Abstract

Multi-mode fiber (MMF) endoscopes are extremely thin and have higher spatial resolution than conventional endoscopes; however, all current MMF endoscope designs require either that the MMF remain rigid during insertion and imaging or that the orientation of the MMF be known. This limits their possible medical applications. We describe an MMF endoscope design that allows the MMF to be arbitrarily bent as it is maneuvered to the target site prior to imaging. This is achieved by the addition of a partial reflector to the distal end of the MMF, which allows measurement of the mode coupling in the MMF using the reflected light arriving at the proximal end of the MMF. This measurement can be performed while the distal end of the endoscope is not directly accessible, as when the endoscope is being maneuvered. We simulate imaging through such a flexible MMF endoscope, where the MMF is step-index with 1588 spatial modes, and obtain an image even after the mode coupling matrix of the MMF is altered randomly, corresponding to an unknown bending of the MMF.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
    [Crossref]
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    [Crossref] [PubMed]
  13. Y. Pu, X. Yang, I. Papadopoulos, S. Farahi, C. Hsieh, C. A. Ong, D. Psaltis, C. Moser, D. Psaltis, and K. M. Stankovic, “Imaging of the mouse cochlea with two-photon microscopy and multimode fiber-based microendoscopy,” in Biomedical Optics (OSA, 2014), paper BT4A.3.
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    [Crossref]
  15. S. Farahi, D. Ziegler, I. N. Papadopoulos, D. Psaltis, and C. Moser, “Dynamic bending compensation while focusing through a multimode fiber,” Opt. Express 21(19), 22504–22514 (2013).
    [Crossref] [PubMed]
  16. M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
    [Crossref]
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  21. R. A. Panicker and J. M. Kahn, “Algorithms for compensation of multimode fiber dispersion using adaptive optics,” J. Lightwave Technol. 27(24), 5790–5799 (2009).
    [Crossref]
  22. T. F. Massoud, “Method and device for treating intracranial vascular aneurysms,” U.S. Patent 5,776,097 (1998).
  23. R. A. Horn, Matrix Analysis, 2nd ed. (Cambridge University, 2013).
  24. M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
    [Crossref]
  25. J. Mertz, Introduction to Optical Microscopy (Roberts and Co. Publishers, 2010).
  26. A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (2005).
    [Crossref]
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    [Crossref] [PubMed]

2015 (3)

2014 (4)

2013 (2)

2012 (1)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

2009 (1)

2005 (2)

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (2005).
[Crossref]

2002 (1)

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

2001 (1)

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

Ando, T.

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

Caravaca Aguirre, A. M.

A. M. Caravaca Aguirre and R. Piestun, “Robustness of multimode fiber focusing through wavefront shaping,” in Latin America Optics and Photonics Conference (2014).
[Crossref]

Cheung, E. L. M.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Choi, W.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

Y. Choi, P. Hosseini, W. Choi, R. R. Dasari, P. T. C. So, and Z. Yaqoob, “Dynamic speckle illumination wide-field reflection phase microscopy,” Opt. Lett. 39(20), 6062–6065 (2014).
[Crossref] [PubMed]

Choi, Y.

Y. Choi, P. Hosseini, W. Choi, R. R. Dasari, P. T. C. So, and Z. Yaqoob, “Dynamic speckle illumination wide-field reflection phase microscopy,” Opt. Lett. 39(20), 6062–6065 (2014).
[Crossref] [PubMed]

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

Cižmár, T.

Cocker, E. D.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Dasari, R. R.

Dholakia, K.

Edelman, A.

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (2005).
[Crossref]

Farahi, S.

Flusberg, B. A.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Gu, R. Y.

Hane, K.

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

Hosseini, P.

Jung, J. C.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Kahn, J. M.

Kim, M.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

Mahalati, R. N.

Massoud, T. F.

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

Morales-Delgado, E. E.

Moser, C.

Murayama, Y.

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

Nogawa, S.

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

Panicker, R. A.

Papadopoulos, I. N.

Piestun, R.

A. M. Caravaca Aguirre and R. Piestun, “Robustness of multimode fiber focusing through wavefront shaping,” in Latin America Optics and Photonics Conference (2014).
[Crossref]

Piyawattanametha, W.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Plöschner, M.

Psaltis, D.

Rao, N. R.

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (2005).
[Crossref]

Sasaki, M.

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

Schnitzer, M. J.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

So, P. T. C.

Straka, B.

Tyc, T.

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Utsumi, A.

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

Viñuela, F.

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

Yaqoob, Z.

Yoon, C.

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

Ziegler, D.

Acta Numer. (1)

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (2005).
[Crossref]

AJNR Am. J. Neuroradiol. (1)

T. F. Massoud, Y. Murayama, F. Viñuela, and A. Utsumi, “Laboratory evaluation of a microangioscope for potential percutaneous cerebrovascular applications,” AJNR Am. J. Neuroradiol. 22(2), 363–365 (2001).
[PubMed]

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

Y. Choi, C. Yoon, M. Kim, W. Choi, and W. Choi, “Optical imaging with the use of a scattering lens,” IEEE J. Sel. Top. Quantum Electron. 20(2), 61–73 (2014).
[Crossref]

J. Lightwave Technol. (1)

Jpn. J. Appl. Phys. (1)

M. Sasaki, T. Ando, S. Nogawa, and K. Hane, “Direct photolithography on optical fiber end,” Jpn. J. Appl. Phys. 41(Part 1, No. 6B), 4350–4355 (2002).
[Crossref]

Nat. Commun. (1)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Nat. Methods (1)

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. J. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2(12), 941–950 (2005).
[Crossref] [PubMed]

Nat. Photonics (1)

M. Plöschner, T. Tyc, and T. Čižmár, “Seeing through chaos in multimode fibres,” Nat. Photonics 9(8), 529–535 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Other (12)

Y. Pu, X. Yang, I. Papadopoulos, S. Farahi, C. Hsieh, C. A. Ong, D. Psaltis, C. Moser, D. Psaltis, and K. M. Stankovic, “Imaging of the mouse cochlea with two-photon microscopy and multimode fiber-based microendoscopy,” in Biomedical Optics (OSA, 2014), paper BT4A.3.

A. M. Caravaca Aguirre and R. Piestun, “Robustness of multimode fiber focusing through wavefront shaping,” in Latin America Optics and Photonics Conference (2014).
[Crossref]

S. Bianchi, V. P. Rajamanickam, L. Ferrara, E. Di Fabrizio, R. Di Leonardo, and C. Liberale, “High numerical aperture imaging by using multimode fibers with micro-fabricated optics,” in CLEO: Science and Innovations (OSA, 2014), paper SM2N.6.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, 1991).

H. A. Haus, Waves and Fields in Optoelectronics, 3rd ed. (Prentice-Hall, 1984).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer Science & Business Media, 1983).

D. Loterie, S. Farahi, I. Papadopoulos, A. Goy, D. Psaltis, and C. Moser, “Digital confocal microscopy through a multimode fiber,” http://arxiv.org/abs/1502.04172 (2015).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” Imaging Appl. Opt. (2014).

J. Mertz, Introduction to Optical Microscopy (Roberts and Co. Publishers, 2010).

T. F. Massoud, “Method and device for treating intracranial vascular aneurysms,” U.S. Patent 5,776,097 (1998).

R. A. Horn, Matrix Analysis, 2nd ed. (Cambridge University, 2013).

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Figures (6)

Fig. 1
Fig. 1 System diagram of a hypothetical MMF with three forward- and three backward-propagating modes. Forward- and backward-propagating modes are represented by arrows pointed to the right and left, respectively. The complex amplitudes of these modes, a and b, are measured at both the proximal and distal facets of the MMF. The matrix (S) represents coupling between the modes.
Fig. 2
Fig. 2 MMF endoscope apparatus for (a) distal calibration and (b) proximal calibration and imaging. In (a), the electric field at the distal end of the MMF is measured, and in (b) the electric field at the proximal end of the MMF is measured. As explained in the text, beam stop S1 is used to obtain a coherent measurement of the electric field; beam stops S2 and S3 are used to isolate different beams incident on the camera, and beam stop S4 is used to block light reflecting from the object during proximal calibration.
Fig. 3
Fig. 3 (a) Electric field amplitude reflectance and transmittance values of partial reflector. The red circle indicates the MMF core. Reflectance is indicated by image brightness; black represents an amplitude reflectance and transmittance of 0.05 and 1.05, respectively, while white represents an amplitude reflectance and transmittance of 0.50 and 0.91, respectively. (b) Entries of the matrix (D)r for an MMF with 1588 modes.
Fig. 4
Fig. 4 Accuracy of proximal calibration with errors in the measurement of the partial reflector. The error in the reflector is shown in (a) for a reflectance error of −23 dB, where reflectance error is characterized by the standard deviation of the error in the measured reflectance divided by the mean reflectance. The intensity pattern of a distal spot at −23 dB error is shown in (b). Calibration accuracy is plotted in (c) for errors ranging from −10 to −30 dB (10% to 0.1%); accuracy is characterized both by the trace divided by the number of rows of the matrix (U)p)actual(U)p)calc−1, as plotted in black on the left axis, and by the ratio of spot peak intensity divided by mean background intensity, as plotted in red on the right axis. The points corresponding to an error of −23 dB are indicated.
Fig. 5
Fig. 5 Formation of a spot through a fiber that has been perturbed after distal calibration. (a) Spot formed with an input electric field computed using (U), the unperturbed mode coupling matrix. (b) Spot formed with an input electric field computed using (U)p, the perturbed mode coupling matrix measured using proximal calibration.
Fig. 6
Fig. 6 (a) Cameraman object. (b) Image formed through a fiber that has not been perturbed after distal calibration, using the unperturbed matrix (U). (c) Image formed through a fiber that has been perturbed after distal calibration, using the perturbed matrix (U)p measured using proximal calibration.

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

b=Sa [ b p b d ]=[ S pp S pd S dp S dd ][ a p a d ]
S 1 = S ,
S T =S.
b d =U a p ,
b p = U T a d .
b=TUa,
b= U T RUa,
M out = TU M in
T 1 ( M out M in 1 )= U,
Q U T RU
Q p U p T R U p ,
Q p = 1 2 ( M out ) p ( M in ) p 1 + 1 2 ( ( M out ) p ( M in ) p 1 ) T .
Q p = V p T D q V p .
R= W T D r W.
Q p = U p T W T D r W U p .
D r W U p =N D q V p ,
D r W U p = N p D q V p
D r WU=N D q V.
U p = W D r 1 N D q V p
N ii =sgn[ Re( v pi v i ) ],
s in M U p (FT) 1 e ^
s out =FT U p M s in ,
s meas = M T U p T ( T T F s refl +R U p M s in ),
s sub = s meas M T U p T R U p M s in .
s fin = ( T T F) 1 U p * M * s sub .
p= s fin 2 s unif 2 ,
Q p = V p T D q X p
Q p = U p T W T D r Y U p .
V p T N * = U p T W T
N X p =Y U p .

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