Abstract

We examine signal degradation effects in fiber arrays from fiber-to-fiber coupling and from cross talk attributable to backscatter from the sample medium originating from adjacent fibers in the array. An analysis of coupling and cross talk for single-mode fibers (SMFs) operating at 1310nm with different core diameters, interaction lengths, core center spacing, and numerical apertures (NAs) is evaluated. The coupling was evaluated using beam propagation algorithms and cross talk was analyzed by using Monte Carlo methods. Several multimode fiber types that are currently used in fiber image guides were also evaluated for comparative purposes. The analysis shows that an optimum NA and core diameter can be found for a specific fiber center separation that maximizes the directly backscattered signal relative to the cross talk. The coupling between fibers can be kept less than 35dB for interaction lengths less than 5mm. The calculations were compared to an experimentally fabricated SMF array with 15μm center spacing and showed good agreement. The experimental fiber array without a lens was also used in a coherent detection configuration to measure the position of a mirror. Accurate depth ranging up to a distance of 250μm from the tip of the fiber was achieved, which was five times the Rayleigh range of the beam emitted from the fiber.

© 2007 Optical Society of America

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References

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2005 (2)

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

T. Xie, D. Mukai, S. Guo, M. Brenner, and Z. Chen, "Fiber-optic-bundle-based optical coherence tomography," Opt. Lett. 30, 1803-1805 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (4)

P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Collection efficiency of a single optical fiber in turbid media," Appl. Opt. 42, 3187-3197 (2003).
[CrossRef] [PubMed]

H. N. Paulsen, K. M. Hilligse, J. Thgersen, S. R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003).
[CrossRef] [PubMed]

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

2002 (2)

M. Larsson, W. Steenbergen, and T. Stromberg, "Influence of optical properties and fiber separation on laser Doppler flowmetry," J. Biomed. Opt. 7, 236-243 (2002).
[CrossRef] [PubMed]

T. J. Pfefer, K. T. Schomacker, M. N. Ediger, and N. S. Nishioka, "Multiple fiber probe design for fluorescence spectroscopy in tissue," Appl. Opt. 41, 4712-4721 (2002).
[CrossRef] [PubMed]

2001 (1)

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6, 167-176 (2001).
[CrossRef] [PubMed]

1999 (2)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., "A bidirectional beam propagation method for multiple dielectric interfaces," Photon. Technol. Lett. 11, 830-832 (1999).
[CrossRef]

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissue," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

1994 (1)

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

1992 (2)

L. Wang and S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (University of Texas, M.D. Anderson Cancer Center, 1992).

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

1991 (1)

Bargo, P. R.

Brenner, M.

Brightwell, A.

Carnohan, M.

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

Chen, Y.

Chen, Z.

Chrostowski, J.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

Chu, S. T.

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

Cobb, M. J.

Cottone, G.

Ding, H.

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Ediger, M. N.

Fang, Q.

Fedder, G. K.

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Gobel, W.

Guo, S.

Helmchen, F.

Hilligse, K. M.

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Hu, X.-H.

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

Huang, W. P.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

Jacobs, K. M.

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

Jacques, S. L.

P. R. Bargo, S. A. Prahl, and S. L. Jacques, "Collection efficiency of a single optical fiber in turbid media," Appl. Opt. 42, 3187-3197 (2003).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissue," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

L. Wang and S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (University of Texas, M.D. Anderson Cancer Center, 1992).

Jones, L. R.

Keiding, S. R.

Kerr, J. N. D.

Kinney, M. B.

Larsen, J. J.

Larsson, M.

M. Larsson, W. Steenbergen, and T. Stromberg, "Influence of optical properties and fiber separation on laser Doppler flowmetry," J. Biomed. Opt. 7, 236-243 (2002).
[CrossRef] [PubMed]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Li, X.

Liu, X.

Lu, J. Q.

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

Marcu, L.

Moes, C. J. M.

Mukai, D.

Nimmerjahn, A.

Nishioka, N. S.

Osgood, R. M.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., "A bidirectional beam propagation method for multiple dielectric interfaces," Photon. Technol. Lett. 11, 830-832 (1999).
[CrossRef]

Pan, Y.

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

Papaioannou, T.

Paulsen, H. N.

Pfefer, T. J.

Prahl, S. A.

Preyer, N. W.

Rao, H.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., "A bidirectional beam propagation method for multiple dielectric interfaces," Photon. Technol. Lett. 11, 830-832 (1999).
[CrossRef]

Ross, R.

Scarmozzino, R.

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., "A bidirectional beam propagation method for multiple dielectric interfaces," Photon. Technol. Lett. 11, 830-832 (1999).
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

Schomacker, K. T.

Steenbergen, W.

M. Larsson, W. Steenbergen, and T. Stromberg, "Influence of optical properties and fiber separation on laser Doppler flowmetry," J. Biomed. Opt. 7, 236-243 (2002).
[CrossRef] [PubMed]

Stromberg, T.

M. Larsson, W. Steenbergen, and T. Stromberg, "Influence of optical properties and fiber separation on laser Doppler flowmetry," J. Biomed. Opt. 7, 236-243 (2002).
[CrossRef] [PubMed]

Thennadil, S. N.

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6, 167-176 (2001).
[CrossRef] [PubMed]

Thgersen, J.

Troy, T. L.

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6, 167-176 (2001).
[CrossRef] [PubMed]

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissue," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

L. Wang and S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (University of Texas, M.D. Anderson Cancer Center, 1992).

Xie, H.

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

Xie, T.

T. Xie, D. Mukai, S. Guo, M. Brenner, and Z. Chen, "Fiber-optic-bundle-based optical coherence tomography," Opt. Lett. 30, 1803-1805 (2005).
[CrossRef] [PubMed]

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

Xu, C. L.

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissue," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Appl. Opt. (4)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissue," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Electron. Lett. (1)

T. Xie, H. Xie, G. K. Fedder, and Y. Pan, "Endoscopic optical coherence tomography with new MEMS mirror," Electron. Lett. 39, 1535-1536 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

J. Biomed. Opt. (2)

M. Larsson, W. Steenbergen, and T. Stromberg, "Influence of optical properties and fiber separation on laser Doppler flowmetry," J. Biomed. Opt. 7, 236-243 (2002).
[CrossRef] [PubMed]

T. L. Troy and S. N. Thennadil, "Optical properties of human skin in the near infrared wavelength range of 1000 to 2200 nm," J. Biomed. Opt. 6, 167-176 (2001).
[CrossRef] [PubMed]

J. Lightwave Technol. (2)

W. P. Huang, C. L. Xu, S. T. Chu, and S. K. Chaudhuri, "The finite difference vector beam propagation method: analysis and assessment," J. Lightwave Technol. 10, 295-305 (1992).
[CrossRef]

C. L. Xu, W. P. Huang, J. Chrostowski, and S. K. Chaudhuri, "A full vectorial beam propagation method for anisotropic waveguides," J. Lightwave Technol. 12, 1926-1931 (1994).
[CrossRef]

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

H. Ding, J. Q. Lu, K. M. Jacobs, and X.-H. Hu, "Determination of refractive indicies of porcine skin tissues and Intralipid at eight wavelengths between 325 and 1557 nm," J. Opt. Soc. Am. A 22, 1-7 (2005).
[CrossRef]

Opt. Lett. (4)

Photon. Technol. Lett. (1)

H. Rao, R. Scarmozzino, and R. M. Osgood, Jr., "A bidirectional beam propagation method for multiple dielectric interfaces," Photon. Technol. Lett. 11, 830-832 (1999).
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography--principles and applications," Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Other (4)

L. Wang and S. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (University of Texas, M.D. Anderson Cancer Center, 1992).

Corning SMF-28 Optical Fiber product information (Corning, Inc., N.Y., 2001).

Stocker Yale BIF-RC-1310-L2 product information, Stocker Yale, Inc., New Hampshire, 2005, http://www.stockeryale.com/o/fiber/products/bif-rc-1310-12.htm.

RSOFT Design Group, BeamPROP V. 6.01, www.rsoftdesign.com.

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Figures (11)

Fig. 1
Fig. 1

Fiber array geometry used for analysis and the experimental design. D T , reduced fiber diameter; d s , fiber center separation; d c o , fiber core diameter; D o , standard fiber diameter; L interaction length of reduced diameter fiber.

Fig. 2
Fig. 2

Description of (a) parallel beam propagation in multiple fibers, (b) light transmitted into a tissue sample and scattered, (c) backscattered photons collected within the acceptance angle of the fiber, and (d) return signals propagating in multiple fibers.

Fig. 3
Fig. 3

Rayleigh range from a fiber (a) with ( 2 L R ) and (b) without a lens ( L R ) . 2 ω is the mode field diameter of the fiber.

Fig. 4
Fig. 4

Coupling between fibers as a function of interaction length (L). MMF A, 9.0 μm core diameter, 0.55 NA, 12 μm fiber separation. SMF A, 8.2 μm core diameter, 0.12 NA, 15 μm fiber separation. SMF B, 6.0 μm core diameter, 0.16 NA, 15 μm fiber separation. MMF B, 8.0 μm core diameter, 0.25 NA, 12 μm fiber separation.

Fig. 5
Fig. 5

Coupling (dB) as a function of fiber separation distance (μm) for SMF A and SMF B fibers described in Fig. 4 with fixed interaction lengths of 2 and 5 mm .

Fig. 6
Fig. 6

Monte Carlo simulation of backscattered light from an Intralipid-10% tissue phantom solution as a function of distance from the launch fiber. Circles, 9.0 μm core diameter, 0.55 NA, 12 μm fiber separation; pluses, 8.2 μm core diameter, 0.12 NA, 12 μm fiber separation; stars, 6.0 μm core diameter, 0.16 NA, 12 μm fiber separation; triangles, 8.0 μm core diameter, 0.25 NA, 12 μm fiber separation; exes, 8.2 μm core diameter, 0.16 NA, 12 μm fiber separation.

Fig. 7
Fig. 7

Ratio of backscattered signal ( P o ) to backscattered cross talk ( P X T ) as a function of different fiber type ( NA / d c ) .

Fig. 8
Fig. 8

Experimental system for measuring the backscattered signal to a fiber of interest and cross talk to adjacent fibers in an array. The source is a super luminescent diode with a center wavelength of 1310 nm and Det 1, Det 2, and Det 3 are detectors.

Fig. 9
Fig. 9

Experimental data for cross-talk measurement from an Intralipid-10% solution with a fiber array consisting of fibers with 8.2 μm core diameters, 0.12 NAs, and 15 μm fiber separation.

Fig. 10
Fig. 10

Experimental coherent fiber system for measuring distances with the experimental fiber array. DAQ is a data acquisition card, M1 is the mirror translated from the fiber array, and L1 is a lens collimating light onto a moving mirror M2.

Fig. 11
Fig. 11

Interference fringes formed within the coherence length of the source with the mirror M1 located 50, 150, and 250 μm from the edge of the fiber array.

Tables (1)

Tables Icon

Table 1 Fiber Parameters Used in the Array and Fraction of Collected Backscatter P o

Equations (5)

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2 ω = d c o [ 0.65 + 1.619 V 3 / 2 + 2.87 V 6 ] ,
P X T S ( d B ) = 10 log ( P m P 0 ) , m = 1 , 2 , , 10 ,
P E - X T ( d B ) = 10 log [ ( B l B S ) ( 1 T adjacent ) ( A l A S ) ( 1 T l aunch ) ( 1 R 3 d B ) ] ,
l c 0.44 λ o 2 Δ λ = 19 μm .
z R = π ( 2 ω ) 2 4 λ = 50 μm .

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