Abstract

We propose a super-resolution technique for multichannel Fourier transform spectrometers, which is advantageous for feeble-light spectroscopy. The spectral resolution of an area sensor is limited by the number of lateral pixels. Our method fills the signals with vertical pixels, which is practically equivalent to increasing the number of lateral pixels. When applying our proposed technique, the resolution of an Ar-lamp spectrum, which is obtained by using an area sensor with 659 lateral pixels, becomes comparable to that of an area sensor with 1,626 lateral pixels. The spectral resolution is improved at least twice. Thus, using our method, a spectrometer with an area sensor can overcome the Nyquist frequency limitations.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

A. Watanabe and H. Furukawa, “High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation,” Opt. Commun. 413, 8–13 (2018).
[Crossref]

2016 (1)

H. Furukawa, “Real-time multi-channel Fourier transform spectroscopy and its application to non-invasive blood fat measurement,” Sensing and Bio-Sensing Research 8, 55–58 (2016).
[Crossref]

2015 (2)

X. Du and B. Anthony, “Concentric circle scanning system for large-area and high-precision imaging,” Opt. Express 23(15), 20014–20029 (2015).
[Crossref] [PubMed]

A. Abd-Almajeed and F. Langevin, “Sub-pixel shifted acquisitions for super-resolution proton magnetic resonance spectroscopy (1H MRS) mapping,” Magn. Reson. Imaging 33(4), 448–458 (2015).
[Crossref] [PubMed]

2011 (1)

2010 (1)

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

2008 (1)

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

2005 (1)

M. Ben-Ezra, A. Zomet, and S. K. Nayar, “Video super-resolution using controlled subpixel detector shifts,” IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 977–987 (2005).
[Crossref] [PubMed]

2004 (1)

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 83–97 (2004).
[Crossref] [PubMed]

2003 (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

2002 (1)

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Multiframe resolution-enhancement methods for compressed video,” IEEE Signal Process. Lett. 9(6), 170–174 (2002).
[Crossref]

2000 (1)

A. R. Faruqi and S. Subramaniam, “CCD detectors in high-resolution biological electron microscopy,” Q. Rev. Biophys. 33(1), 1–27 (2000).
[Crossref] [PubMed]

1998 (1)

K. J. Barnard, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37(1), 247–260 (1998).
[Crossref]

1997 (1)

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6(12), 1646–1658 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (1)

1993 (1)

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

1992 (3)

H. Ur and D. Gross, “Improved resolution from sub-pixel shifted pictures,” CVGIP Graph. Models Image Process. 54(2), 181–186 (1992).
[Crossref]

M. Hashimoto and S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31(28), 6096–6101 (1992).
[Crossref] [PubMed]

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

1989 (1)

S. Kawata, Y. Inouye, and S. Minami, “Compact multichannel FTIR-sensor with a Savart-plate Interferometer,” Proc. SPIE 1145, 567–568 (1989).
[Crossref]

1986 (1)

1985 (1)

1984 (1)

1971 (1)

1965 (1)

G. W. Stroke and A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16(3), 272–274 (1965).
[Crossref]

Abd-Almajeed, A.

A. Abd-Almajeed and F. Langevin, “Sub-pixel shifted acquisitions for super-resolution proton magnetic resonance spectroscopy (1H MRS) mapping,” Magn. Reson. Imaging 33(4), 448–458 (2015).
[Crossref] [PubMed]

Aizawa, K.

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

Altunbasak, Y.

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Multiframe resolution-enhancement methods for compressed video,” IEEE Signal Process. Lett. 9(6), 170–174 (2002).
[Crossref]

Anthony, B.

Barnard, K. J.

K. J. Barnard, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37(1), 247–260 (1998).
[Crossref]

Barnes, T. H.

Ben-Ezra, M.

M. Ben-Ezra, A. Zomet, and S. K. Nayar, “Video super-resolution using controlled subpixel detector shifts,” IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 977–987 (2005).
[Crossref] [PubMed]

Du, X.

Du, Y.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

Ebizuka, N.

Eiju, T.

Elad, M.

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6(12), 1646–1658 (1997).
[Crossref] [PubMed]

Faruqi, A. R.

A. R. Faruqi and S. Subramaniam, “CCD detectors in high-resolution biological electron microscopy,” Q. Rev. Biophys. 33(1), 1–27 (2000).
[Crossref] [PubMed]

Feuer, A.

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6(12), 1646–1658 (1997).
[Crossref] [PubMed]

Funkhouser, A. T.

G. W. Stroke and A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16(3), 272–274 (1965).
[Crossref]

Furukawa, H.

A. Watanabe and H. Furukawa, “High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation,” Opt. Commun. 413, 8–13 (2018).
[Crossref]

H. Furukawa, “Real-time multi-channel Fourier transform spectroscopy and its application to non-invasive blood fat measurement,” Sensing and Bio-Sensing Research 8, 55–58 (2016).
[Crossref]

Gigoux, P.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Gross, D.

H. Ur and D. Gross, “Improved resolution from sub-pixel shifted pictures,” CVGIP Graph. Models Image Process. 54(2), 181–186 (1992).
[Crossref]

Gunturk, B. K.

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Multiframe resolution-enhancement methods for compressed video,” IEEE Signal Process. Lett. 9(6), 170–174 (2002).
[Crossref]

Hamuy, M.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Hashimoto, M.

Heathcote, S. R.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Heussler, S. P.

Igarashi, T.

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

Inouye, Y.

S. Kawata, Y. Inouye, and S. Minami, “Compact multichannel FTIR-sensor with a Savart-plate Interferometer,” Proc. SPIE 1145, 567–568 (1989).
[Crossref]

Ishii, H.

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

Kalaiselvi, S. M.

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Katsaggelos, A. K.

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images,” Proceedings of 1995 IEEE International Conference on Image Processing, (1995), pp. 539–542.

Kawata, S.

Kobayashi, Y.

Komatsu, T.

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

Langevin, F.

A. Abd-Almajeed and F. Langevin, “Sub-pixel shifted acquisitions for super-resolution proton magnetic resonance spectroscopy (1H MRS) mapping,” Magn. Reson. Imaging 33(4), 448–458 (2015).
[Crossref] [PubMed]

Lin, Z.

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 83–97 (2004).
[Crossref] [PubMed]

Ling, F.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

Matsuda, K.

McCreery, R. L.

Mersereau, R. M.

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Multiframe resolution-enhancement methods for compressed video,” IEEE Signal Process. Lett. 9(6), 170–174 (2002).
[Crossref]

Minami, S.

Moser, H. O.

Nakata, M.

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

Nayar, S. K.

M. Ben-Ezra, A. Zomet, and S. K. Nayar, “Video super-resolution using controlled subpixel detector shifts,” IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 977–987 (2005).
[Crossref] [PubMed]

Okamoto, T.

Ozkan, M. K.

A. M. Tekalp, M. K. Ozkan, and M. I. Sezan, “High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration,” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), p. 169 (1992).

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Peek, T. H.

Phillips, M. M.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Quan, C. G.

Saito, T.

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

Sato, S.

Satoh, T.

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

Sezan, M. I.

A. M. Tekalp, M. K. Ozkan, and M. I. Sezan, “High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration,” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), p. 169 (1992).

Shum, H.-Y.

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 83–97 (2004).
[Crossref] [PubMed]

Stroke, G. W.

G. W. Stroke and A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16(3), 272–274 (1965).
[Crossref]

Subramaniam, S.

A. R. Faruqi and S. Subramaniam, “CCD detectors in high-resolution biological electron microscopy,” Q. Rev. Biophys. 33(1), 1–27 (2000).
[Crossref] [PubMed]

Suntzeff, N. B.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Tay, C. J.

Tekalp, A. M.

A. M. Tekalp, M. K. Ozkan, and M. I. Sezan, “High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration,” IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), p. 169 (1992).

Tom, B. C.

B. C. Tom and A. K. Katsaggelos, “Reconstruction of a high-resolution image by simultaneous registration, restoration, and interpolation of low-resolution images,” Proceedings of 1995 IEEE International Conference on Image Processing, (1995), pp. 539–542.

Tsukino, K.

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

Ur, H.

H. Ur and D. Gross, “Improved resolution from sub-pixel shifted pictures,” CVGIP Graph. Models Image Process. 54(2), 181–186 (1992).
[Crossref]

Wakaki, M.

Walker, A. R.

M. Hamuy, A. R. Walker, N. B. Suntzeff, P. Gigoux, S. R. Heathcote, and M. M. Phillips, “Southern Spectrophotometric Standards. 1,” Publ. Astron. Soc. Pac. 104, 533–552 (1992).
[Crossref]

Watanabe, A.

A. Watanabe and H. Furukawa, “High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation,” Opt. Commun. 413, 8–13 (2018).
[Crossref]

Wu, S.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

Xiao, F.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

Xue, H.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31(19), 5023–5040 (2010).
[Crossref]

Zhao, J.

Zomet, A.

M. Ben-Ezra, A. Zomet, and S. K. Nayar, “Video super-resolution using controlled subpixel detector shifts,” IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 977–987 (2005).
[Crossref] [PubMed]

Appl. Opt. (6)

Appl. Spectrosc. (1)

Chem. Phys. Lett. (1)

K. Tsukino, T. Satoh, H. Ishii, and M. Nakata, “Development of a multichannel Fourier-transform spectrometer to measure weak chemiluminescence: application to the emission of singlet-oxygen dimol in the decomposition of hydrogen peroxide with gallic acid and K3[Fe(CN)6],” Chem. Phys. Lett. 457(4–6), 444–447 (2008).
[Crossref]

CVGIP Graph. Models Image Process. (1)

H. Ur and D. Gross, “Improved resolution from sub-pixel shifted pictures,” CVGIP Graph. Models Image Process. 54(2), 181–186 (1992).
[Crossref]

IEE Proc., I, Commun. Speech Vis. (1)

T. Komatsu, K. Aizawa, T. Igarashi, and T. Saito, “Signal-processing based method for acquiring very high resolution image with multiple cameras and its theoretical analysis,” IEE Proc., I, Commun. Speech Vis. 140(1), 19–25 (1993).
[Crossref]

IEEE Signal Process. Lett. (1)

B. K. Gunturk, Y. Altunbasak, and R. M. Mersereau, “Multiframe resolution-enhancement methods for compressed video,” IEEE Signal Process. Lett. 9(6), 170–174 (2002).
[Crossref]

IEEE Signal Process. Mag. (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

IEEE Trans. Image Process. (1)

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images,” IEEE Trans. Image Process. 6(12), 1646–1658 (1997).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

M. Ben-Ezra, A. Zomet, and S. K. Nayar, “Video super-resolution using controlled subpixel detector shifts,” IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 977–987 (2005).
[Crossref] [PubMed]

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 83–97 (2004).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic image of sampling theorem. (a) Intrinsic interferogram. Dashed lines are the center positions of lateral pixels, and their intervals are equal to the pixel pitch. (b), (c), and (d) Disperse sampling points of low-resolution area sensors. The sets of (b) gray points, (c) black points, and (d) white points are slightly shifted with respect to each other. All signals of (b), (c), and (d) are combined to reconstruct (e).
Fig. 2
Fig. 2 Concept of positional relationship between the interferogram of Fourier transform spectroscopy and each pixel of the area sensor. (a) Conventional positioning, where the vertical lines of the area sensor are parallel to the stripe of the interferogram. The fringe marked with circles represents an identical bright fringe of the interferogram. (b) Method proposed in this study, where the area sensor is tilted slightly toward the stripe of the interferogram. The fringe marked with stars represents an identical bright fringe of the interferogram. θ is the tilting angle of the area sensor.
Fig. 3
Fig. 3 Schematic diagram of experimental setup.
Fig. 4
Fig. 4 (a) Two-dimensional interferogram signal with our method tilting the area sensor slightly. (b) The center-part enlarged interferograms of 184th line (bold gray line) and 291st line (dashed line) from the top end. (c) Reconstructed interferogram by the proposed method; center part corresponding to Fig. 4 (b) was enlarged.
Fig. 5
Fig. 5 The schematic image of the case when two stars positions are different slightly in Fig. 2. The interferogram pattern becomes enlarged at s > 0.
Fig. 6
Fig. 6 (a) (Above bold line) and (b) (Above bold line) are Fourier transformed spectra, of Fig. 4 (b) and Fig. 4 (c), respectively. Both figures are over layered by dotted reference spectrum, which appears in Fig. 6 (c) (Above). (a) (Bottom) and (b) (Bottom) are entire interferograms of Fig. 4 (b) and Fig. 4 (c), respectively. (c) (Above) Accurate Ar lamp spectrum and (c) (Bottom) the acquired interferogram using high-resolution area sensor.
Fig. 7
Fig. 7 The schematic image of the lateral size of a area sensor and the practically sensitive area of a pixel.

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