Abstract

We report on a new configuration of fiber-based polarization-sensitive Mueller matrix optical coherence tomography that permits the acquisition of the round-trip Jones matrix of a biological sample using only one light source and a single depth scan. In this new configuration, a polarization modulator is used in the source arm to continuously modulate the incident polarization state for both the reference and the sample arms. The Jones matrix of the sample can be calculated from the two frequency terms in the two detection channels. The first term is modulated by the carrier frequency, which is determined by the longitudinal scanning mechanism, whereas the other term is modulated by the beat frequency between the carrier frequency and the second harmonic of the modulation frequency of the polarization modulator. One important feature of this system is that, for the first time to our knowledge, the Jones matrix of the sample can be calculated with a single detection channel and a single measurement when diattenuation is negligible. The system was successfully tested by imaging both standard polarization elements and biological samples.

© 2005 Optical Society of America

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References

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  1. M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
    [CrossRef]
  2. 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).
    [CrossRef] [PubMed]
  3. J. F. de Boer, T. E. Milner, J. S. Nelson, “Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography,” Opt. Lett. 24, 300–302 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. C. E. Saxer, J. F. de Boer, B. H. Park, Y. H. Zhao, Z. P. Chen, J. S. Nelson, “High-speed fiber-based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355–1357 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. S. Jiao, L.-H. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101–103 (2002).
    [CrossRef]
  10. S. Jiao, W. Yu, G. Stoica, L.-H. V. Wang, “Optical-fiber-based Mueller optical coherence tomography,” Opt. Lett. 28, 1206–1208 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. M. Todorović, S. Jiao, L.-H. V. Wang, G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29, 2402–2404 (2004).
    [CrossRef]
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    [PubMed]

2004 (1)

2003 (3)

2002 (2)

S. Jiao, L.-H. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

S. Jiao, L.-H. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101–103 (2002).
[CrossRef]

2001 (2)

2000 (1)

1999 (2)

1997 (1)

1993 (1)

1992 (1)

1991 (1)

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Akkin, T.

Aspect, A.

Chen, Z. P.

Davé, D. P.

de Boer, J. F.

Fercher, A. F.

Fujimoto, J. G.

Gotzinger, E.

Hee, M. R.

Hitzenberger, C. K.

Huang, D.

Hunter, P. J.

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Izatt, J. A.

Jiao, S.

Kozak, J. A.

Le Grice, I. J.

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Milner, T. E.

Nelson, J. S.

Nielsen, P. M. F.

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Oakberg, T. C.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Park, B. H.

Pircher, M.

Rollins, A. M.

Roth, J. E.

Saxer, C. E.

Smaill, B. H.

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Sticker, M.

Stoica, G.

Swanson, E. A.

Todorovic, M.

van Gemert, M. J. C.

Vansteenkiste, N.

Vignolo, P.

Wang, B.

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

Wang, L.-H. V.

Yazdanfar, S.

Yu, W.

S. Jiao, W. Yu, G. Stoica, L.-H. V. Wang, “Optical-fiber-based Mueller optical coherence tomography,” Opt. Lett. 28, 1206–1208 (2003).
[CrossRef] [PubMed]

S. Jiao, W. Yu, G. Stoica, L.-H. V. Wang, “Contrast mechanisms in polarization-sensitive Mueller-matrix optical coherence tomography and application in burn imaging,” Appl. Opt. 42, 5192–5197 (2003).
[CrossRef]

Zhao, Y. H.

Am. J. Physiol. (1)

P. M. F. Nielsen, I. J. Le Grice, B. H. Smaill, P. J. Hunter, “Mathematical model of geometry and fibrous structure of the heart,” Am. J. Physiol. 260, H1365 (1991).
[PubMed]

Appl. Opt. (1)

S. Jiao, W. Yu, G. Stoica, L.-H. V. Wang, “Contrast mechanisms in polarization-sensitive Mueller-matrix optical coherence tomography and application in burn imaging,” Appl. Opt. 42, 5192–5197 (2003).
[CrossRef]

J. Biomed. Opt. (1)

S. Jiao, L.-H. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

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

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

Opt. Express (1)

Opt. Lett. (8)

D. P. Davé, T. Akkin, T. E. Milner, “Polarization-maintaining fiber-based optical low-coherence reflectometer for characterization and ranging of birefringence,” Opt. Lett. 28, 1775–1777 (2003).
[CrossRef] [PubMed]

C. E. Saxer, J. F. de Boer, B. H. Park, Y. H. Zhao, Z. P. Chen, J. S. Nelson, “High-speed fiber-based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355–1357 (2000).
[CrossRef]

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).
[CrossRef] [PubMed]

J. F. de Boer, T. E. Milner, J. S. Nelson, “Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography,” Opt. Lett. 24, 300–302 (1999).
[CrossRef]

J. E. Roth, J. A. Kozak, S. Yazdanfar, A. M. Rollins, J. A. Izatt, “Simplified method for polarization-sensitive optical coherence tomography,” Opt. Lett. 26, 1069–1071 (2001).
[CrossRef]

S. Jiao, L.-H. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101–103 (2002).
[CrossRef]

S. Jiao, W. Yu, G. Stoica, L.-H. V. Wang, “Optical-fiber-based Mueller optical coherence tomography,” Opt. Lett. 28, 1206–1208 (2003).
[CrossRef] [PubMed]

M. Todorović, S. Jiao, L.-H. V. Wang, G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29, 2402–2404 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

B. Wang, T. C. Oakberg, “A new instrument for measuring both the magnitude and angle of low level linear birefringence,” Rev. Sci. Instrum. 70, 3847–3854 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental system. SLD, superluminescent diode, horizontally polarized; PM, polarization modulator; FG, function generator; NBS, nonpolarizing beam splitter; LP, linear polarizer; M, mirror; PBS, polarizing beam splitter; SMF, single-mode optical fiber; PDH and PDV, photodiodes for the horizontal (H) and vertical (V) polarization components, respectively. The vertical channel can be removed when diattenuation can be neglected in a sample (S).

Fig. 2
Fig. 2

Mean values and standard deviations of the round-trip retardation and orientation of the fast axis for a λ/4 plate calculated from the measured Jones matrix. Most of the error bars are smaller than the size of the marker.

Fig. 3
Fig. 3

(a) M00 image of the Mueller matrix and (b) retardation image for a piece of porcine tendon. (c) M00 image of the Mueller matrix and (d) retardation image for the skin of a rat tail measured in vivo. The gray scale is for the retardation images. The M00 image is on a logarithmic scale and the retardation images are on a linear scale. The height of each image is 1 mm. EP, epidermis; DP, dermal papilla; DJ, epidermal–dermal junction.

Fig. 4
Fig. 4

Muscle fiber orientation in a rat heart septum calculated from the differentiated Jones matrix.

Equations (16)

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J m ( φ , π / 4 ) = [ cos φ / 2 i sin φ / 2 i sin φ / 2 cos φ / 2 ] ,
E i = [ cos φ / 2 i sin φ / 2 ] .
E o = J T E i = [ J ( 1 , 1 ) cos φ / 2 + i J ( 1 , 2 ) sin φ / 2 J ( 1 , 2 ) cos φ / 2 + i J ( 2 , 2 ) sin φ / 2 ] ,
J T = [ J ( 1 , 1 ) J ( 1 , 2 ) J ( 1 , 2 ) J ( 2 , 2 ) ]
J ref = J l p J r f 2 J l p , J l p = 1 / 2 [ 1 1 1 1 ] ,
E ref = [ E r h E r v ] exp ( i φ / 2 ) ,
I x = E r h exp [ i ( φ / 2 + k ¯ z r ) ] + [ J ( 1 , 1 ) cos φ / 2 + i J ( 1 , 2 ) sin φ / 2 ] exp ( i k ¯ z s ) 2 = I x 0 + I ˜ x , I y = E r v exp [ i ( φ / 2 + k ¯ z r ) ] + [ J ( 1 , 2 ) cos φ / 2 + i J ( 2 , 2 ) sin φ / 2 ] exp ( i k ¯ z s ) 2 = I y 0 + I ˜ y ,
I ˜ x = E r h Re { [ ( 1 , 1 ) + J ( 1 , 2 ) ] exp [ - i ( k ¯ z + φ r ) ] + [ J ( 1 , 1 ) - J ( 1 , 2 ) ] exp [ - i ( k ¯ z + φ + φ r ) ] } , I ˜ y = E r v Re { [ J ( 1 , 2 ) + J ( 2 , 2 ) ] exp [ - i ( k ¯ z + φ r ) ] + [ J ( 1 , 2 ) - J ( 2 , 2 ) ] exp [ - i ( k ¯ z + φ + φ r ) ] } ,
I ˜ x = E r x J ( 1 , 1 ) + J ( 1 , 2 ) cos ( k ¯ z + φ r - φ x 1 ) + E r x J ( 1 , 1 ) - J ( 1 , 2 ) [ cos ( k ¯ z + φ r - φ x 2 ) × cos φ - sin ( k ¯ z + φ r - φ x 2 ) sin φ ] , I ˜ y = E r y J ( 1 , 2 ) + J ( 2 , 2 ) cos ( k ¯ z + φ r - φ y 1 ) + E r y J ( 1 , 2 ) - J ( 2 , 2 ) [ cos ( k ¯ z + φ r - φ y 2 ) × cos φ - sin ( k ¯ z + φ r - φ y 2 ) sin φ ] ,
sin φ = l = 0 2 J 2 l + 1 ( A 0 ) sin [ ( 2 l + 1 ) ω m t ] , cos φ = J 0 ( A 0 ) + l = 1 2 J 2 l ( A 0 ) cos [ ( 2 l ) ω m t ] ,
I ˜ x = E r x J ( 1 , 1 ) + J ( 1 , 2 ) cos ( k ¯ z + φ r - φ x 1 ) + E r x J ( 1 , 1 ) - J ( 1 , 2 ) { cos ( k ¯ z + φ r - φ x 2 ) × 2 J 2 l ( 2.405 ) cos [ ( 2 l ) ω m t ] - sin ( k ¯ z + φ r - φ x 2 ) × 2 J 2 l + 1 ( 2.405 ) sin [ ( 2 l + 1 ) ω m t ] } , I ˜ y = E r y J ( 1 , 2 ) + J ( 2 , 2 ) cos ( k ¯ z + φ r - φ y 1 ) + E r y J ( 1 , 2 ) - J ( 2 , 2 ) { cos ( k ¯ z + φ r - φ y 2 ) × 2 J 2 l ( 2.405 ) cos [ ( 2 l ) ω m t ] - sin ( k ¯ z + φ r - φ y 2 ) × 2 J 2 l + 1 ( 2.405 ) sin [ ( 2 l + 1 ) ω m t ] } .
J ( 1 , 1 ) = 0.5 [ I ˜ a x * ( k ¯ z ) + I ˜ a x × ( 2 ω m t - k ¯ z ) / J 2 ( 2.405 ) ] / E r x , J ( 1 , 2 ) = 0.5 [ I ˜ a x * ( k ¯ z ) - I ˜ a x × ( 2 ω m t - k ¯ z ) / J 2 ( 2.405 ) ] / E r x ,
J ( 1 , 2 ) = 0.5 [ I ˜ a y * ( k ¯ z ) + I ˜ a y × ( 2 ω m t - k ¯ z ) / J 2 ( 2.405 ) ] / E r y ,
J ( 2 , 2 ) = 0.5 [ I ˜ a y * ( k ¯ z ) - I ˜ a y × ( 2 ω m t - k ¯ z ) / J 2 ( 2.405 ) ] / E r y ,
I c x 1 / 2 [ 1 + cos ( φ ) ] , I c y 1 / 2 [ 1 - cos ( φ ) ] ,
I c x ( 2 ω m ) I c x ( 4 ω m ) = I c y ( 2 ω m ) I c y ( 4 ω m ) = J 2 ( 2.405 ) J 4 ( 2.405 ) .

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