Abstract

Snapshot spectral imaging is rapidly gaining interest for remote sensing applications. Acquiring spatial and spectral data within one image promotes fast measurement times, and reduces the need for stabilized scanning imaging systems. Many current snapshot technologies, which rely on gratings or prisms to characterize wavelength information, are difficult to reduce in size for portable hyperspectral imaging. Here, we show that a multicore multimode fiber can be used as a compact spectral imager with sub-nanometer resolution, by encoding spectral information within a monochrome CMOS camera. We characterize wavelength-dependent speckle patterns for up to 3000 fiber cores over a broad wavelength range. A clustering algorithm is employed in combination with l1-minimization to limit data collection at the acquisition stage for the reconstruction of spectral images that are sparse in the wavelength domain. We also show that in the non-compressive regime these techniques are able to accurately reconstruct broadband information.

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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2018 (1)

2017 (4)

2016 (5)

S. F. Liew, B. Redding, M. A. Choma, H. D. Tagare, and H. Cao, “Broadband multimode fiber spectrometer,” Opt. Lett. 41, 2029–2032 (2016).
[Crossref] [PubMed]

A. Porat, E. R. Andresen, H. Rigneault, D. Oron, S. Gigan, and O. Katz, “Widefield lensless imaging through a fiber bundle via speckle correlations,” Opt. Express 24, 16835–16855 (2016).
[Crossref] [PubMed]

G. C. Valley, G. A. Sefler, and T. J. Shaw, “Multimode waveguide speckle patterns for compressive sensing,” Opt. Lett. 41, 2529–2532 (2016).
[Crossref] [PubMed]

X. Cao, T. Yue, X. Lin, S. Lin, X. Yuan, Q. Dai, L. Carin, and D. J. Brady, “Computational snapshot multispectral cameras: toward dynamic capture of the spectral world,” IEEE Signal Process. Mag. 33, 95–108 (2016).
[Crossref]

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep 6, 23524(2016).
[Crossref] [PubMed]

2015 (8)

L. V. Amitonova, A. P. Mosk, and P. W. H. Pinkse, “Rotational memory effect of a multimode fiber,” Opt. Express 23, 20569–20575 (2015).
[Crossref] [PubMed]

N. H. Wan, F. Meng, T. Schröder, R. Shiue, E. H. Chen, and D. Englund, “High-resolution optical spectroscopy using multimode interference in a compact tapered fibre,” Nat. Commun 6, 7762 (2015).
[Crossref]

H. Rueda, D. Lau, and G. R. Arce, “Multi-spectral compressive snapshot imaging using rgb image sensors,” Opt. Express 23, 12207–12221 (2015).
[Crossref] [PubMed]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep 5, 10347 (2015).
[Crossref] [PubMed]

P. Wang and R. Menon, “Ultra-high-sensitivity color imaging via a transparent diffractive-filter array and computational optics,” Optica 2, 933–939 (2015).
[Crossref]

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

N. Drory, N. MacDonald, M. A. Bershady, K. Bundy, J. Gunn, D. R. Law, M. Smith, R. Stoll, C. A. Tremonti, D. A. Wake, R. Yan, A. M. Weijmans, N. Byler, B. Cherinka, F. Cope, A. Eigenbrot, P. Harding, D. Holder, J. Huehnerhoff, K. Jaehnig, T. C. Jansen, M. Klaene, A. M. Paat, J. Percival, and C. Sayres, “The MaNGA integral field unit fiber feed system for the sloan 2.5 m telescope,” The Astron. J. 149, 77 (2015).
[Crossref]

M. Chakrabarti, M. L. Jakobsen, and S. G. Hanson, “Speckle-based spectrometer,” Opt. Lett. 40, 3264–3267 (2015).
[Crossref] [PubMed]

2014 (4)

M. Mazilu, T. Vettenburg, A. D. Falco, and K. Dholakia, “Random super-prism wavelength meter,” Opt. Lett. 39, 96–99 (2014).
[Crossref]

A. Liutkus, D. Martina, S. Popoff, G. Chardon, O. Katz, G. Lerosey, S. Gigan, L. Daudet, and I. Carron, “Imaging with nature: compressive imaging using a multiply scattering medium,” Sci. Rep 4, 5552 (2014).
[PubMed]

B. Redding, M. Alam, M. Seifert, and H. Cao, “High-resolution and broadband all-fiber spectrometers,” Optica 1, 175–180 (2014).
[Crossref]

X. Lin, Y. Liu, J. Wu, and Q. Dai, “Spatial-spectral encoded compressive hyperspectral imaging,” ACM Trans. Graph. 33, 233 (2014).
[Crossref]

2013 (4)

R. W. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baranuik, “Sparsity and structure in hyperspectral imaging : sensing, reconstruction, and target detection,” IEEE Signal Process. Mag. 31, 116–126 (2013).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photonics 7, 746–751 (2013).
[Crossref]

N. A. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng 52, 090901 (2013).
[Crossref]

Y. August, C. Vachman, Y. Rivenson, and A. Stern, “Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains,” Appl. Opt. 52, D46–D54 (2013).
[Crossref] [PubMed]

2012 (3)

M. A. Peters, T. Groff, N. J. Kasdin, M. W. McElwain, M. Galvin, M. A. Carr, R. Lupton, J. E. Gunn, G. Knapp, Q. Gong, A. Carlotti, T. Brandt, M. Janson, O. Guyon, F. Martinache, M. Hayashi, and N. Takato, “Conceptual design of the coronagraphic high angular resolution imaging spectrograph (CHARIS) for the subaru telescope,” Proc. SPIE 8446, 84467U (2012).
[Crossref]

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37, 3384–3386 (2012).
[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 (2012).
[Crossref]

2010 (3)

T. W. Kohlgraf-Owens and A. Dogariu, “Transmission matrices of random media: means for spectral polarimetric measurements,” Opt. Lett. 35, 2236–2238 (2010).
[Crossref] [PubMed]

Q. Hang, B. Ung, I. Syed, N. Guo, and M. Skorobogatiy, “Photonic bandgap fiber bundle spectrometer,” Appl. Opt. 49, 4791–4800 (2010).
[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]

2008 (2)

A. Wagadarikar, R. John, R. Willett, and D. Brady, “Single disperser design for coded aperture snapshot spectral imaging,” Appl. Opt. 47, B44–B51 (2008).
[Crossref] [PubMed]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83 (2008).
[Crossref]

2007 (3)

2006 (2)

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289 – 1306 (2006).
[Crossref]

2003 (2)

Z. Xu, Z. Wang, M. E. Sullivan, D. J. Brady, S. H. Foulger, and A. Adibi, “Multimodal multiplex spectroscopy using photonic crystals,” Opt. Express 11, 2126–2133 (2003).
[Crossref] [PubMed]

F. Eisenhauer, K. B. R. Abuter, F. Biancat-Marchet, H. Bonnet, J. Brynnel, R. D. Conzelmann, B. Delabre, R. Donaldson, J. Farinato, E. Fedrigo, R. Genzel, N. N. Hubin, C. Iserlohe, M. E. Kasper, M. Kissler-Patig, C. R. G. J. Monnet, J. Schreiber, S. Stroebele, M. Tecza, N. A. Thatte, and H. Weisz, “SINFONI - Integral field spectroscopy at 50 milli-arcsecond resolution with the ESO VLT,” Proc. SPIE 4841, 1548–1561 (2003).
[Crossref]

1997 (1)

1994 (1)

Abdulhalim, I.

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep 6, 23524(2016).
[Crossref] [PubMed]

AbuLeil, M.

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep 6, 23524(2016).
[Crossref] [PubMed]

Abuter, K. B. R.

F. Eisenhauer, K. B. R. Abuter, F. Biancat-Marchet, H. Bonnet, J. Brynnel, R. D. Conzelmann, B. Delabre, R. Donaldson, J. Farinato, E. Fedrigo, R. Genzel, N. N. Hubin, C. Iserlohe, M. E. Kasper, M. Kissler-Patig, C. R. G. J. Monnet, J. Schreiber, S. Stroebele, M. Tecza, N. A. Thatte, and H. Weisz, “SINFONI - Integral field spectroscopy at 50 milli-arcsecond resolution with the ESO VLT,” Proc. SPIE 4841, 1548–1561 (2003).
[Crossref]

Adam, G.

R. Bacon, G. Adam, A. Baranne, G. Courtès, D. Dubet, J.-P. Dubois, Y. Georgelin, G. Monnet, E. Pecontal, and J. Urios, “The integral field spectrograph TIGER,” in European Southern Observatory Conference and Workshop Proceedings, (ESO, 1988) 30, pp. 1185.

Adibi, A.

Alam, M.

Amitonova, L. V.

Andreoli, D.

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep 5, 10347 (2015).
[Crossref] [PubMed]

Andresen, E. R.

Arce, G. R.

August, I.

I. August, Y. Oiknine, M. AbuLeil, I. Abdulhalim, and A. Stern, “Miniature compressive ultra-spectral imaging system utilizing a single liquid crystal phase retarder,” Sci. Rep 6, 23524(2016).
[Crossref] [PubMed]

August, Y.

Bacon, R.

R. Bacon, G. Adam, A. Baranne, G. Courtès, D. Dubet, J.-P. Dubois, Y. Georgelin, G. Monnet, E. Pecontal, and J. Urios, “The integral field spectrograph TIGER,” in European Southern Observatory Conference and Workshop Proceedings, (ESO, 1988) 30, pp. 1185.

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. E. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83 (2008).
[Crossref]

Baranne, A.

R. Bacon, G. Adam, A. Baranne, G. Courtès, D. Dubet, J.-P. Dubois, Y. Georgelin, G. Monnet, E. Pecontal, and J. Urios, “The integral field spectrograph TIGER,” in European Southern Observatory Conference and Workshop Proceedings, (ESO, 1988) 30, pp. 1185.

Baranuik, R. G.

R. W. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baranuik, “Sparsity and structure in hyperspectral imaging : sensing, reconstruction, and target detection,” IEEE Signal Process. Mag. 31, 116–126 (2013).
[Crossref]

Bershady, M. A.

N. Drory, N. MacDonald, M. A. Bershady, K. Bundy, J. Gunn, D. R. Law, M. Smith, R. Stoll, C. A. Tremonti, D. A. Wake, R. Yan, A. M. Weijmans, N. Byler, B. Cherinka, F. Cope, A. Eigenbrot, P. Harding, D. Holder, J. Huehnerhoff, K. Jaehnig, T. C. Jansen, M. Klaene, A. M. Paat, J. Percival, and C. Sayres, “The MaNGA integral field unit fiber feed system for the sloan 2.5 m telescope,” The Astron. J. 149, 77 (2015).
[Crossref]

Biancat-Marchet, F.

F. Eisenhauer, K. B. R. Abuter, F. Biancat-Marchet, H. Bonnet, J. Brynnel, R. D. Conzelmann, B. Delabre, R. Donaldson, J. Farinato, E. Fedrigo, R. Genzel, N. N. Hubin, C. Iserlohe, M. E. Kasper, M. Kissler-Patig, C. R. G. J. Monnet, J. Schreiber, S. Stroebele, M. Tecza, N. A. Thatte, and H. Weisz, “SINFONI - Integral field spectroscopy at 50 milli-arcsecond resolution with the ESO VLT,” Proc. SPIE 4841, 1548–1561 (2003).
[Crossref]

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]

Bonnet, H.

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Figures (7)

Fig. 1
Fig. 1 Characterizing a fiber imaging spectrometer. (a) Setup showing broadband supercontinuum calibration laser (CL), 10× beam expansion (f1 and f2), and diffraction grating (DG). One wavelength from the resulting spectrum is selected using a 10 µm pinhole (PH) and single mode fiber (SMF). (b) Light from the SMF is collimated using lens f3. Objects are imaged onto the input of a multicore multimode fiber (MCMMF) using a 3 cm lens (f4) and a 10× objective (O). Light transmitted through the fiber bundle is imaged onto a CMOS camera using a relay lens pair with 3 cm focal length (RL). (c) SMF is mounted on a rotation stage, with lens f5, to deliver light at angle, θ to the MCMMF. Output light is imaged onto a monochrome CCD using f6 and f7. (d) Spectral correlation width of: the MCMMF, with full-width half maximum (FWHM) of 1.4 nm obtained using narrowband laser source; the system when using the supercontinuum calibration laser source (CL), resulting in FWHM of 2.1 nm. (e) Camera images of speckle patterns produced by MCMMF cores, with incident angles of θ=0°, 2°, 4°. The corresponding angle correlation functions are shown for each θ. The shaded regions in (d) and (e) correspond to the standard deviation across all fiber cores.
Fig. 2
Fig. 2 A schematic showing the principle of the MCMMF STM calibration. Light travels through a MCMMF and the cross-section of the end of the fiber is imaged on to a camera. A clustering algorithm, DBSCAN, detects the positions of the speckle patterns produced by each fiber core on the camera. These coordinates are then used to calibrate a STM by measuring wavelength-dependent speckle patterns at every position and storing them in a 3-dimensional data cube. The coordinates are also used to search any arbitrary image for spectral signatures at those positions after calibration.
Fig. 3
Fig. 3 Imaging spectrometer robustness. (a) A STM illustrates the ratio between the number of camera pixels sampled, Y, and the number of calibrated wavelength increments, X. The resulting correlation between a known input spectrum and the resulting output spectrum is determined as Y/X is varied for two different spectra: Nλ=1 and Nλ=10, where Nλ is the number of wavelengths contained within the spectrum. The letters A, B, C, and D correspond to those labeled in (c) and (e). (b) Correlation between a known input spectrum and reconstructed spectrum, with an increasing Nλ, for three different sampling rates. The upper x axis shows the percentage of wavelengths in the spectrum from the STM wavelength calibration. (c) A speckle pattern produced by one fiber core. Illustrated are four different areas selected to build a STM, each labeled A to D enclosing the smallest to largest pixel number, respectively. (d) Camera image showing resulting light after light travels through the multimode multicore fiber. The coordinates identified by the DBSCAN clustering algorithm are plotted to show the areas where the STM will be applied to. (e) Four reconstructed images, each with a different sampling rate (Y/X=0.14, 0.32, 0.90, 2.01) for both the STM and the output data recorded. (f) Computational experiment to probe the robustness of the CS technique for three different sampling rates as artificial random i.i.d. noise is increased.
Fig. 4
Fig. 4 Reconstructing spatial and spectral information. (a) Spectrum from one spatial position (orange circle) reconstructed using the CS technique, with the letters corresponding to the wavelength labeled. The reconstructed spectrum is compared with that measured by a commercial spectrometer. (b) Conjugate camera image of 16 letters, each measured using a different wavelength. (c) As in (a), a spectrum reconstructed from the speckle pattern highlighted with red circle in (b). (d) Reconstructed spatial information for each spectral channel for the speckle image in (b). In total 16 letters are reconstructed from one application of the STM to the output information.
Fig. 5
Fig. 5 Fiber length-dependent characterization. (a) Spectral correlation function for 25 mm-length of MCMMF with a fiber core diameter of 50 µm and spectral correlation width of 11.5 nm. (b) Spectral correlation function for a 50 µm fiber core diameter and 150 mm-length of MCMMF with a spectral correlation width of 3.5 nm. (c) The spectral correlation width scales linearly with 1/L, where L is the fiber length.
Fig. 6
Fig. 6 Spatial reconstruction across multiple spectral channels for different sampling rates: (a) when Nλ=1 and Y/X=4, the letter ‘M’ is reconstructed in the spectral channels corresponding to 674.2 nm and 673.8 nm. Input information is not reconstructed in neighboring channels, however small noise fluctuations are observed. (b) when Nλ=1 and Y/X=0.32, the letter ‘M’ is reconstructed in the same spectral bands as in (a), although larger amounts of noise are observed in neighboring spectral bands.
Fig. 7
Fig. 7 Angle dependence of speckle patterns. The relationship between angle correlation width and the incident angle of light.

Equations (2)

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m i n i m i z e A N x N y N 1 s . t . x 0 .
N m 4 π 2 V 2 = 4 π 2 ( π D × NA λ ) 2 ,