Abstract

Multimode fiber endoscopes have recently been shown to provide sub-micrometer resolution, however, imaging through a multimode fiber is highly sensitive to bending. Here we describe the implementation of a coherent beacon source placed at the distal tip of the multimode fiber, which can be used to compensate for the effects of bending. In the first part of this paper, we show that a diffraction limited focused spot can be generated at the distal tip of the multimode fiber using the beacon. In the second part, we demonstrate focusing even when the fiber is bent by dynamically compensating for it. The speckle pattern at the proximal fiber end, generated by the beacon source placed at its distal end, is highly dependent on the fiber conformation. We experimentally show that by intensity correlation, it is possible to identify the fiber conformation and maintain a focus spot while the fiber is bent over a certain range. Once the fiber configuration is determined, previously calibrated phase patterns could be stored for each fiber conformation and used to scan the distal spot and perform imaging.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2013 (2)

2012 (5)

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express20(10), 10583–10590 (2012).
[CrossRef] [PubMed]

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip12(3), 635–639 (2012).
[CrossRef] [PubMed]

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat Commun3, 1027 (2012).
[CrossRef] [PubMed]

2011 (2)

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

2008 (1)

2006 (1)

2005 (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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

2004 (1)

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

2002 (1)

F. Helmchen, “Miniaturization of fluorescence microscopes using fibre optics,” Exp. Physiol.87(6), 737–745 (2002).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

1987 (1)

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9(9), 919–933 (1973).
[CrossRef]

Anderson, D. Z.

Beckwith, P. H.

Bellanger, C.

Berneth, H.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Bianchi, S.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip12(3), 635–639 (2012).
[CrossRef] [PubMed]

Bolshtyansky, M. A.

Brignon, A.

Brown, C. M.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Bruder, F. K.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Caravaca-Aguirre, A. M.

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Choi, W.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Choi, Y.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Cižmár, T.

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat Commun3, 1027 (2012).
[CrossRef] [PubMed]

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Colineau, J.

Conkey, D. B.

Dasari, R. R.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Dholakia, K.

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat Commun3, 1027 (2012).
[CrossRef] [PubMed]

Di Leonardo, R.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip12(3), 635–639 (2012).
[CrossRef] [PubMed]

Dombeck, D. A.

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Fäcke, T.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Fang-Yen, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Hagen, R.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Helmchen, F.

F. Helmchen, “Miniaturization of fluorescence microscopes using fibre optics,” Exp. Physiol.87(6), 737–745 (2002).
[CrossRef] [PubMed]

Hönel, D.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Howard, S. S.

Huignard, J. P.

Huland, D. M.

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Jurbergs, D.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Kasischke, K. A.

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Kim, M.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Kobat, D.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Lee, K. J.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Levene, M. J.

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Li, X.

MacDonald, D. J.

McMichael, I.

Molloy, R. P.

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Moser, C.

Myaing, M. T.

Niv, E.

Ouzounov, D. G.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Papadopoulos, I. N.

Pavlova, I.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Piestun, R.

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Psaltis, D.

Rivera, D. R.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Rölle, T.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Ruffin, P. B.

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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Wang, K.

Webb, W. W.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Weiser, M.-S.

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Xu, C.

D. M. Huland, C. M. Brown, S. S. Howard, D. G. Ouzounov, I. Pavlova, K. Wang, D. R. Rivera, W. W. Webb, and C. Xu, “In vivo imaging of unstained tissues using long gradient index lens multiphoton endoscopic systems,” Biomed. Opt. Express3(5), 1077–1085 (2012).
[CrossRef] [PubMed]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Yang, T. D.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9(9), 919–933 (1973).
[CrossRef]

Yeh, P.

Yin, S.

Yoon, C.

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Yu, F. T.

Zel’dovich, B. Y.

Zhang, J.

Appl. Opt. (1)

Biomed. Opt. Express (2)

Exp. Physiol. (1)

F. Helmchen, “Miniaturization of fluorescence microscopes using fibre optics,” Exp. Physiol.87(6), 737–745 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron.9(9), 919–933 (1973).
[CrossRef]

J. Neurophysiol. (1)

M. J. Levene, D. A. Dombeck, K. A. Kasischke, R. P. Molloy, and W. W. Webb, “In vivo multiphoton microscopy of deep brain tissue,” J. Neurophysiol.91(4), 1908–1912 (2004).
[CrossRef] [PubMed]

Lab Chip (1)

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip12(3), 635–639 (2012).
[CrossRef] [PubMed]

Nat Commun (1)

T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat Commun3, 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. Methods2(12), 941–950 (2005).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

Y. Choi, C. Yoon, M. Kim, T. D. Yang, C. Fang-Yen, R. R. Dasari, K. J. Lee, and W. Choi, “Scanner-Free and Wide-Field Endoscopic Imaging by Using a Single Multimode Optical Fiber,” Phys. Rev. Lett.109(20), 203901 (2012).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

D. R. Rivera, C. M. Brown, D. G. Ouzounov, I. Pavlova, D. Kobat, W. W. Webb, and C. Xu, “Compact and flexible raster scanning multiphoton endoscope capable of imaging unstained tissue,” Proc. Natl. Acad. Sci. U.S.A.108(43), 17598–17603 (2011).
[CrossRef] [PubMed]

Proc. SPIE (1)

H. Berneth, F. K. Bruder, T. Fäcke, R. Hagen, D. Hönel, D. Jurbergs, T. Rölle, and M.-S. Weiser, “Holographic recording aspects of high-resolution Bayfol® HX photopolymer,” Proc. SPIE7957, 79570H(2011).
[CrossRef]

Other (1)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, Sixth Edition (Oxford University, 2007).

Supplementary Material (1)

» Media 1: MOV (2946 KB)     

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Fig. 1
Fig. 1

Principle for recording a virtual beacon source on a photosensitive holographic material. The object beam is a diffraction-limited spot generated by an objective lens on the position where the virtual source is desired. The reference beam is delivered by a fiber using two different geometries. The object beam interferes with the reference beam and a hologram is recorded in the polymer film. We reconstruct the object point source (virtual holographic beacon) by illuminating the hologram with the same reference beam that acts as calibration beam for phase conjugation. In this step, the object beam is removed. The calibration beam is diffracted by the hologram as if it was coming from the initial focus spot, which is a virtual beacon, and gets coupled into the multimode fiber. (a) Geometry using a double-clad fiber where the reference beam comes from the single-mode core and the diffracted light is coupled in the multimode cladding. The polymer film is directly laminated on the fiber tip. (b) Geometry using a multimode fiber and a separate single-mode fiber to bring the reference beam. The polymer film is laminated on a glass slide, which acts as a planar waveguide for the reference beam coupled into it using a prism.

Fig. 2
Fig. 2

(a) Experimental setup of Digital Phase Conjugation (DPC) through a multimode fiber using a virtual holographic beacon source. The initial beam is split into two arms with BS1. A first beam is expanded by the telescope formed by lenses L1-L2 and goes through the spatial filter OBJ3, pinhole and L4. This cleaned up and expanded beam is used as an off-axis reference beam for the recording of a digital interferogram on CMOS1. The second beam is coupled into a single mode fiber with OBJ4. The light at the distal side of the single mode fiber is coupled into a glass plate (planar waveguide) through a microprism [Fig. 1] where it acts as a calibration beam to read-out the hologram placed at the fiber distal tip. The light diffracted from the hologram is collected by the multi-mode fiber. The proximal facet of the fiber is imaged on the CMOS sensor through the 4f imaging system (OBJ2 and L3). The reference is combined with the image using the non-polarizing beamsplitter BS2 and thus generating a digital off-axis interferogram. By displaying the digital conjugate phase on the SLM and illuminating it with the off-axis reference beam, the phase conjugate wavefront is generated and is following redirected towards the fiber by reflecting on BS2. The quality of the generated focus is examined on CMOS2 through the imaging system formed by OBJ1 and L5. (b) and (c) show two different bending positions of the fiber where ΔR is the relative change in bending radius.

Fig. 3
Fig. 3

Digital Phase Conjugation (DPC) using a virtual holographic beacon source. (a) Focal spot obtained after phase conjugation from a real beacon source (by directly focusing light at the distal tip of a 200μm core/ 0.39 NA fiber). The enhancement is evaluated to be approximately 340. (b) is the output of the fiber when a random phase is displayed on the SLM in the same experimental conditions. (c) Focal spot obtained after phase conjugation from a virtual holographic beacon source placed at the distal facet of the fiber. The enhancement is evaluated to be approximately 220, which is around 65% of what was achieved with a real beacon in (a). (d) is the output of the fiber when a random phase is displayed on the SLM. The units of the transverse axis are pixels.

Fig. 4
Fig. 4

(a) to (c) normalized enhancement of the focal spot obtained after phase conjugation (blue dots) and the correlation function of the intensity speckle patterns (red dots) with the reference intensity speckle pattern, as a function of the relative bending radius, for three fibers with different core diameters (50μm, 105μm and 200μm). The full widths at half maximum (FWHM) are respectively 1 mm, 2.7 mm and 10 mm. Figure (d) gives the absolute values for the three measurements to show that for a large core fiber the enhancement is much higher even if it drops faster.

Fig. 5
Fig. 5

(a) to (d) normalized enhancement of the focal spot obtained after phase conjugation (blue dots) and the correlation function of the speckle pattern (red crosses) as a function of bending for different excitation positions at the distal facet of a 105μm core fiber. The excitation position is indicated with a green dot on the gray circle representing the fiber facet. The decay of the enhancement is slower when the fiber excitation is moved towards the edge. The FWHM are respectively 1.1 mm, 1.7 mm, 1.9 mm and 2 mm. For edge excitation more modes are excited and the absolute value of enhancement increases which is shown in (e).

Fig. 6
Fig. 6

Focusing through a fiber bent within a restricted radius of curvature range using the intensity speckle patterns generated by a holographic beacon source as a conformation sensor. The focus is generated by DPC. The blue dots give the enhancement of the focal spot obtained after phase conjugation. The red dots give the correlation of the intensity speckle pattern obtained at the proximal facet of the fiber, with the intensity speckle pattern of the closest prerecorded position of the fiber. (a) shows the case of under sampling (N = 3) which means that a significant drop of enhancement is observed between the precalibrated positions. For (b) we choose N = 9 and thus the enhancement between the precalibrated positions is maintained at a high value. Therefore the focus is maintained over the whole bending range.

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