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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 19 — Sep. 23, 2013
  • pp: 22504–22514
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Dynamic bending compensation while focusing through a multimode fiber

Salma Farahi, David Ziegler, Ioannis N. Papadopoulos, Demetri Psaltis, and Christophe Moser  »View Author Affiliations


Optics Express, Vol. 21, Issue 19, pp. 22504-22514 (2013)
http://dx.doi.org/10.1364/OE.21.022504


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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

1. Introduction

Imaging inaccessible structures has become possible by modern endoscopy with applications in medical diagnosis and treatment as well as in manufacturing where the visualization of hidden structures is important to increase the quality of manufactured goods. Today there are two main approaches to build a miniaturized endoscope. The first is the miniaturization of optical elements (micro GRIN lenses) [1

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]

3

3. 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]

] and the second is a fiber-based approach [1

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]

,4

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

6

6. 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]

] for flexible endoscopes. A conventional endoscope is a fiber bundle where each fiber corresponds to a single pixel of the captured image. However, the image resolution is limited by the fibers core-to-core separation. There are also approaches using a single mode fiber for excitation and a multimode fiber for light collection of reflected or fluorescent signal whereby miniaturized actuators scan a focused light spot at the distal tip [1

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]

].

In this paper, we present a method that can be used to dynamically compensate for bending while focusing light through a multimode fiber by digital phase conjugation. The key element of the presented approach is a virtual coherent point light source (a beacon) placed at the distal end of the MMF.

The virtual beacon point source is experimentally implemented by recording at the fiber tip, a permanent hologram of a spherical wave whose virtual focus point is in front of the fiber facet. This hologram is recorded in a thin polymer material. The method consists of recording, with a digital camera, the speckled wavefront generated by this virtual point source beacon at the proximal end of the MMF and extracting its phase and amplitude. We then use the extracted information in two separate ways. First, the phase conjugate is sent back through the fiber, which generates a real point source at the same location as the virtual point source. In this way, the focus at the distal end of the MMF is maintained even if the fiber is continuously bent. Second, we show how this virtual beacon source is used to sense the fiber conformation. The speckle pattern at the proximal MMF end is highly dependent on its conformation. We demonstrate that by comparing the intensity speckle pattern generated by the beacon to previously stored patterns corresponding to various conformations, it is possible to determine the fiber conformation without having access to its distal tip. Once the fiber conformation is known, previously extracted phase patterns can be used for phase conjugation to perform focusing. Also, the phase patterns corresponding to an array of spots could be stored in computer memory for each fiber conformation so that scanning based imaging could be performed. While scanning and imaging has not been performed in this study the result we show pave the way for the implementation of a high-resolution semi-flexible lensless endoscope based on digital scanning through an optical multimode fiber.

2. Experimental results

2.1 Digital phase conjugation on a virtual beacon source

To focus through a multimode fiber using DPC, it is necessary, first, to place a point source (beacon of light) at the position where the focal spot is required. For a practical implementation of a multimode fiber based endoscope, the beacon needs to be generated in real-time and in reflection i.e. from the same side as the DPC apparatus. In the approach presented here, the virtual point source is recorded on a hologram, which is placed at the distal tip of the multi-mode fiber as described in 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.
. This virtual holographic beacon generates a wavefront that propagates from the distal to the proximal side of the fiber and is used to recreate, by phase conjugation, the original focus point, independently of the fiber conformation, as long as the phase pattern on the SLM is changed accordingly. To create such a beacon, a double clad fiber can be used to bring the calibration beam to the fiber tip through the single mode core. The calibration beam is diffracted by the hologram into the multimode cladding as if it would be coming from a point source [Fig. 1(a)]. Unfortunately double clad fibers are not commercially available for visible wavelengths. We propose then an alternative implementation where the double-clad fiber is replaced by a separate single-mode fiber alongside a multimode fiber [Fig. 1(b)]. This configuration is bulky and thus is not intended as a final endoscopic device, rather it is to demonstrate the principle of the virtual holographic beacon. However, the same process could be applied with the device showed in Fig. 1(a) whose size would be that of the double-clad fiber itself.

A multi-mode fiber with a core thickness of 200μm, NA = 0.39, 1m length is used for the experiment. The laser source is an Oxxius SLIM laser emitting at 532nm. In 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.
we compare the focus obtained using the virtual holographic beacon source generated by the hologram and the one obtained using a real beacon source. This real beacon source is placed at the same position by directly focusing light at the distal tip of the fiber using OBJ1 and a beam splitter to couple light through it from the laser (this part is not shown in Fig. 2). After phase conjugation, the distal tip of the fiber is imaged on CMOS2 to control the quality and the position of the generated focus spot. In Fig. 3(c) we show that a sharp focus spot is obtained by using a virtual holographic beacon point source as a seed for phase conjugation. To quantify the quality of the focus spot we calculate the enhancement, which is defined as the peak intensity over the mean intensity of the image recorded on CMOS2. The enhancement of the focus spot obtained by phase conjugation on a real source is 340 while the value obtained with the virtual beacon is lower and equal to 220. The difference between these two values can be explained by the quality of the virtual beacon generated by the hologram recorded on the polymer film and that might be not a perfect Gaussian beam as the one generated by OBJ1.

Using the same hologram placed at the distal tip of the fiber, a new interferogram can be recorded for another bending configuration and used for focusing again. For this process the calibration beam is brought by the single mode fiber so that the distal tip of the MMF is free.

2.2 Effects of fiber bending on the focal spot obtained by digital phase conjugation

In order to implement a system that compensates for fiber bending effects, we first characterize how bending degrades a focus spot. For this, we quantify the focus spot enhancement while the fiber is bent as well as the variations of the output speckle pattern. For the latter, we calculate the correlation coefficient between an initial intensity speckle pattern and all the new speckle patterns generated while bending the fiber.

The larger the core diameter, the higher is the sensitivity [17

17. F. T. Yu, J. Zhang, S. Yin, and P. B. Ruffin, “Analysis of a fiber specklegram sensor by using coupled-mode theory,” Appl. Opt. 34(16), 3018–3023 (1995). [CrossRef] [PubMed]

]. Qualitatively, that can be explained by the strong dependency of the coupling coefficients to the mode propagation constants [18

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

]. For closely spaced mode propagation constants, the coupling coefficients between the modes are high, which leads to a high bending sensitivity of these modes. For fibers supporting many modes and with a fixed numerical aperture, the difference between the mode propagation constant of the highest order mode and the lowest order mode is constant and doesn’t depend on the fiber diameter. However the number of modes strongly depends on the fiber core diameter (approximately as 4D2NA22 where D is the core diameter, NA the fiber numerical aperture and λ the wavelength). For fibers supporting a large number of modes, the spacing between adjacent mode propagation constants is very small and therefore high coupling between the modes occurs when the fiber is bent. Hence large core fibers are much more sensitive to bending than small core fibers with a same NA. We also notice that the absolute enhancement value is higher for a larger core fiber [Fig. 4(d)] as expected since a larger number of modes are excited. Indeed, the enhancement increases with the number of controlled modes and thus with the number of excited modes [14

14. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012). [CrossRef] [PubMed]

].

In another experiment, a focal spot is positioned at different lateral positions on the distal fiber facet. This experiment aims to acquire a better understanding of the influence of the number of excited modes on the enhancement degradation of the focal spot obtained after phase conjugation as the ROC is changed. We have previously shown that an edge illumination excites more modes than center core illumination [14

14. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012). [CrossRef] [PubMed]

]. In 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).
, we present the results of enhancement as a function of ΔR for different lateral excitation positions. The fiber is excited at four different positions indicated in Fig. 5(a)-5(d). The excitation position is shown with a green dot on the grey circle representing the fiber facet. The blue dots correspond to the normalized enhancement and the red dots to the correlation function between the measured and the original speckle pattern. In Fig. 5(e) the absolute values of enhancement are shown and confirm that the enhancement of the focal spot obtained after phase conjugation for an edge excitation is higher than for a central excitation. We notice that the enhancement drops faster as a function of ΔR for a more central excitation [Fig. 5(a)]. The FWHM are respectively 1.1 mm, 1.7 mm, 1.9 mm and 2 mm. The reason is that central core excitation produces fewer high-order modes than edge excitation and thus a higher ratio of low-order modes in comparison to the total number of modes. The spacing between adjacent propagation constants for low-order modes is smaller than for high-order modes, leading to more intermodal coupling [19

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

]. Thus, the high ratio of low-order modes (in comparison with the total number of modes) generated in case of central core excitation leads to a larger sensitivity with respect to bending than in the case of edge excitation. In deed for an edge excitation, more modes are excited in total and with a higher ratio of high-order modes leading to a slower decay of the enhancement.

2.3 Focusing through a semi-flexible multimode fiber

As mentioned earlier, one solution to the fiber bending problem consists of using a rigid endoscope [10

10. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4(2), 260–270 (2013). [CrossRef] [PubMed]

] for which the calibration of the fiber is done once for good prior to imaging. Indeed, to perform imaging through a multimode fiber, we first need to raster scan the focus on a sample. Then for each focus position, light scattered back by the sample is collected through the same fiber and measured by a detector. In this way, an image if formed [10

10. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4(2), 260–270 (2013). [CrossRef] [PubMed]

]. Thus for every single position of the focused spot, a new phase pattern is displayed on the SLM, meaning that an interferogram has already been recorded for every position during the fiber calibration.

For certain applications flexibility is needed and thus we need to be able to dynamically compensate for the effects of bending. With the proposed beacon method, it is possible for the first time, to focus on a fixed single point without having access to the distal tip of the fiber distal end. Unfortunately, it does not provide the ability to perform imaging.

We suggest thus, the use of a semi-flexible multimode fiber for which the number of conformation is limited. For example, the ROC can be changed at a limited number of bending points along the fiber. It is then necessary to find a method to recover the fiber conformation.

The approach devised here is to use the speckle pattern generated by the virtual beacon source, propagating in the fiber from its distal to proximal end, to sense the fiber conformation (see section 2.1). This speckle pattern is then compared by correlation to previously recorded speckle patterns for different fiber conformations. We suggest then the following process for imaging: first, the fiber conformation is determined by correlation with the intensity speckle pattern stored in a database, second the ensemble of phase patterns used for raster scanning corresponding the fiber conformation are recalled form the database and displayed sequentially on the SLM. In the following experiment, we only stored one such phase pattern (not the ensemble for raster scanning) and demonstrate dynamic bending compensation by focusing on a single spot as described below.

The aim is to maintain a constant focus enhancement at the distal fiber end while the ROC is modified. We first calibrate the MMF by measuring and storing, in computer memory, the conjugated phase patterns needed to generate a focus. We calculate this patterns only for a fixed number N of fiber ROC at the chosen bending point. We also store for all the ROC values in the chosen bending range, the intensity speckle patterns generated by the virtual beacon. The vertical black lines in 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.
indicate the values of ΔR for which an interferogram has been recorded. The ROC of the fiber is then changed randomly. For each increment of ΔR, the holographic beacon [Fig. 1] produces a speckle pattern after propagating in the bent MMF. This pattern is correlated with the speckle patterns corresponding to the prerecorded calibrated patterns. The phase pattern that returns the highest correlation coefficient is selected as the most likely candidate for the fiber configuration. The corresponding phase pattern is displayed on the SLM to create a focal spot at the distal fiber facet and the enhancement is calculated.

The results are presented in Fig. 6. If N = 3, in the specified bending range [Fig. 6(a)], we are in a case of under-sampling and the enhancement plotted in blue, can decrease by 50% between the pre-calibrated positions. In Fig. 6(b) the results of the same experiment, with a larger number of prerecorded positions (N = 9), are shown. The enhancement is maintained at an average of 0.8 for the full range of ROC. This demonstrates that a focal spot can be maintained when the fiber is bent. Without using the virtual beacon as a fiber conformation sensor, the enhancement would drop as shown in Figs. 4-5. Thus, with this system it is possible to retrieve the bending position of the fiber from the speckle pattern obtained from a holographic beacon source and to keep a high enhancement of the focal spot obtained after phase conjugation. The video attached in supplementary material (Media 1) shows the focus spot when bending is compensated for and when it is not.

The crucial point of this method is to determine the number of prerecorded positions necessary to always recognize the actual bending configuration of the fiber and to keep the focal spot within an acceptable enhancement. If there are not enough patterns (under sampling), focusing will not be possible at all positions. If the number of patterns is too high (over sampling) the speed of computation could become a problem and real-time implementation might not be possible anymore.

These results show that it is possible to recover the spatial configuration of a multimode fiber within a limited known range. Once the configuration of the fiber is known, any of the methods used to image through a multimode fiber can be applied. For scanning based imaging, the phase patterns for all focal spots have to be recorded for each possible configuration of the fiber.

This technique can be applied with a reasonable computational time for a limited number of bending joints of the fiber. Otherwise the memory required to store and computational time might be too large. The actual experiment is not optimized regarding time since only mechanical shutters and liquid crystals SLM are used. For two bending joint with a ΔR from infinity to 10mm for example, we would need to calibrate the fiber for 20 positions for each joint to keep the same ratio as in Fig. 6(b). This will result in a number of calibration positions of 202. We need then to learn the patterns needed for phase conjugation for 400 conformations of the fiber.

3. Discussion

The use of a virtual beacon to recover the spatial configuration of the fiber provides the basis for the implementation of a semi-flexible endoscope using a multimode fiber. However, the allowed bending configurations have to be fixed in advance in order to calibrate the fiber.

We showed an implementation using a single mode fiber alongside the MMF. We hence demonstrated that focusing through a bent multimode fiber could be done without having access to the distal tip of the fiber. An implementation with a double clad fiber would simplify the geometry and provide a compact system by avoiding a separate single mode fiber to bring the calibration beam to the fiber tip.

4. Conclusion

We have shown in this work that we can dynamically compensate for bending while focusing through a multimode fiber. The method consists of creating a virtual holographic beacon by using a single mode fiber illuminating a hologram of a point source at the distal tip of the multimode fiber. We demonstrated that the bending configuration of a multimode fiber can be found by comparing the speckle pattern originating from the virtual beacon source with previously recorded speckle patterns corresponding to various bending configurations of the fiber. Up to now, all methods to image through multimode fibers were restricted to rigid fibers, which was a major limitation. The proposed method lifts this limitation, which may pave the way to many new applications of high-resolution lens-less endoscopes based on digital scanning through optical multimode fibers.

Acknowledgments

We would like to thank Zahra Monemhagdoust for helping with the hologram recording and the polymer film, as well as Arnaud Mader for helping with the fabrication of mechanical parts.

References and links

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]

2.

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. Express 3(5), 1077–1085 (2012). [CrossRef] [PubMed]

3.

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]

4.

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

5.

M. T. Myaing, D. J. MacDonald, and X. Li, “Fiber-optic scanning two-photon fluorescence endoscope,” Opt. Lett. 31(8), 1076–1078 (2006). [CrossRef] [PubMed]

6.

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]

7.

S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip 12(3), 635–639 (2012). [CrossRef] [PubMed]

8.

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]

9.

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

10.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express 4(2), 260–270 (2013). [CrossRef] [PubMed]

11.

P. H. Beckwith, I. McMichael, and P. Yeh, “Image distortion in multimode fibers and restoration by polarization-preserving phase conjugation,” Opt. Lett. 12(7), 510–512 (1987). [CrossRef] [PubMed]

12.

D. Z. Anderson, M. A. Bolshtyansky, and B. Y. Zel’dovich, “Stabilization of the speckle pattern of a multimode fiber undergoing bending,” Opt. Lett. 21(11), 785–787 (1996). [CrossRef] [PubMed]

13.

A. M. Caravaca-Aguirre, E. Niv, D. B. Conkey, and R. Piestun, “Real-time resilient focusing through a bending multimode fiber,” Opt. Express 21(10), 12881–12887 (2013). [CrossRef] [PubMed]

14.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20(10), 10583–10590 (2012). [CrossRef] [PubMed]

15.

C. Bellanger, A. Brignon, J. Colineau, and J. P. Huignard, “Coherent fiber combining by digital holography,” Opt. Lett. 33(24), 2937–2939 (2008). [CrossRef] [PubMed]

16.

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. SPIE 7957, 79570H(2011). [CrossRef]

17.

F. T. Yu, J. Zhang, S. Yin, and P. B. Ruffin, “Analysis of a fiber specklegram sensor by using coupled-mode theory,” Appl. Opt. 34(16), 3018–3023 (1995). [CrossRef] [PubMed]

18.

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

19.

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

OCIS Codes
(070.5040) Fourier optics and signal processing : Phase conjugation
(090.1000) Holography : Aberration compensation
(110.2350) Imaging systems : Fiber optics imaging
(090.1995) Holography : Digital holography
(090.5694) Holography : Real-time holography

ToC Category:
Imaging Systems

History
Original Manuscript: July 9, 2013
Revised Manuscript: September 7, 2013
Manuscript Accepted: September 10, 2013
Published: September 17, 2013

Citation
Salma Farahi, David Ziegler, Ioannis N. Papadopoulos, Demetri Psaltis, and Christophe Moser, "Dynamic bending compensation while focusing through a multimode fiber," Opt. Express 21, 22504-22514 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-19-22504


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References

  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]
  2. 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]
  3. 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]
  4. F. Helmchen, “Miniaturization of fluorescence microscopes using fibre optics,” Exp. Physiol.87(6), 737–745 (2002). [CrossRef] [PubMed]
  5. M. T. Myaing, D. J. MacDonald, and X. Li, “Fiber-optic scanning two-photon fluorescence endoscope,” Opt. Lett.31(8), 1076–1078 (2006). [CrossRef] [PubMed]
  6. 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]
  7. S. Bianchi and R. Di Leonardo, “A multi-mode fiber probe for holographic micromanipulation and microscopy,” Lab Chip12(3), 635–639 (2012). [CrossRef] [PubMed]
  8. 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]
  9. T. Čižmár and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat Commun3, 1027 (2012). [CrossRef] [PubMed]
  10. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “High-resolution, lensless endoscope based on digital scanning through a multimode optical fiber,” Biomed. Opt. Express4(2), 260–270 (2013). [CrossRef] [PubMed]
  11. P. H. Beckwith, I. McMichael, and P. Yeh, “Image distortion in multimode fibers and restoration by polarization-preserving phase conjugation,” Opt. Lett.12(7), 510–512 (1987). [CrossRef] [PubMed]
  12. D. Z. Anderson, M. A. Bolshtyansky, and B. Y. Zel’dovich, “Stabilization of the speckle pattern of a multimode fiber undergoing bending,” Opt. Lett.21(11), 785–787 (1996). [CrossRef] [PubMed]
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