Abstract

A new set-up is proposed to measure the full polarimetric properties of a sample through an optical fiber, paving the way to full-Mueller endoscopic imaging. The technique combines a channeled spectrum polarimeter and an interferometer. This permits high-speed measurement of two Mueller matrices simultaneously. The first matrix characterizes only the fiber while the second characterizes both fiber and sample. The instrument is validated on vacuum, a quarter-wave plate and a linear polarizer for single-point measurements. Insensitivity of the polarimetric measurement to fiber disturbances is proven while manipulating the fiber.

© 2015 Optical Society of America

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References

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2015 (2)

2013 (1)

2012 (1)

2011 (2)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

2005 (1)

2004 (1)

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

2002 (1)

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

2001 (2)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

1996 (1)

1986 (1)

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttg.) 75(1), 26–36 (1986).

1982 (1)

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Akiba, M.

Antonelli, M.-R.

Babilotte, P.

Backman, V.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Badizadegan, K.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Benali, A.

Boito, P.

Cariou, J.

Cense, B.

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

Chan, K.-P.

Chen, T. C.

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

Chipman, R. A.

Chong, C.

Cloude, S. R.

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttg.) 75(1), 26–36 (1986).

Cohen, H.

Dasari, R. R.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

de Boer, J. F.

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

De Martino, A.

Deby, S.

Dubreuil, M.

Fallet, C.

Feld, M. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Gayet, B.

Georgakoudi, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Ghosh, N.

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16(11), 110801 (2011).
[Crossref] [PubMed]

Gurjar, R. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Ibrahim, B. H.

Itoh, M.

Itzkan, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Jacques, S. L.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Le Brun, G.

Le Grand, Y.

Le Gratiet, A.

Le Jeune, B.

Lee, K.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Lemaillet, P.

Lu, S. Y.

Madjarova, V. D.

Makita, S.

Manhas, S.

Martin, L.

Martino, A. D.

Morosawa, A.

Nazac, A.

Nelson, J. S.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

Novikova, T.

Pagnoux, D.

Park, B. H.

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

Perelman, L. T.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Pierangelo, A.

Pierce, M. C.

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

Ramella-Roman, J. C.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

Rivet, S.

Sakai, T.

Saxer, C.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

Sevrain, D.

Simon, R.

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Srinivas, S. M.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

Turlin, B.

Validire, P.

Vanel, J.-C.

Verdier, M.

Vitkin, I. A.

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16(11), 110801 (2011).
[Crossref] [PubMed]

Vizet, J.

Yamanari, M.

Yasuno, Y.

Yatagai, T.

Appl. Opt. (1)

Invest. Ophthalmol. Vis. Sci. (1)

B. Cense, T. C. Chen, B. H. Park, M. C. Pierce, and J. F. de Boer, “Thickness and Birefringence of Healthy Retinal Nerve Fiber Layer Tissue Measured with Polarization-Sensitive Optical Coherence Tomography,” Invest. Ophthalmol. Vis. Sci. 45(8), 2606–2612 (2004).
[Crossref] [PubMed]

J. Biomed. Opt. (3)

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7(3), 329–340 (2002).
[Crossref] [PubMed]

N. Ghosh and I. A. Vitkin, “Tissue polarimetry: concepts, challenges, applications, and outlook,” J. Biomed. Opt. 16(11), 110801 (2011).
[Crossref] [PubMed]

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6(4), 474–479 (2001).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Nat. Med. (1)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

R. Simon, “The connection between Mueller and Jones matrices of polarization optics,” Opt. Commun. 42(5), 293–297 (1982).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Optik (Stuttg.) (1)

S. R. Cloude, “Group theory and polarization algebra,” Optik (Stuttg.) 75(1), 26–36 (1986).

Supplementary Material (1)

NameDescription
» Visualization 1: AVI (1041 KB)      Fourier transform of the channeled spectrum

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Figures (9)

Fig. 1
Fig. 1 Block diagram of the Mueller polarimeter operating in reflection. SLD: super luminescent diode, C: passive polarization state coding block, D: passive polarization state decoding block, NPBS: non-polarizing beam splitter cube, RM: reference mirror, PaR: 50% partial reflector, PrM: probe mirror. Cube faces are numbered from ① to ④. In the paper, the scattering sample will be replaced by a specific medium, such as a linear birefringence or a linear diattenuator, with the mirror PrM to reflect light to the probe fiber. For the Coding and Decoding blocks, P1, P2: linear polarizers are crossed, R1, R2, R3, R4: YVO4 retarder oriented respectively at 45°, 0°, 0° and 45° according to the orientation of P1.
Fig. 2
Fig. 2 Simulation of the Fourier transform of the channeled spectrum I(ν) according to the OPD L measured between the reference arm length and the path length measured from the Partial Reflector (PaR). By adjusting L, it is possible to measure simultaneously the Fourier transform of IDC, FT{IDC}, and of Ainterference, FT{Ainterference} (Visualization 1).
Fig. 3
Fig. 3 Diagram of steps to obtain the two matrices M ¯ P a R and M ¯ PrM . Iref0 and IPar0 are measured before measuring the sample.
Fig. 4
Fig. 4 Experimental amplitude of the Fourier transform of the channeled spectrum I(ν) without frequency calibration (a) and with frequency calibration (b).
Fig. 5
Fig. 5 Experimental response (arbitrary units) of the detection by comparing the amplitude of the experimental peaks to the theoretical peaks. This curve corresponds to the roll-off due to the spectrometer.
Fig. 6
Fig. 6 Experimental retardance of the reference fiber in time.
Fig. 7
Fig. 7 Experimental retardance of the “vacuum” sample (a) and the probe fiber (b) in time. Red line: retardance of the medium by using the matrix MPaR(t) measured from the interference components simultaneously. Blue line: retardance of the medium by using the matrix MPaR(t0) measured once previously. Diattenuation value of the “vacuum” equals to 0.012 ± 0.004, depolarization index equal to 0.937 ± 0.006 for M ¯ PaR ( t ) 1 M ¯ PrM ( t ) and M ¯ PaR ( t 0 ) 1 M ¯ PrM ( t ) .
Fig. 8
Fig. 8 Experimental retardance of a double-pass quarter wave plate (a) and the sample fiber (b) in time. Red line: retardance of the material by using the matrix MPaR(t) measured from interference components simultaneously. Blue line: retardance of the medium by using the matrix MPaR(t0) measured prior to handling. Diattenuation value of the material equals to 0.071 ± 0.002, depolarization index Pd equals to 0.876 ± 0.007 for M ¯ PaR ( t ) 1 M ¯ PrM ( t ) and M ¯ PaR ( t 0 ) 1 M ¯ PrM ( t ) . Pd is inferior to one obtained for “vacuum” due to the chromaticity of the quarter wave plate.
Fig. 9
Fig. 9 Experimental diattenuation of a linear polarizer (a) and of the probe fiber (b) in time. Red line: diattenuation of the medium by using the matrix MPaR(t) measured from interference simultaneously. Blue dots: diattenuation of the material by using the matrix MPaR(t0) measured prior to handling. Depolarization index of the material is equal to 0.95 ± 0.07 for M ¯ PaR ( t ) 1 M ¯ PrM ( t ) and M ¯ PaR ( t 0 ) 1 M ¯ PrM ( t ) .

Tables (4)

Tables Icon

Table 1 Magnitude of real and imaginary peaks according to mij coefficients. The time dependence in coefficients is omitted to simplify the notation.

Tables Icon

Table 2 Complex values of the peaks according to rj coefficients of J r e f = [ r 1 r 2 r 3 r 4 ] and fj coefficients of J P a R = [ f 1 f 2 f 3 f 4 ] depending on the probe fiber. The time dependence in fj coefficients is omitted to simplify the expressions.

Tables Icon

Table 3 Transmission measurements of the non-polarizing beam splitter cube from face ① of the cube to ③ and from ② to ④. Reflection measurements from ① to ② and from ③ to ④. R should be equal to 0 in transmission and π in reflection for a non-retarding medium. Precision is calculated with four different measurements after calibration.

Tables Icon

Table 4 Complex values of the peaks according to rj coefficients of J r e f = [ r 1 r 2 r 3 r 4 ] and fj coefficients of J P a R = [ f 1 f 2 f 3 f 4 ] depending on the probe fiber and phase errors of the YVO4 retarder plates.

Equations (24)

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A interference ( ν , t ) = E PaR ( ν , t ) * E ref ( ν ) E x p [ i L 2 π c ν ] + E PaR ( ν , t ) E ref ( ν ) * E x p [ i L 2 π c ν ] ,
E ref = J D J ref J C E in ,
E PaR ( t ) = J D J PaR ( t ) J C E in ,
I DC ( ν , t ) = I ref ( ν ) + I PaR ( ν , t ) + I PrM ( ν , t ) ,
S ref = M D M ref M C S in ,
S P a R ( t ) = M D M P a R ( t ) M C S i n ,
S PrM ( t ) = M D M PrM ( t ) M C S in ,
I D C ( ν , t ) = m = 0 12 [ a m ( t ) cos ( m 2 π Δ n e c ν ) + b m ( t ) sin ( m 2 π Δ n e c ν ) ] ,
F DC [ F T { I D C } ] = α M ¯ ,
F DC 1 [ α M ¯ ] = F T { I D C }
A interference ( ν , t ) = m = 12 12 c m ( t ) E x p [ i 2 π c ν ( L + m Δ n e c ) ] + C C ,
F interf ( J ref ) [ F T { A interference } ] = M ¯ P a R ,
F T { I P a R ( t ) } = α P a R F DC 1 [ M ¯ P a R ( t ) ] ,
M ¯ PaR ( t ) = M ¯ o u t ( t ) M ¯ i n ( t ) .
M ¯ PrM ( t ) = M ¯ o u t ( t ) M ¯ m e d i u m M ¯ i n ( t ) .
[ M ¯ PaR ( t ) ] 1 M ¯ PrM ( t ) = [ M ¯ in ( t ) ] 1 M ¯ medium M ¯ in ( t )
A interference ( ν , t ) = m = 12 12 d m ( t ) E x p [ i 2 π c ν ( L + m ( Δ n e c + ϕ w ) ) + i φ m ] + C C ,
[ M ¯ PaR ( t 0 ) ] 1 M ¯ PrM ( t ) = [ M ¯ in ( t0 ) ] 1 [ M ¯ out ( t0 ) ] 1 [ M ¯ out ( t ) ] M ¯ medium M ¯ in ( t ) .
M ¯ o u t = M ¯ D ( c u b e ) M ¯ R ( o u t ) .
[ M ¯ PaR ( t 0 ) ] 1 M ¯ PrM ( t ) = [ M ¯ i n ( t0 ) ] 1 [ M ¯ R ( t0 ) ( o u t ) ] 1 [ M ¯ R ( t ) ( o u t ) ] M ¯ medium M ¯ i n ( t ) .
M = A ( J J * ) A 1 ,
A = [ 1 0 0 1 1 0 0 1 0 1 1 0 0 i i 0 ] .
N = i = 0 3 j = 0 3 m i , j σ i σ j ,
W i [ J 11 (i) J 12 (i) J 21 (i) J 22 (i) ] .

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