Abstract

Fiber-optic sensors have numerous existing and emerging applications spanning areas from industrial process monitoring to medical diagnosis. Two of the most common fiber sensors are based on the fabrication of Bragg gratings or Fabry-Perot etalons. While these techniques offer a large array of sensing targets, their utility can be limited by the difficulties involved in fabricating forward viewing probes (Bragg gratings) and in obtaining sufficient signal-to-noise ratios (Fabry-Perot systems). In this article we present a micro-scale fiber-optic force sensor produced using direct laser writing (DLW). The fabrication entails a single-step process that can be undertaken in a reliable and repeatable manner using a commercial DLW system. The sensor is made of a series of thin plates (i.e. Fabry-Perot etalons), which are supported by springs that compress under an applied force. At the proximal end of the fiber, the interferometric changes that are induced as the sensor is compressed are read out using reflectance spectroscopy, and the resulting spectral changes are calibrated with respect to applied force. This calibration is performed using either singular value decomposition (SVD) followed by linear regression or artificial neural networks. We describe the design and optimization of this device, with a particular focus on the data analysis required for calibration. Finally, we demonstrate proof-of-concept force sensing over the range 0-50 μN, with a measurement error of approximately 1.5 μN.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2018 (1)

M. Power, A. J. Thompson, S. Anastasova, and G.-Z. Yang, “A Monolithic Force-Sensitive 3D Microgripper Fabricated on the Tip of an Optical Fiber Using 2-Photon Polymerization,” Small 1002, 1703964 (2018).
[Crossref] [PubMed]

2016 (3)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

2015 (1)

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

2014 (4)

M. Kowalczyk, J. Haberko, and P. Wasylczyk, “Microstructured gradient-index antireflective coating fabricated on a fiber tip with direct laser writing,” Opt. Express 22(10), 12545–12550 (2014).
[Crossref] [PubMed]

A. Zukauskas, V. Melissinaki, D. Kaskelyte, M. Farsari, and M. Malinauskas, “Improvement of the Fabrication Accuracy of Fiber Tip Microoptical Components via Mode Field Expansion,” J. Laser Micro Nanoeng. 9(1), 68–72 (2014).
[Crossref]

S. Coda, A. J. Thompson, G. T. Kennedy, K. L. Roche, L. Ayaru, D. S. Bansi, G. W. Stamp, A. V. Thillainayagam, P. M. French, and C. Dunsby, “Fluorescence lifetime spectroscopy of tissue autofluorescence in normal and diseased colon measured ex vivo using a fiber-optic probe,” Biomed. Opt. Express 5(2), 515–538 (2014).
[Crossref] [PubMed]

M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

2012 (4)

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

M. Schroder, M. Bulters, C. von Kopylow, and R. B. Bergmann, “Novel concept for three-dimensional polymer waveguides for optical on-chip interconnects,” J. Eur. Opt. Soc. 7, 12027 (2012).

N. Lindenmann, G. Balthasar, D. Hillerkuss, R. Schmogrow, M. Jordan, J. Leuthold, W. Freude, and C. Koos, “Photonic wire bonding: a novel concept for chip-scale interconnects,” Opt. Express 20(16), 17667–17677 (2012).
[Crossref] [PubMed]

2011 (2)

J. Fischer and M. Wegener, “Three-dimensional direct laser writing inspired by stimulated-emission-depletion microscopy (Invited),” Opt. Mater. Express 1(4), 614–624 (2011).
[Crossref]

X. Yang, C. Gu, F. Qian, Y. Li, and J. Z. Zhang, “Highly Sensitive Detection of Proteins and Bacteria in Aqueous Solution Using Surface-Enhanced Raman Scattering and Optical Fibers,” Anal. Chem. 83(15), 5888–5894 (2011).
[Crossref] [PubMed]

2010 (2)

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
[Crossref] [PubMed]

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

2009 (1)

M. Farsari and B. N. Chichkov, “Two-photon fabrication,” Nat. Photonics 3(8), 450–452 (2009).
[Crossref]

2007 (2)

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

P. C. A. Jerónimo, A. N. Araújo, and M. Montenegro, “Optical sensors and biosensors based on sol-gel films,” Talanta 72(1), 13–27 (2007).
[Crossref] [PubMed]

2006 (2)

Y. J. Rao, “Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12(3), 227–237 (2006).
[Crossref]

R. Guo, S. Xiao, X. Zhai, J. Li, A. Xia, and W. Huang, “Micro lens fabrication by means of femtosecond two photon photopolymerization,” Opt. Express 14(2), 810–816 (2006).
[Crossref] [PubMed]

2004 (1)

1999 (1)

1997 (1)

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

1995 (1)

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

1990 (1)

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Ahmad, H.

M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

Ali, M. M.

M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

Anastasova, S.

M. Power, A. J. Thompson, S. Anastasova, and G.-Z. Yang, “A Monolithic Force-Sensitive 3D Microgripper Fabricated on the Tip of an Optical Fiber Using 2-Photon Polymerization,” Small 1002, 1703964 (2018).
[Crossref] [PubMed]

Ang, X. M.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Araújo, A. N.

P. C. A. Jerónimo, A. N. Araújo, and M. Montenegro, “Optical sensors and biosensors based on sol-gel films,” Talanta 72(1), 13–27 (2007).
[Crossref] [PubMed]

Askins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

Ayaru, L.

Backman, V.

Balamurali, P.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Baldacchini, T.

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

Balthasar, G.

Bansi, D. S.

Bergholt, M. S.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Bergmann, R. B.

M. Schroder, M. Bulters, C. von Kopylow, and R. B. Bergmann, “Novel concept for three-dimensional polymer waveguides for optical on-chip interconnects,” J. Eur. Opt. Soc. 7, 12027 (2012).

Brambilla, G.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Bulters, M.

M. Schroder, M. Bulters, C. von Kopylow, and R. B. Bergmann, “Novel concept for three-dimensional polymer waveguides for optical on-chip interconnects,” J. Eur. Opt. Soc. 7, 12027 (2012).

Busch, K.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

Butler, T.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

Chan, C. C.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Chen, J.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

Chen, L. H.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Chichkov, B. N.

M. Farsari and B. N. Chichkov, “Two-photon fabrication,” Nat. Photonics 3(8), 450–452 (2009).
[Crossref]

Claus, R. O.

Coda, S.

Cui, H. L.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Cui, L.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

Cutruzzola, F. W.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

Deckelbaum, L. I.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Ding, M.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Dunsby, C.

Enriquez, R.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Essig, S.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

Farrer, R. A.

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

Farsari, M.

A. Zukauskas, V. Melissinaki, D. Kaskelyte, M. Farsari, and M. Malinauskas, “Improvement of the Fabrication Accuracy of Fiber Tip Microoptical Components via Mode Field Expansion,” J. Laser Micro Nanoeng. 9(1), 68–72 (2014).
[Crossref]

M. Farsari and B. N. Chichkov, “Two-photon fabrication,” Nat. Photonics 3(8), 450–452 (2009).
[Crossref]

Feld, M. S.

Feng, J.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Feng, S.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

Feng, S. F.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Fischer, J.

Fitzmaurice, M.

Fourkas, J. T.

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
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Freude, W.

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

Giessen, H.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Gissibl, T.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Gu, C.

X. Yang, C. Gu, F. Qian, Y. Li, and J. Z. Zhang, “Highly Sensitive Detection of Proteins and Bacteria in Aqueous Solution Using Surface-Enhanced Raman Scattering and Optical Fibers,” Anal. Chem. 83(15), 5888–5894 (2011).
[Crossref] [PubMed]

Guo, R.

Haberko, J.

Han, P.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

He, J. S.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Herkommer, A.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Hillerkuss, D.

Ho, K. Y.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Huang, Q.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Huang, W.

Huang, Z.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

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M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

Jerónimo, P. C. A.

P. C. A. Jerónimo, A. N. Araújo, and M. Montenegro, “Optical sensors and biosensors based on sol-gel films,” Talanta 72(1), 13–27 (2007).
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Jordan, M.

Kapadia, C. R.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Kaskelyte, D.

A. Zukauskas, V. Melissinaki, D. Kaskelyte, M. Farsari, and M. Malinauskas, “Improvement of the Fabrication Accuracy of Fiber Tip Microoptical Components via Mode Field Expansion,” J. Laser Micro Nanoeng. 9(1), 68–72 (2014).
[Crossref]

Kennedy, G. T.

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

Klar, P. J.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
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Koos, C.

Kou, J. L.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Kowalczyk, M.

LaFratta, C. N.

C. N. LaFratta, J. T. Fourkas, T. Baldacchini, and R. A. Farrer, “Multiphoton fabrication,” Angew. Chem. Int. Ed. Engl. 46(33), 6238–6258 (2007).
[Crossref] [PubMed]

Lai, M. H.

M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
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Ledermann, A.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

Leong, K. C.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Leuthold, J.

Li, J.

Li, T.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Li, Y.

X. Yang, C. Gu, F. Qian, Y. Li, and J. Z. Zhang, “Highly Sensitive Detection of Proteins and Bacteria in Aqueous Solution Using Surface-Enhanced Raman Scattering and Optical Fibers,” Anal. Chem. 83(15), 5888–5894 (2011).
[Crossref] [PubMed]

Lim, K. S.

M. R. Islam, M. M. Ali, M. H. Lai, K. S. Lim, and H. Ahmad, “Chronology of Fabry-Perot interferometer fiber-optic sensors and their applications: a review,” Sensors (Basel) 14(4), 7451–7488 (2014).
[Crossref] [PubMed]

Lin, K.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Lindenmann, N.

Lu, Y. Q.

J. L. Kou, M. Ding, J. Feng, Y. Q. Lu, F. Xu, and G. Brambilla, “Microfiber-Based Bragg Gratings for Sensing Applications: A Review,” Sensors (Basel) 12(7), 8861–8876 (2012).
[Crossref] [PubMed]

Maccraith, B. D.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

Malinauskas, M.

A. Zukauskas, V. Melissinaki, D. Kaskelyte, M. Farsari, and M. Malinauskas, “Improvement of the Fabrication Accuracy of Fiber Tip Microoptical Components via Mode Field Expansion,” J. Laser Micro Nanoeng. 9(1), 68–72 (2014).
[Crossref]

Manoharan, R.

Mcdonagh, C. M.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
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Mcevoy, A. K.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

Melissinaki, V.

A. Zukauskas, V. Melissinaki, D. Kaskelyte, M. Farsari, and M. Malinauskas, “Improvement of the Fabrication Accuracy of Fiber Tip Microoptical Components via Mode Field Expansion,” J. Laser Micro Nanoeng. 9(1), 68–72 (2014).
[Crossref]

Menon, R.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
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Migden, M. R.

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
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Montenegro, M.

P. C. A. Jerónimo, A. N. Araújo, and M. Montenegro, “Optical sensors and biosensors based on sol-gel films,” Talanta 72(1), 13–27 (2007).
[Crossref] [PubMed]

Neu, B.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
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Nguyen, T. H.

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
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O’Brien, K. M.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
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Oh, K. D.

Okeeffe, G.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
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Perelman, L. T.

Power, M.

M. Power, A. J. Thompson, S. Anastasova, and G.-Z. Yang, “A Monolithic Force-Sensitive 3D Microgripper Fabricated on the Tip of an Optical Fiber Using 2-Photon Polymerization,” Small 1002, 1703964 (2018).
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Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[Crossref]

Qian, F.

X. Yang, C. Gu, F. Qian, Y. Li, and J. Z. Zhang, “Highly Sensitive Detection of Proteins and Bacteria in Aqueous Solution Using Surface-Enhanced Raman Scattering and Optical Fibers,” Anal. Chem. 83(15), 5888–5894 (2011).
[Crossref] [PubMed]

Rajaram, N.

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
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Rao, Y. J.

Y. J. Rao, “Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12(3), 227–237 (2006).
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Reichenberg, J. S.

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
[Crossref] [PubMed]

Ren, J. L.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Ren, X.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
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Roche, K. L.

Schmogrow, R.

Schroder, M.

M. Schroder, M. Bulters, C. von Kopylow, and R. B. Bergmann, “Novel concept for three-dimensional polymer waveguides for optical on-chip interconnects,” J. Eur. Opt. Soc. 7, 12027 (2012).

Shaillender, M.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Sheridan, F. R.

B. D. Maccraith, C. M. Mcdonagh, G. Okeeffe, A. K. Mcevoy, T. Butler, and F. R. Sheridan, “Sol-Gel Coatings for Optical Chemical Sensors and Biosensors,” Sens. Actuator B-Chem. 29(1-3), 51–57 (1995).
[Crossref]

Srivastava, S.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
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Stamp, G. W.

Staude, I.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
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Stetz, M. L.

C. R. Kapadia, F. W. Cutruzzola, K. M. O’Brien, M. L. Stetz, R. Enriquez, and L. I. Deckelbaum, “Laser-induced fluorescence spectroscopy of human colonic mucosa,” Gastroenterology 99(1), 150–157 (1990).
[Crossref] [PubMed]

Sun, W.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
[Crossref]

Sun, W. F.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Teh, M.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Thiel, M.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

Thiele, S.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Thillainayagam, A. V.

Thompson, A. J.

Tunnell, J. W.

N. Rajaram, J. S. Reichenberg, M. R. Migden, T. H. Nguyen, and J. W. Tunnell, “Pilot clinical study for quantitative spectral diagnosis of non-melanoma skin cancer,” Lasers Surg. Med. 42(10), 716–727 (2010).
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Van Dam, J.

von Freymann, G.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
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von Kopylow, C.

M. Schroder, M. Bulters, C. von Kopylow, and R. B. Bergmann, “Novel concept for three-dimensional polymer waveguides for optical on-chip interconnects,” J. Eur. Opt. Soc. 7, 12027 (2012).

Wang, A.

Wang, H.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Wang, J.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Wang, P.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
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Wang, X.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
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Wang, X. K.

H. Wang, Z. W. Xie, M. L. Zhang, H. L. Cui, J. S. He, S. F. Feng, X. K. Wang, W. F. Sun, J. S. Ye, P. Han, and Y. Zhang, “A miniaturized optical fiber microphone with concentric nanorings grating and microsprings structured diaphragm,” Opt. Laser Technol. 78, 110–115 (2016).
[Crossref]

Wang, Y.

Z. Xie, S. Feng, P. Wang, L. Zhang, X. Ren, L. Cui, T. Zhai, J. Chen, Y. Wang, X. Wang, W. Sun, J. Ye, P. Han, P. J. Klar, and Y. Zhang, “Demonstration of a 3D Radar-Like SERS Sensor Micro- and Nanofabricated on an Optical Fiber,” Adv. Opt. Mater. 3(9), 1232–1239 (2015).
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Wasylczyk, P.

Wegener, M.

J. Fischer and M. Wegener, “Three-dimensional direct laser writing inspired by stimulated-emission-depletion microscopy (Invited),” Opt. Mater. Express 1(4), 614–624 (2011).
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G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-Dimensional Nanostructures for Photonics,” Adv. Funct. Mater. 20(7), 1038–1052 (2010).
[Crossref]

Wong, B.

M. S. Bergholt, K. Lin, J. Wang, W. Zheng, H. Xu, Q. Huang, J. L. Ren, K. Y. Ho, M. Teh, S. Srivastava, B. Wong, K. G. Yeoh, and Z. Huang, “Simultaneous fingerprint and high-wavenumber fiber-optic Raman spectroscopy enhances real-time in vivo diagnosis of adenomatous polyps during colonoscopy,” J. Biophotonics 9(4), 333–342 (2016).
[Crossref] [PubMed]

Wong, W. C.

L. H. Chen, T. Li, C. C. Chan, R. Menon, P. Balamurali, M. Shaillender, B. Neu, X. M. Ang, P. Zu, W. C. Wong, and K. C. Leong, “Chitosan based fiber-optic Fabry-Perot humidity sensor,” Sens. Actuator B-Chem. 169, 167–172 (2012).
[Crossref]

Xia, A.

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Supplementary Material (1)

NameDescription
» Visualization 1       Movie demonstrating the force and compression sensing capability of the fiber-optic sensor.

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Figures (7)

Fig. 1
Fig. 1 Fiber-optic force sensor and optical setup used for sensor readout. (a, b) CAD (Computer-aided design) model of the fiber-optic force sensor showing dimetric view (a) and side view (b). The optical fiber is shown in grey and the sensor in yellow. The dimensions of the sensor are annotated in (b). (c) Scanning Electron Microscopy (SEM) image of the optical force sensor. The tip of the optical fiber is visible in the bottom left corner. The white, blue and red arrowheads respectively indicate the polymer plates that act as Fabry-Perot etalons for compression/force sensing, the springs that support the sensing plates, and the upper pad onto which forces are applied. Scale bar 25 μm. (d) Optical setup used for sensor readout. SL – supercontinuum laser; ND – variable neutral density filter; BS – 50/50 beam splitter; P – polarizer; WP – quarter waveplate; L1 – 10x microscope objective; L2 – lens (f = 20 mm); S – spectrometer; SMF – single mode fiber with force sensor fabricated at distal tip.
Fig. 2
Fig. 2 Optical compression sensing. (a&b) Images of the fiber-optic sensor being compressed by a commercially available MEMS force sensor, showing uncompressed (a) and compressed (b) states. (c) Reflectance spectra obtained in the uncompressed (a, blue line) and compressed (b, red line) states. Red dotted lines in (a) and (b) indicate the position of the face of the optical fiber in the uncompressed state (i.e. its location in image (a)). These aid the visualization of the small compression of the sensor, which is otherwise difficult to observe.
Fig. 3
Fig. 3 Fiber-optic force sensing using SVD and linear regression in a leave-one-out protocol. (a) 2D array of spectra – acquired over a range of known applied forces – that is used as a calibration data set for the optical force sensor. The blue and yellow arrows indicate the areas of the array in which the force, F, is increasing and decreasing respectively. The spectrum for the maximum applied force occurs at the center of the graph. (b&c) Relative contributions (scores) of the second (b) and third (c) base spectral components (loadings) extracted using SVD as functions of the applied force. (d) Graph showing the force calculated using the SVD-regression algorithm (using a leave-one-out protocol) against the ground truth force values measured using the commercial MEMS force sensor.
Fig. 4
Fig. 4 Effect of SVD truncation on force prediction accuracy. Graphs show the force predicted using the SVD-regression algorithm (in a leave-one-out-protocol) as a function of the known applied force for a range of SVD truncations. For panels (a) to (f), the force prediction algorithm was generated using the relative contributions of the first 3, 5, 8, 10, 15 and 20 SVD spectral components respectively. Only negligible improvements were observed in the force prediction accuracy above a truncation of 15 (e).
Fig. 5
Fig. 5 Force prediction with the SVD-regression algorithm using separate training and test data sets for two example sensors. (a) Predicted force vs. applied force for the first sensor using separate training and test data sets. An algorithm was generated using a large training set and then tested on an unseen data set. (b) Predicted force vs. applied force for the data shown in (a) calculated using a leave-one-out protocol. In panel (b), the relative contributions for each ‘left out’ spectrum were fitted using linear regression (rather than being directly calculated using SVD) in order to allow a fair comparison to the train-test approach. (c&d) Predicted force vs. applied force graphs for a second sensor generated using the train-test approach (c) and the leave-one-out protocol with regression-based fitting of the relative contributions (d).
Fig. 6
Fig. 6 Predicted force vs. applied force graphs generated using a leave-one-out protocol with direct SVD calculation of the relative contributions. (a) Leave-one-out SVD force prediction based on the data presented in Fig. 5(a&b). (b) Leave-one-out SVD force prediction based on the data presented in Fig. 5(c&d). Note that when using a leave-one-out protocol, the regression-based fitting of the relative contributions of the spectral components (shown in Fig. 5(b&d)) provides near identical results to those obtained with direct SVD calculation of the relative contributions (shown in this Fig.). Importantly, this is true both in the case where we observe good force prediction using a train-test protocol ((a); Fig. 5(a&b)) and in the case that the train-test approach provides poor performance ((b); Fig. 5(c&d)). This demonstrates that the errors observed when using separate training and test data are not a result of the regression-based fitting of the relative contributions.
Fig. 7
Fig. 7 Neural network force prediction (using separate training and test data). Graphs show the force calculated using a trained artificial neural network as a function of the known applied force for: (a) the data shown in Fig. 5(a&b); (b) the data shown in Fig. 5(c&d). In both cases the trained networks have been applied to entirely unseen test data.

Equations (3)

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M n=1...N,λ = U n=1...N,n=1...N Σ n=1...N,n=1...N V λ,n=1...N * .
M n=1...N,λ M ^ n=1...N,λ U n=1...N,s=1...tr Σ s=1...tr,s=1...tr V λ,s=1...tr *
F= x 1 U i,1 + x 2 U i,2 + x 3 U i,3 ...+ x tr U i,tr +c.

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