Abstract

Rigid endoscopes like graded-index (GRIN) lenses are known tools in biological imaging, but it is conceptually difficult to miniaturize them. In this letter, we demonstrate an ultra-thin rigid endoscope with a diameter of only 125 μm. In addition, we identify a domain where two-photon endoscopic imaging with fs-pulse excitation is possible. We validate the ultra-thin rigid endoscope consisting of a few cm of graded-index multi-mode fiber by using it to acquire optically sectioned two-photon fluorescence endoscopic images of three-dimensional samples.

© 2016 Optical Society of America

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References

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2015 (5)

2014 (3)

2013 (5)

2012 (4)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photon. 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

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, 203901 (2012).
[Crossref] [PubMed]

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

2011 (1)

2010 (2)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

2008 (1)

J. N. D. Kerr and W. Denk, “Imaging in vivo: watching the brain in action,” Nat. Rev. Neurosci. 9, 195–205 (2008).
[Crossref] [PubMed]

2005 (2)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

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

1990 (1)

W. Denk, J. H. Strickler, and W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref] [PubMed]

Andresen, E. R.

Bianchi, S.

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Bouwmans, G.

Caravaca-Aguirre, A. M.

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Carpenter, J.

Cheung, E. L. M.

B. A. Flusberg, E. D. Cocker, W. Piyawattanametha, J. C. Jung, E. L. M. Cheung, and M. Schnitzer, “Fiber-optic fluorescence imaging,” Nat. Methods 2, 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, 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, 203901 (2012).
[Crossref] [PubMed]

Cizmar, T.

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

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

Cižmár, T.

Cocker, E. D.

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

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, 203901 (2012).
[Crossref] [PubMed]

Denk, W.

J. N. D. Kerr and W. Denk, “Imaging in vivo: watching the brain in action,” Nat. Rev. Neurosci. 9, 195–205 (2008).
[Crossref] [PubMed]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

W. Denk, J. H. Strickler, and W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref] [PubMed]

Dholakia, K.

Di Fabrizio, E.

Di Leonardo, R.

Eggleton, B. J.

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, 203901 (2012).
[Crossref] [PubMed]

Farahi, S.

Ferrara, L.

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Flusberg, B. A.

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

Gallais, L.

Gigan, S.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Grewe, B. F.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

Jung, J. C.

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

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photon. 6, 549–553 (2012).
[Crossref]

Kerr, J. N. D.

J. N. D. Kerr and W. Denk, “Imaging in vivo: watching the brain in action,” Nat. Rev. Neurosci. 9, 195–205 (2008).
[Crossref] [PubMed]

Kim, H.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[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, 203901 (2012).
[Crossref] [PubMed]

Kitch, L. J.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[Crossref]

Lecoq, J.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[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, 203901 (2012).
[Crossref] [PubMed]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Li, J. Z.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Liberale, C.

Monneret, S.

Morales-Delgado, E. E.

Moser, C.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[Crossref]

Niv, E.

Papadopoulos, I. N.

Piestun, R.

Piyawattanametha, W.

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

Plöschner, M.

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Psaltis, D.

Rajamanickam, V. P.

Rigneault, H.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1991).
[Crossref]

Savall, J.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Schnitzer, M.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

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

Schroder, J.

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photon. 6, 549–553 (2012).
[Crossref]

Sivankutty, S.

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photon. 6, 549–553 (2012).
[Crossref]

Straka, B.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref] [PubMed]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1991).
[Crossref]

Tyc, T.

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

Vellekoop, I. M.

I. M. Vellekoop, “Feedback-based wavefront shaping,” Opt. Express 23, 12189–12206 (2015).
[Crossref] [PubMed]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[Crossref]

Vucinic, D.

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[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, 203901 (2012).
[Crossref] [PubMed]

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, 203901 (2012).
[Crossref] [PubMed]

Ziegler, D.

Biomed. Opt. Express (1)

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

Nat. Commun. (1)

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

Nat. Methods (2)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods 2, 932–940 (2005).
[Crossref] [PubMed]

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

Nat. Neurosci. (1)

J. Lecoq, J. Savall, D. Vucinic, B. F. Grewe, H. Kim, J. Z. Li, L. J. Kitch, and M. Schnitzer, “Visualizing mammalian brain area interactions by dual-axis two-photon calcium imaging,” Nat. Neurosci. 17, 1825–1829 (2014).
[Crossref] [PubMed]

Nat. Photon. (4)

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

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nat. Photon. 6, 549–553 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283–292 (2012).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photon. 4, 320–322 (2010).
[Crossref]

Nat. Rev. Neurosci. (1)

J. N. D. Kerr and W. Denk, “Imaging in vivo: watching the brain in action,” Nat. Rev. Neurosci. 9, 195–205 (2008).
[Crossref] [PubMed]

Opt. Express (8)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

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, 203901 (2012).
[Crossref] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref] [PubMed]

Science (1)

W. Denk, J. H. Strickler, and W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[Crossref] [PubMed]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., 1991).
[Crossref]

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Figures (15)

Fig. 1
Fig. 1 Conceptual sketch of the rigid endoscope and the employed formalism. Light travels from left to right. (Left) A full set of experimental input modes. (Right) A full set of experimental output modes; the output light can be injected into any one of these.
Fig. 2
Fig. 2 (a) Experimental setup ’Setup1’. Laser, either a fs-laser (Amplitude Systems, t-Pulse) at 1030 nm with a spectral width of 6 nm or a continuous wave fiber laser (IPG Laser Gmbh) at 1053 nm, λ/2, half-wave plate. Pol, polarizer. 2D-SLM, two-dimensional spatial light modulator (Hamamatsu X8267-15). SF, spatial filter. MMF, multi-mode fiber (Thorlabs GIF625, 16.1, 6.5, or 2.3 cm long). CMOS, CMOS camera. f1 = 500 mm; f2 = 80 mm; f3 = 6.24 mm; f4, 9 mm; f5 = 150 mm. (b) Example mask on the 2D-SLM during transmission matrix measurement. (c) Example mask on the 2D-SLM during output mode intensity measurement.
Fig. 3
Fig. 3 A graphical sketch of the procedure for measuring the transmission matrix. (Left) The stack of 8 images acquired on the CMOS camera for 8 equidistant ϕj. (Right) Intensity |b(u)|2 in the output mode u (the pixel marked by the white dot) as a function of ϕj; stack of 1089.
Fig. 4
Fig. 4 Sketch of how to arrive at |bu|2(xu, yu), the measure of MMF performance with a chosen laser. The output intensity maps are the images of the MMF distal endface seen by the CMOS camera; from each of these images the achievable intensity is measured as the intensity of the mode at (xu, yu) marked by the arrow; then, from the entire stack of these images the achievable intensities in all modes are measured and used to create the map |b(u)|2(xu, yu).
Fig. 5
Fig. 5 Finding the optimal MMF length. (a,b) Achievable intensity in output mode u vs. (x(u), y(u)) for MMF length of 16.1 cm; (c,d) 6.5 cm; and (e,f) 2.3 cm; and for (a,c,e) fs illumination; and (b,d,f) cw illumination. The intensity values for each MMF length are normalized to the maximum of the cw-case intensity. g) and h) are a discrete subset of the data in e) and f) plotted for better visualization and for a comparison of absolute enhancement of intensity in the output modes in fs and cw illumination schemes. Dashed line, outline of the core of the MMF (Ø62.5 μm).
Fig. 6
Fig. 6 (a) Experimental setup ’Setup 2’. Laser, fs-laser (Coherent Inc., Chameleon) at 920 nm (spectral width = 5 nm). λ/2, half-wave plate.Pol, Polarizer. 2D-SLM, two-dimensional spatial light modulator (Hamamatsu X10468-07). DM, deformable mirror (Iris AO, PTT-489). SF, spatial filter. DC, dichroic mirror. MMF, multi-mode fiber. S, sample. Pol, polarizer. CMOS, CMOS camera. BP, Bandpass filter. APD, avalanche photodiode. DC -Long pass Dichroic Mirror (LPD02-785RU-25, Semrock), f1 = 300 mm; f2 = 150 mm; f3 = 500 mm; f4 = 80 mm; f5 = 3.1 mm; f6 = 9 mm, NA = 0.45; f7 = 150 mm; f8 = 100 mm; f9 = 150 mm; f10 = 4.55 mm. (b) The static mask on the 2D-SLM during the experiments.
Fig. 7
Fig. 7 (a,b) Transverse and axial two-photon point-spread function measured in the epi direction and Z = 50 μm. Dots, slices of the images. Full lines, fits to the slices. FWHMs retrieved from the fits: (a, top) 1.55, 2.01, 2.72 μm. (a, right) 1.97, 1.80, 1.19 μm. (b) 18.1 μm.
Fig. 8
Fig. 8 Two-photon endoscopic images of a 3-dimensional sample consisting of two layers of 2 μm fluorescent beads. Images acquired at different Z: (a) 10 μm; (b) 40 μm; (c) 70 μm; (d) 100 μm The intensity scale is the same in all images. Scale bar, 10 μm.
Fig. 9
Fig. 9 Two-photon (forward and epi-collected) images of cellular samples.Total average power on the sample 4 mW, Pixel dwell = 2 ms.
Fig. 10
Fig. 10 Measurements of MMF mode scrambling properties. (a–d) Example input k-spaces. (e–h) Corresponding output k-space with input k-space as in (a–d). Dashed circles, delimitation of the MMF k-space corresponding to an NA of 0.275. Note that the input k-space is indeed under-filled to illustrate the generation of new k-vectors as a result of mode scrambling.
Fig. 11
Fig. 11 Consequences of the MMF mode scrambling properties. (a–h) Images of the actual intensity distribution when injecting maximally into the output mode marked by the arrow for (a–d) MMF length of 0 cm, i.e. without MMF. (e–h) MMF length of 2.5 cm. Dashed circles, delimitation of the MMF core (Ø62.5 μm).
Fig. 12
Fig. 12 Side-by-side comparison of the efficiency in forward detection and epi- detection. (a,b) Image of 200 nm fluorescent beads acquired by distal collection. (c,d) Image of the same sample acquired by proximal (epi) detection. All images are on the same scale. Scale bars, 10 μm.
Fig. 13
Fig. 13 One-photon PSF versus distance from the MMF Z. (a) Axial width FWHM versus Z, measured for the output mode in the center of the MMF. (b) Minimum transverse (x and y) width FWHM versus Z.
Fig. 14
Fig. 14 Lateral width of the one-photon PSF (x-direction) for different Z: (a) 0 μm; (b) 50 μm; (c) 100 μm; (d) 150 μm; and (e) 200 μm. Dashed circle, outline of the core of the MMF (Ø62.5 μm).
Fig. 15
Fig. 15 Two-photon endoscopic images of a 3-dimensional sample consisting of two layers of 2 μm fluorescent beads. Images taken at different Z: (a) 0 μm; (b) 10 μm; (c) 20 μm; (d) 30 μm; (e) 40 μm; (f) 50 μm; (g) 60 μm; (h) 70 μm; (i) 80 μm; (j) 90 μm; (k) 100 μm; (l) 110 μm; (m) 120 μm; (n) 130 μm; (o) 140 μm; (p) 150 μm. Pixel dwell time 8 ms. Total average power on the sample 1 mW. Scale bar, 20 μm.

Equations (11)

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V = 2 π a λ NA = 51.4
M p p + 1 V 2 2
v lm step index c n 1 ( 1 ( l + 2 m ) 2 M Δ ) , 2 ( l + 2 m ) M
v q graded index c n 1 ( 1 q M Δ 2 2 ) , 1 q M
Φ i mask ( R ) = sawtooth [ ϕ i + 2 π f c ( R R i ) ] ,
H i u = A i u e i P i u
| b ( u ) | 2 = | H i u e i ϕ j + H 0 u | 2 = | A i u e i P i u e i ϕ j + A 0 u e i P 0 u | 2 = | A i u | 2 + | A 0 u | 2 + | A i u A 0 u | cos ( P i u P 0 u + ϕ j ) .
| b ( u ) | 2 = | i H i u e i ϕ i | 2 = | i A i u e i P i u e i P i u | 2 = | i A i u | 2 .
Φ i mask = π λ f conc | R R i | 2 ,
Δ x = 0.61 λ NA
Δ z = 2 λ NA

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