Abstract

We present a new polarimetric imaging system based on liquid-crystal modulators, a spectrally filtered white-light source, and a CCD camera. The whole Mueller matrix image of the sample is measured in approximately 5 s in the transmission mode. The instrument design, together with an original and easy-to-operate calibration procedure, provides high accuracy over a wide spectral range (500–700 nm). This accuracy has been assessed by measurement of a linear polarizer at different orientations and a thick wedged quartz plate as an example of a partially depolarized retarder. Polarimetric images of a stained hepatic biopsy with significant fibrosis have been taken at several wavelengths. The optical properties of Picrosirius Red stained collagen (diattenuation, retardance, and polarizance) have been measured independently from each other between 500 and 700 nm.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
    [CrossRef]
  7. J. S. Tyo, T. S. Turner, “Imaging spectropolarimeters for use in visible and infrared remote sensing,” in Imaging Spectrometry V, M. R. Descour, S. S. Shen, eds., Proc. SPIE3753, 214–225 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  16. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
    [CrossRef]
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    [CrossRef]
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  19. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22, 934–936 (1997).
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2003 (1)

2002 (2)

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic errors,” Appl. Opt. 41, 619–630 (2002).
[CrossRef] [PubMed]

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

2000 (1)

1999 (4)

1998 (1)

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

1997 (2)

1996 (1)

1995 (1)

P. Whittaker, “Polarized light in biomedical research,” Microsc. Anal. 44, 15–17 (1995).

1977 (1)

R. M. A. Azzam, “Photopolarimeter using two modulated optical rotators,” Opt. Lett. 2, 181–183 (1977).
[CrossRef]

1969 (1)

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Artal, P.

Azzam, R. M. A.

R. M. A. Azzam, “Photopolarimeter using two modulated optical rotators,” Opt. Lett. 2, 181–183 (1977).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands, 1989).

Baba, J. S.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands, 1989).

Bueno, J. M.

Cameron, B. D.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

Chipman, R. A.

P.-Y. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999), http://www.opticsexpress.org.
[CrossRef] [PubMed]

S.-Y. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

J. L. Pezzaniti, R. A. Chipman, “High-resolution Mueller matrix imaging polarimetry for understanding high-resolution optoelectronic modulators,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. SPIE2297, 468–480 (1994).
[CrossRef]

Chung, J.-R.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

Collins, R. W.

Compain, E.

E. Compain, S. Poirier, B. Drévillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999).
[CrossRef]

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

Coté, G. L.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

de Boer, J. F.

De Martino, A.

DeLaughter, A. H.

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

Delplancke, F.

Dereniak, E. L.

Descour, M. R.

Drévillon, B.

Garcia-Caurel, E.

Gerligand, P.-Y.

Jasperson, S. N.

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Kemme, S. A.

Kim, Y.-K.

Koh, J.

Laude, B.

Lu, S.-Y.

Milner, T. E.

Nelson, J. S.

Pezzaniti, J. L.

J. L. Pezzaniti, R. A. Chipman, “High-resolution Mueller matrix imaging polarimetry for understanding high-resolution optoelectronic modulators,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. SPIE2297, 468–480 (1994).
[CrossRef]

Phipps, G. S.

Poirier, S.

Sabatke, D. S.

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Smith, M. H.

Sweatt, W. C.

Tuchin, V. V.

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, Vol. TT38 of Tutorial Texts in Optical Engineering (SPIE Press, Bellingham, Wash., 2000).

Turner, T. S.

J. S. Tyo, T. S. Turner, “Imaging spectropolarimeters for use in visible and infrared remote sensing,” in Imaging Spectrometry V, M. R. Descour, S. S. Shen, eds., Proc. SPIE3753, 214–225 (1999).
[CrossRef]

Tyo, J. S.

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic errors,” Appl. Opt. 41, 619–630 (2002).
[CrossRef] [PubMed]

J. S. Tyo, T. S. Turner, “Imaging spectropolarimeters for use in visible and infrared remote sensing,” in Imaging Spectrometry V, M. R. Descour, S. S. Shen, eds., Proc. SPIE3753, 214–225 (1999).
[CrossRef]

van Gemert, M. J. C.

Whittaker, P.

P. Whittaker, “Polarized light in biomedical research,” Microsc. Anal. 44, 15–17 (1995).

Appl. Opt. (3)

J. Biomed. Opt. (1)

J. S. Baba, J.-R. Chung, A. H. DeLaughter, B. D. Cameron, G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Microsc. Anal. (1)

P. Whittaker, “Polarized light in biomedical research,” Microsc. Anal. 44, 15–17 (1995).

Opt. Express (1)

Opt. Lett. (5)

Rev. Sci. Instrum. (2)

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

E. Compain, B. Drévillon, “High-frequency modulation of the four states of polarization of light with a single phase modulator,” Rev. Sci. Instrum. 69, 1574–1580 (1998).
[CrossRef]

Other (4)

J. S. Tyo, T. S. Turner, “Imaging spectropolarimeters for use in visible and infrared remote sensing,” in Imaging Spectrometry V, M. R. Descour, S. S. Shen, eds., Proc. SPIE3753, 214–225 (1999).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, The Netherlands, 1989).

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, Vol. TT38 of Tutorial Texts in Optical Engineering (SPIE Press, Bellingham, Wash., 2000).

J. L. Pezzaniti, R. A. Chipman, “High-resolution Mueller matrix imaging polarimetry for understanding high-resolution optoelectronic modulators,” in Photonics for Processors, Neural Networks, and Memories II, J. L. Horner, B. Javidi, S. T. Kowel, eds., Proc. SPIE2297, 468–480 (1994).
[CrossRef]

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Figures (16)

Fig. 1
Fig. 1

Schematic of the imaging polarimeter: Sc, white-light source; F, filter wheel; P, linear polarizer (the arrow indicates the direction of the transmission axis); LC, liquid-crystal variable retarders (for each LC, the arrow indicates the direction of its variable index axis); Sp, sample; A, linear analyzer; L, imaging lens (achromat); D, detector (CCD camera). Higher magnifications can be achieved by insertion of a condenser (C) and a microscope objective (O) (dotted lines) into the optical path.

Fig. 2
Fig. 2

Mueller matrices measured with a linear polarizer set at various azimuthal angles. Only the nonvanishing elements (symbols) and single parameter fits (solid curves) have been represented.

Fig. 3
Fig. 3

Same experiment as in Fig. 2 with elements that are expected to vanish.

Fig. 4
Fig. 4

Schematic of the wedged quartz plate. The optical axis is parallel to the x axis.

Fig. 5
Fig. 5

Retardance (rad) image of the wedged quartz plate. The field of view is 2.7 mm × 2.7 mm.

Fig. 6
Fig. 6

Retardance as a function of pixel number for the row indicated in Fig. 5.

Fig. 7
Fig. 7

Depolarization power as a function of pixel number for the row indicated in Fig. 5.

Fig. 8
Fig. 8

Typical hepatic biopsy stained with Picrosirius Red (classical nonpolarized microscopic image). The field of view is 0.5 mm × 0.7 mm. Fibrotic zones appear darker than the normal tissue that consists of clearly visible hepatocytes. Courtesy of Thierry Boulesteix, E. Beaurepaire, and Marie Claire Schanne-Klein, Laboratoire d’Optique et Biosciences, Centre National de la Recherche Scientifique, Ecole Polytechnique, France.

Fig. 9
Fig. 9

Unpolarized image (m 11) of a stained hepatic biopsy taken between a plate and a cover plate for three different wavelengths. The patient suffers from liver cirrhosis, which separates the liver into nodules. The field of view is 2 mm × 2 mm.

Fig. 10
Fig. 10

Diattenuation image of the same sample as in Fig. 10. The field of view is 2 mm × 2 mm.

Fig. 11
Fig. 11

Retardance (rad) image of the same sample as in Fig. 10. The field of view is 2 mm × 2 mm.

Fig. 12
Fig. 12

Depolarization power image of the same sample as in Fig. 10. The field of view is 2 mm × 2 mm.

Fig. 13
Fig. 13

Diattenuation as a function of wavelength for three different pixels chosen for fibrosis and for a point of the cover plate.

Fig. 14
Fig. 14

Polarizance as a function of wavelength for three different pixels chosen for fibrosis and for a point of the cover plate.

Fig. 15
Fig. 15

Retardance as a function of wavelength for three different pixels chosen for fibrosis and for a point of the cover plate.

Fig. 16
Fig. 16

Localization of the four pixels taken into account in Figs. 14 16 for a diattenuation image of the sample at 550 nm. The field of view is 3 mm × 2 mm.

Equations (19)

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ST=I, Q, U, V=I0+I90, I0-I90, I+45-I-45, IR-IL,
P=1IQ2+U2+V21/21.
Mτ, ϕ=τ21cos2ϕsin2ϕ0cos2ϕcos22ϕcos2ϕsin2ϕ0sin2ϕcos2ϕsin2ϕsin22ϕ00000.
Mτ, ψ, Δ=τ1-cos 2ψ00-cos 2ψ10000sin 2ψ cos Δsin 2ψ sin Δ00-sin 2ψ sin Δsin 2ψ cos Δ,
Uθ=10000cos2ϕ-sin2ϕ00sin2ϕcos2ϕ00001.
M=m111DTPm,
D=Tmax-TminTmax+Tmin=1m11m122+m132+m1421/2,
P=1m11m212+m312+m4121/2.
M=MρMRMD,
MD=m111DTDmD,mD=1-D2I+1-1-D2DˆDˆT,
ρ=1-|TrMρ-1|3, 0ρ1.
R=cos-112 TrMR-1.
Δ1=315°, Δ2=135°,θ1=ε27.4°, θ2=ε72.4°,
WX, Y=i=1225 fiX, YWXi, Yii=1225 fiX, Y,
fiX, Y=exp-a|X-Xi2+Y-Yi2|.
Δx=2πδλ x tanα+2πδλ e,
i=λδ tanα1.37 mm.
M=1Δ2-Δ1Δ1Δ21000010000cos Δsin Δ00-sin Δcos ΔdΔ=1000010000a=sin Δ2-sin Δ1/Δ2-Δ1-b00b=cos Δ2-cos Δ1/Δ2-Δ1a.
M=1000010000-0.125-0.28000.28-0.125,

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