 - tan - 1 tan δ 0 2 F 2 ,
F 1 , 2 = cos 2 α - 2 γ ± cos 2 β - 2 γ 1 ± cos 2 β - 2 α .
tan δ Al = 2 n κ   sin θ   tan θ n 2 κ 2 + 1 - sin 2 θ   tan 2 θ ,
ϕ PE = tan - sin δ 0 + ϵ   sin - δ 0 cos δ 0 + ϵ   cos - δ 0 .

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