Abstract

Theoretical analysis of a method for transmitting a complex image field through a single multimode optical fiber is presented. Using a known reference image, we show that it would be possible to evaluate the instantaneous modal dispersion of the fiber and use the knowledge of accumulated modal phases to recover the object field. For measuring the complex object and reference fields emanating from the fiber, we propose using a simple arrangement of two cameras for recording the intensity and Fourier images, followed by a modified Gerchberg–Saxton algorithm for full complex field reconstruction. While some experimental challenges could still be expected in any future implementation of this approach, we believe it would eventually allow the first image transmission through a long, multimode optical fiber.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  15. C. Bamber, B. Sutherland, A. Patel, C. Stewart, and J. S. Lundeen, “Measurement of the transverse electric field profile of light by a self-referencing method with direct phase determination,” Opt. Express 20, 2034–2044 (2012).
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    [CrossRef]

2012 (3)

2011 (1)

2010 (1)

2007 (1)

2006 (2)

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

2003 (2)

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
[CrossRef]

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).

1998 (1)

1996 (1)

1990 (1)

1985 (1)

B. Fischer and S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

1982 (1)

1976 (1)

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

1972 (1)

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Agour, M.

Bamber, C.

Bergmann, R. B.

Bishop, A. I.

Bouma, B. E.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

G. J. Tearney, R. H. Webb, and B. E. Bouma, “Spectrally encoded confocal microscopy,” Opt. Lett. 23, 1152–1154 (1998).
[CrossRef]

Brown, C. M.

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

Bruck, J. A.

J. A. Bruck, Fundamentals of Optical Fibers, 2nd ed. (Wiley, 2004).

Cizmar, T.

Depeursinge, C.

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Dholakia, K.

Dickensheets, D. L.

Dunning, G. J.

Eastwood, S. A.

Falldorf, C.

Fischer, B.

B. Fischer and S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

Froehly, L.

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Fukui, M.

Gerchberg, R. W.

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Hasan, T.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Karasawa, S.

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

Kino, G. S.

Kitayama, K.-I.

Kopylow, C. V.

Lang, F.

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Lasser, T.

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Lee, B.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
[CrossRef]

Lind, R. C.

Lucesoli, A.

Lundeen, J. S.

Martin, S. N.

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Morgan, M. J.

Motz, J. T.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Paganin, D. M.

Patel, A.

Petersen, T. C.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).

Reinhall, P. G.

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

Rizvi, I.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Rozzi, T.

Saxton, W.

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Seibel, E. J.

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).

Sternklar, S.

B. Fischer and S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

Stewart, C.

Sutherland, B.

Tearney, G. J.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

G. J. Tearney, R. H. Webb, and B. E. Bouma, “Spectrally encoded confocal microscopy,” Opt. Lett. 23, 1152–1154 (1998).
[CrossRef]

Webb, R. H.

White, W. M.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Yariv, A.

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

Yelin, D.

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

B. Fischer and S. Sternklar, “Image transmission and interferometry with multimode fibers using self-pumped phase conjugation,” Appl. Phys. Lett. 46, 113–114 (1985).
[CrossRef]

A. Yariv, “Three-dimensional pictorial transmission in optical fibers,” Appl. Phys. Lett. 28, 88–89 (1976).
[CrossRef]

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).

Nat. Commun. (1)

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

Nature (1)

D. Yelin, I. Rizvi, W. M. White, J. T. Motz, T. Hasan, B. E. Bouma, and G. J. Tearney, “Three-dimensional miniature endoscopy,” Nature 443, 765–765 (2006).
[CrossRef]

Opt. Commun. (1)

L. Froehly, S. N. Martin, T. Lasser, C. Depeursinge, and F. Lang, “Multiplexed 3D imaging using wavelength encoded spectral interferometry: a proof of principle,” Opt. Commun. 222, 127–136 (2003).
[CrossRef]

Opt. Eng. (1)

C. M. Brown, P. G. Reinhall, S. Karasawa, and E. J. Seibel, “Optomechanical design and fabrication of resonant microscanners for a scanning fiber endoscope,” Opt. Eng. 45, 043001 (2006).
[CrossRef]

Opt. Express (3)

Opt. Fiber Technol. (1)

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9, 57–79 (2003).
[CrossRef]

Opt. Lett. (4)

Optik (1)

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Other (1)

J. A. Bruck, Fundamentals of Optical Fibers, 2nd ed. (Wiley, 2004).

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Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic of the method for transmitting an image through a single optical fiber. (b) Flow chart outlining the various steps for computing the accumulated modal phases and recovering the object image.

Fig. 2.
Fig. 2.

(a) Input field coupling into a multimode fiber. (b) The resulting images expressed as superposition of LP modes of different core diameters (2rc).

Fig. 3.
Fig. 3.

Number of resolvable points (blue circles) and number of propagation modes (red squares) as a function of the fiber’s core diameter and normalized frequency parameter. Dashed curve: Nm=V2/4 (see text).

Fig. 4.
Fig. 4.

Image propagation in 150 μm core diameter fiber (V=72.985).

Fig. 5.
Fig. 5.

Input reference field for calculating modal phase. (a) Intensity image. (b) Amplitudes (top) and phases (bottom) of the modes comprising the reference field.

Fig. 6.
Fig. 6.

Extracting the complex output fields from two intensity images. (a) The output field is split into two imaging channels; one captures an intensity image, the other captures a Fourier image. (b) The captured images serve as the inputs to a modified Gerchberg–Saxton algorithm with a small-error monitor. FFT, fast Fourier transform; IFFT, inverse fast Fourier transform. : angle.

Fig. 7.
Fig. 7.

Reference field transmission, acquisition, and calculation of the complex mode coefficients. (a) Reference field intensity at the fiber input. (b) Intensity image recorded by the imaging camera. (c) Intensity image recorded by the Fourier camera (logarithmic scale). (d) Left: error parameter during algorithm convergence. Middle: resulting intensity (top) and phase (bottom) of the output field calculated by the Gerchberg–Saxton algorithm. Right: amplitudes (top) and phases (bottom) of the lm mode coefficients comprising the calculated output field.

Fig. 8.
Fig. 8.

Simulating image transmission and recovery. (a) Input image and its comprising mode coefficients. (b) Output image recorded by the imaging camera. (c) Output image recorded by the Fourier camera (logarithmic scale). (d) Intensity (top) and phase (bottom) of the output complex field calculated by the Gerchberg–Saxton algorithm. (e) Intensity and the mode coefficients of the recovered image, showing good correlation with the input image (a).

Fig. 9.
Fig. 9.

Phase-only image transmission and recovery. (a) Object phase image (top) and its corresponding mode coefficients (bottom). (b) Intensity output image recorded by the imaging camera. (c) Intensity output image recorded by the Fourier camera (logarithmic scale). (d) Recovered phase image (left) and the corresponding mode coefficients (right) of the input field, showing good correlation with the input image (a).

Fig. 10.
Fig. 10.

Simulated transmission of input amplitude-only (top) and phase-only (bottom) fields through a 150 μm core diameter optical fiber (V=72.985) for different SNR levels.

Equations (13)

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

Exlm(r,θ,z)={E0lmJl(ulmrrc)cos(lθ)exp(iβlmz),rrcE0lmJl(ulm)Kl(wlm)Kl(wlmrrc)cos(lθ)exp(iβlmz),rrc,
βlm=β(ulm,rc)=k02nc2ulm2rc2,
Ein=l,mainlmElm,
ainlm=sEinElmds,
Npπ83(2rc)2a2.
Eout=l,mainlmblm(z0)Elm=l,mainlmeiΔϕlm(z0)Elm,
aoutlm=sEoutElmds,
Ein=l,maoutlmeiΔϕiElm.
Δϕreflm=angle(aref,outlm)angle(aref,inlm),
aref,outlm=sEref,outElmds,
aref,inlm=sEref,inElmds=1.
Δϕlm=Δϕreflm,
εj=1SS||FFT{Ej}|2I˜out|2ds,

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