Abstract

This paper documents the accuracy and precision of the U. S. Air Force Research Laboratory APCL laser polarimeter in arbitrary bistatic geometries at the three laser wavelengths 633nm, 1064nm, and 1550nm. The difference between measured and theoretical-truth Mueller matrices of calibration components is used as the calibration metric and justified relative to block ellipsometer calibration methods. Calibration of the polarimeter ellipsometry mode is demonstrated first, at quasi-monostatic and large bistatic angles, employing a metallic mirror and a dielectric window as the calibration component, respectively, the latter in order to avoid uncertainty in the retardance of typical metallic mirrors at large incident angles. This uncertainty is demonstrated in measurements of COTS protected-silver mirrors from two vendors, revealing an approximately λ/8 retardance difference, for reflection through 90°, between nominally-identical mirrors from the two vendors. Polarimeter calibration is finally extended beyond ellipsometry by calibrating depolarization measurements using a new technique employing ensembles of polarized states as calibration components.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  15. D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
    [Crossref]
  16. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53(8), 4265–4274 (1996).
    [Crossref]
  17. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998).
    [Crossref]
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  20. The physically-realizable Stokes and Mueller sets are not formal vector spaces due to the requirement that S0 and M00 be non-negative.

2012 (2)

2008 (1)

I.J. Vaughn and B.G. Hoover, “Noise-reduction in a laser polarimeter based on discrete waveplate rotations,” Opt. Exp. 16(3), 2091–2108 (2008).
[Crossref]

2007 (2)

2006 (1)

J. Zallat, S. Aïnouz, and M.Ph. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Optics A 8, 807–814 (2006).
[Crossref]

2003 (1)

2002 (2)

2000 (1)

1999 (2)

1998 (1)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998).
[Crossref]

1996 (1)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53(8), 4265–4274 (1996).
[Crossref]

1995 (1)

A. Ambirajan and D.C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng. 34, 1651–1655 (1995).
[Crossref]

1990 (1)

1987 (1)

1979 (1)

D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[Crossref]

Aïnouz, S.

J. Zallat, S. Aïnouz, and M.Ph. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Optics A 8, 807–814 (2006).
[Crossref]

Ambirajan, A.

A. Ambirajan and D.C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng. 34, 1651–1655 (1995).
[Crossref]

Arteaga, O.

Aspnes, D.E.

D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[Crossref]

Beaudry, N.A.

Bruegge, C.J.

Chipman, R.

Chipman, R.A.

Compain, E.

DeMartino, A.

Dereniak, E.L.

Descour, M.R.

Drevillon, B.

Freudenthal, J.

Garcia-Caurel, E.

Goldstein, D.H.

Haner, D.A.

Hoover, B.G.

I.J. Vaughn, B.G. Hoover, and J.S. Tyo, “Classification using active polarimetry,” Proc. SPIE 8364, 83640S (2012).
[Crossref]

I.J. Vaughn and B.G. Hoover, “Noise-reduction in a laser polarimeter based on discrete waveplate rotations,” Opt. Exp. 16(3), 2091–2108 (2008).
[Crossref]

B.G. Hoover and J.S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46, 8364–8373 (2007).
[Crossref] [PubMed]

Hottier, F.

D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[Crossref]

Kahr, B.

Kemme, S.A.

Kim, K.

Kim, Y.-K.

Laude, B.

Look, D.C.

A. Ambirajan and D.C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng. 34, 1651–1655 (1995).
[Crossref]

Mandel, L.

McGuckin, B.T.

Phipps, G.S.

Poirier, S.

Sabatke, D.S.

Schubert, M.

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998).
[Crossref]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53(8), 4265–4274 (1996).
[Crossref]

Smith, M.H.

Stoll, M.Ph.

J. Zallat, S. Aïnouz, and M.Ph. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Optics A 8, 807–814 (2006).
[Crossref]

Sweatt, W.C.

Theeten, J.B.

D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[Crossref]

Tyo, J.S.

Vaughn, I.J.

I.J. Vaughn, B.G. Hoover, and J.S. Tyo, “Classification using active polarimetry,” Proc. SPIE 8364, 83640S (2012).
[Crossref]

I.J. Vaughn and B.G. Hoover, “Noise-reduction in a laser polarimeter based on discrete waveplate rotations,” Opt. Exp. 16(3), 2091–2108 (2008).
[Crossref]

Wang, B.

Wolf, E.

Zallat, J.

J. Zallat, S. Aïnouz, and M.Ph. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Optics A 8, 807–814 (2006).
[Crossref]

Zhao, Y.

Appl. Opt. (6)

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

J. Optics A (1)

J. Zallat, S. Aïnouz, and M.Ph. Stoll, “Optimal configurations for imaging polarimeters: impact of image noise and systematic errors,” J. Optics A 8, 807–814 (2006).
[Crossref]

Opt. Eng. (1)

A. Ambirajan and D.C. Look, “Optimum angles for a polarimeter: part 1,” Opt. Eng. 34, 1651–1655 (1995).
[Crossref]

Opt. Exp. (1)

I.J. Vaughn and B.G. Hoover, “Noise-reduction in a laser polarimeter based on discrete waveplate rotations,” Opt. Exp. 16(3), 2091–2108 (2008).
[Crossref]

Opt. Lett. (2)

Phys. Rev. B (2)

D.E. Aspnes, J.B. Theeten, and F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20(8), 3292–3302 (1979).
[Crossref]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53(8), 4265–4274 (1996).
[Crossref]

Proc. SPIE (1)

I.J. Vaughn, B.G. Hoover, and J.S. Tyo, “Classification using active polarimetry,” Proc. SPIE 8364, 83640S (2012).
[Crossref]

Thin Solid Films (1)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 323–332 (1998).
[Crossref]

Other (2)

The physically-realizable Stokes and Mueller sets are not formal vector spaces due to the requirement that S0 and M00 be non-negative.

R.A. Chipman, “Polarimetry,” in Handbook of Optics (McGraw-Hill, 1994), Chap. 22.

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Figures (7)

Fig. 1
Fig. 1

Laser polarimeter in the Air Force Research Laboratory Active Polarimetric Characterization Lab (APCL).

Fig. 2
Fig. 2

Error matrix of the APCL laser polarimeter in the quasi-monostatic configuration at 633nm wavelength, including aperture relay. Error bars represent standard deviations over 40 measurements.

Fig. 3
Fig. 3

Error matrix of the APCL laser polarimeter in the quasi-monostatic configuration at 1064nm wavelength. Error bars represent standard deviations over 40 measurements.

Fig. 4
Fig. 4

Error matrix of the APCL laser polarimeter in the quasi-monostatic configuration at 1550nm wavelength. Error bars represent standard deviations over 40 measurements.

Fig. 5
Fig. 5

Error matrix of the APCL laser polarimeter in the 90° bistatic configuration at 1064nm wavelength. Error bars represent standard deviations over 40 measurements.

Fig. 6
Fig. 6

Error matrix of the APCL laser polarimeter in the 90° bistatic configuration at 1550nm wavelength. Error bars represent standard deviations over 40 measurements.

Fig. 7
Fig. 7

Polarization ellipses reflected by nominally-identical protected-silver mirrors from two catalog vendors (A & B) when illuminated at 45° AOI by the same circularly-polarized state.

Tables (1)

Tables Icon

Table 1 The depolarization ensemble used to calibrate depolarization measurements.

Equations (22)

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M E = 1 2 [ ( | R p | 2 + | R s | 2 ) ( | R p | 2 | R s | 2 ) 0 0 ( | R p | 2 | R s | 2 ) ( | R p | 2 + | R s | 2 ) 0 0 0 0 2 Re ( R p R s ) 2 Im ( R p R s ) 0 0 2 Im ( R p R s ) 2 Re ( R p R s ) ] ,
tan Ψ exp ( j Δ ) R p / R s .
M E = τ [ 1 cos 2 Ψ 0 0 cos 2 Ψ 1 0 0 0 0 sin 2 Ψ cos Δ sin 2 Ψ sin Δ 0 0 sin 2 Ψ sin Δ sin 2 Ψ cos Δ ] ,
s o = [ E x o E x o + E y o E y o E x o E x o E y o E y o 2 Re E x o E y o 2 Im E x o E y o ] ,
s o = m S i .
s o = S o = m S i ,
M = m < m ,
M m o n o = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ]
M b i = [ 1 ( q 1 ) 0 0 ( q 1 ) 1 0 0 0 0 q ( 2 q ) 0 0 0 0 q ( 2 q ) ] ,
M A ( 45 ° ) = [ 1 .0032 ± .0005 .0023 ± .0004 .0018 ± .0005 .0023 ± .0008 .9994 ± .0010 .0010 ± .0008 .0041 ± .0007 .0035 ± .0006 .0038 ± .0008 0.9273 ± .0007 .3717 ± .0006 .0008 ± .0005 .0075 ± .0004 .3724 ± .0004 .9276 ± .0002 ] &
M B ( 45 ° ) = [ 1 .0048 ± .0014 .0017 ± .0006 .0016 ± .0007 .0013 ± .0009 1.0074 ± .0018 .0050 ± .0010 .0021 ± .0009 .0020 ± .0007 .0022 ± .0010 .9120 ± .0011 .4141 ± .0011 .0005 ± .0006 .0088 ± .0005 .4124 ± .0004 .9114 ± .0002 ] ,
M A ( 45 ° ) [ 1 0 0 0 0 1 0 0 0 0 0.93 0.37 0 0 0.37 0.93 ] & M B ( 45 ° ) [ 1 0 0 0 0 1 0 0 0 0 0.91 0.41 0 0 0.41 0.91 ] .
ID = [ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] .
( 1 + HWP ( 45 ° ) + QWP ( 45 ° ) HWP ( 0 ° ) + QWP ( 45 ° ) HWP ( 0 ° ) ) / 4 = ID ,
1 m e a s = [ 1 .0017 ± .0012 .0023 ± .0013 .0000 ± .0007 .0015 ± .0010 .9969 ± .0023 .0075 ± .0019 .0053 ± .0011 .0008 ± .0012 .0037 ± .0016 .9982 ± .0017 .0008 ± .0008 .0006 ± .0003 .0001 ± .0008 .0017 ± .0010 1.0001 ± .0004 ] ,
HWP ( 45 ° ) m e a s = [ 1 .0001 ± .0010 .0017 ± .0008 .0007 ± .0006 .0008 ± .0011 .9983 ± .0015 .0004 ± .0016 .0107 ± .0009 .0005 ± .0007 .0025 ± .0023 .9987 ± .0017 .0044 ± .0011 .0001 ± .0005 .0056 ± .0008 .0055 ± .0007 1.0000 ± .0004 ] ,
QWP ( 45 ° ) HWP ( 0 ° ) m e a s = [ 1 .0015 ± .0004 .0023 ± .0003 .0025 ± .0001 .0018 ± .0004 .0081 ± .0007 .0003 ± .0005 .9994 ± .0004 .0004 ± .0004 .0019 ± .0006 .9963 ± .0005 .0011 ± .0004 .0008 ± .0002 .9993 ± .0003 .0021 ± .0003 .0003 ± .0002 ] ,
QWP ( 45 ° ) HWP ( 0 ° ) m e a s = [ 1 .0004 ± .0003 .0025 ± .0003 .0011 ± .0001 .0012 ± .0003 .0040 ± .0007 .0043 ± .0007 1.0001 ± .0003 .0013 ± .0005 .0055 ± .0007 .9969 ± .0006 .0038 ± .0004 .0011 ± .0002 .9997 ± .0003 .0013 ± .0003 .0069 ± .0001 ] ,
I D m e a s = [ 1 .0000 ± .0004 .0002 ± .0004 .0005 ± .0002 .0006 ± .0004 .0027 ± .0007 .0008 ± .0007 .0015 ± .0004 .0001 ± .0004 .0021 ± .0008 .0009 ± .0006 .0025 ± .0004 .0002 ± .0002 .0013 ± .0003 .0018 ± .0003 .0018 ± .0001 ] ,
S [ E x E x + E y E y E x E x E y E y 2 Re E x E y 2 Im E x E y ] = [ S 0 S 1 S 2 S 3 ] ,
S o [ E x o E x o + E y o E y o E x o E x o E y o E y o 2 Re E x o E y o 2 Im E x o E y o ] = [ S 0 o S 1 o S 2 o S 3 o ] .
S o = M S i = [ M 00 M 01 M 02 M 03 M 10 M 11 M 12 M 13 M 20 M 21 M 22 M 23 M 30 M 31 M 32 M 33 ] [ S 0 i S 1 i S 2 i S 3 i ] .

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