Abstract

A spectral imager constructs a three-dimensional (two spatial and one spectral) image from a series of two-dimensional images. We discuss a technique for spectral imaging that multiplexes the spatial and spectral information on a staring focal plane and then demultiplexes the resulting imagery to obtain the spectral image. The spectral image consists of 100×100 spatial pixels and 25 spectral bands. The current implementation operates over the 3–5-μm band, but can easily be applied to other spectral regions. This approach to spectral imaging has high optical throughput and is robust to focal plane array nonuniformities. A hardware description, the mathematical development, and experimental results are presented.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
    [CrossRef]
  2. R. Basedow, D. Carmer, M. Anderson, “Hydice systems, implementation and performance,” in Imaging Spectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 258–267 (1995).
    [CrossRef]
  3. G. G. Levin, G. N. Vishnyakov, “On the possibilities of chronotomography of high-speed processes,” Opt. Commun. 56, 231–234 (1985).
    [CrossRef]
  4. T. Okamoto, A. Takahashi, I. Yamaguchi, “Simultaneous acquisition of spectral and spatial intensity distribution,” Appl. Spectrosc. 47, 1198–1202 (1993).
    [CrossRef]
  5. Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
    [CrossRef]
  6. M. Descour, E. Dereniak, “Computed-tomography imaging spectrometer: experimental calibrationand reconstruction results,” Appl. Opt. 34, 4817–4826 (1995).
    [CrossRef] [PubMed]
  7. P. A. Bernhardt, “Direct reconstruction methods for hyperspectral imaging with rotationalspectrotomography,” J. Opt. Soc. Am. A 12, 1884–1901 (1995).
    [CrossRef]
  8. J. M. Mooney, “Spectral imaging via computed tomography,” in Proceedings of the 1994 Meeting of the Infrared Information Symposia Specialty Group on Passive Sensors (Defense Technical Information Center, Alexandria, Va., 1994), Vol. 1, pp. 203–215.
  9. J. M. Mooney, “Angularly multiplexed spectral imager,” in ImagingSpectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 65–77 (1995).
    [CrossRef]
  10. H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 433–434.
  11. K. C. Tam, V. Perez-Mendez, “Tomographical imaging with limited-angle input,” J. Opt. Soc. Am. 71, 582–592 (1981).
    [CrossRef]
  12. P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).
  13. H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
    [CrossRef]
  14. C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
    [CrossRef]
  15. D. M. Lyons, K. Whitcomb, “Characterization of the DIOS prototype: a diffractive optic image spectrometer,”in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 206–217 (1996).
    [CrossRef]
  16. M. Hinnrichs, M. A. Massie, “Image multispectral sensing: a new and innovative instrument for hyperspectralimaging using dispersive techniques,” in Imaging SpectrometryI, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 93–104 (1995).
    [CrossRef]
  17. A. Erhardt, G. Zinser, D. Komitowski, J. Bille, “Reconstructing 3-D light-microscope images by digital image processing,” Appl. Opt. 24, 194–200 (1985).
    [CrossRef]
  18. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.
  19. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.
  20. H. H. Barrett, “Editorial: Limited-angle tomography for the nineties,” J. Nucl. Med. 31, 1688–1692 (1990).
    [PubMed]
  21. H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 375–446.
  22. A. K. Brodzik, J. M. Mooney, M. An, “Image restoration by convex projections: application to image spectrometry,”in Imaging Spectrometry II,M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 231–242 (1996).
    [CrossRef]
  23. A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
    [CrossRef]
  24. R. Tolimieri, M. An, C. Lu, Algorithms for Discrete Fourier Transform and Convolution (Springer, New York, 1989).
  25. I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).
  26. J. W. Boardman, “Analysis, understanding and visualization of hyperspectral data asa convex set in n-space,” in Imaging Spectrometry I,M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 14–22 (1995).
    [CrossRef]

1995 (2)

1993 (2)

T. Okamoto, A. Takahashi, I. Yamaguchi, “Simultaneous acquisition of spectral and spatial intensity distribution,” Appl. Spectrosc. 47, 1198–1202 (1993).
[CrossRef]

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

1990 (1)

H. H. Barrett, “Editorial: Limited-angle tomography for the nineties,” J. Nucl. Med. 31, 1688–1692 (1990).
[PubMed]

1989 (1)

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

1985 (2)

G. G. Levin, G. N. Vishnyakov, “On the possibilities of chronotomography of high-speed processes,” Opt. Commun. 56, 231–234 (1985).
[CrossRef]

A. Erhardt, G. Zinser, D. Komitowski, J. Bille, “Reconstructing 3-D light-microscope images by digital image processing,” Appl. Opt. 24, 194–200 (1985).
[CrossRef]

1981 (1)

1980 (3)

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

1975 (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

An, M.

A. K. Brodzik, J. M. Mooney, M. An, “Image restoration by convex projections: application to image spectrometry,”in Imaging Spectrometry II,M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 231–242 (1996).
[CrossRef]

R. Tolimieri, M. An, C. Lu, Algorithms for Discrete Fourier Transform and Convolution (Springer, New York, 1989).

Anderson, M.

R. Basedow, D. Carmer, M. Anderson, “Hydice systems, implementation and performance,” in Imaging Spectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Barrett, H. H.

H. H. Barrett, “Editorial: Limited-angle tomography for the nineties,” J. Nucl. Med. 31, 1688–1692 (1990).
[PubMed]

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 375–446.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 433–434.

Basedow, R.

R. Basedow, D. Carmer, M. Anderson, “Hydice systems, implementation and performance,” in Imaging Spectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Bernhardt, P. A.

Betremieux, Y.

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

Bille, J.

Boardman, J. W.

J. W. Boardman, “Analysis, understanding and visualization of hyperspectral data asa convex set in n-space,” in Imaging Spectrometry I,M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 14–22 (1995).
[CrossRef]

Brodzik, A. K.

A. K. Brodzik, J. M. Mooney, M. An, “Image restoration by convex projections: application to image spectrometry,”in Imaging Spectrometry II,M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 231–242 (1996).
[CrossRef]

Carmer, D.

R. Basedow, D. Carmer, M. Anderson, “Hydice systems, implementation and performance,” in Imaging Spectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Chakrabarti, S.

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

Cook, T. A.

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

Cotton, D. M.

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

Dereniak, E.

Descour, M.

Edholm, P.

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

Erhardt, A.

Ewing, W.

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.

Granlund, G.

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

Hinnrichs, M.

M. Hinnrichs, M. A. Massie, “Image multispectral sensing: a new and innovative instrument for hyperspectralimaging using dispersive techniques,” in Imaging SpectrometryI, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 93–104 (1995).
[CrossRef]

Jolliffe, I. T.

I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).

Knutsson, H.

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

Komitowski, D.

Levin, G. G.

G. G. Levin, G. N. Vishnyakov, “On the possibilities of chronotomography of high-speed processes,” Opt. Commun. 56, 231–234 (1985).
[CrossRef]

Lu, C.

R. Tolimieri, M. An, C. Lu, Algorithms for Discrete Fourier Transform and Convolution (Springer, New York, 1989).

Lyons, D. M.

D. M. Lyons, K. Whitcomb, “Characterization of the DIOS prototype: a diffractive optic image spectrometer,”in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 206–217 (1996).
[CrossRef]

Massie, M. A.

M. Hinnrichs, M. A. Massie, “Image multispectral sensing: a new and innovative instrument for hyperspectralimaging using dispersive techniques,” in Imaging SpectrometryI, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 93–104 (1995).
[CrossRef]

Mooney, J.

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Mooney, J. M.

J. M. Mooney, “Spectral imaging via computed tomography,” in Proceedings of the 1994 Meeting of the Infrared Information Symposia Specialty Group on Passive Sensors (Defense Technical Information Center, Alexandria, Va., 1994), Vol. 1, pp. 203–215.

J. M. Mooney, “Angularly multiplexed spectral imager,” in ImagingSpectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 65–77 (1995).
[CrossRef]

A. K. Brodzik, J. M. Mooney, M. An, “Image restoration by convex projections: application to image spectrometry,”in Imaging Spectrometry II,M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 231–242 (1996).
[CrossRef]

Murguia, J.

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Okamoto, T.

Papoulis, A.

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

Perez-Mendez, V.

Petersson, C.

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.

Shepherd, F.

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Silverman, J.

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 433–434.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 375–446.

Takahashi, A.

Tam, K. C.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.

Tolimieri, R.

R. Tolimieri, M. An, C. Lu, Algorithms for Discrete Fourier Transform and Convolution (Springer, New York, 1989).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.

Vishnyakov, G. N.

G. G. Levin, G. N. Vishnyakov, “On the possibilities of chronotomography of high-speed processes,” Opt. Commun. 56, 231–234 (1985).
[CrossRef]

Whitcomb, K.

D. M. Lyons, K. Whitcomb, “Characterization of the DIOS prototype: a diffractive optic image spectrometer,”in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 206–217 (1996).
[CrossRef]

Yamaguchi, I.

Zinser, G.

Acta Radiol. Diagn. (1)

P. Edholm, G. Granlund, H. Knutsson, C. Petersson, “Ectomography—a new radiographic method for reproducing a selectedslice of varying thickness,” Acta Radiol. Diagn. 21, 433–442 (1980).

Appl. Opt. (2)

Appl. Spectrosc. (1)

IEEE Trans. Biomed. Eng. (2)

H. Knutsson, P. Edholm, G. Granlund, C. Petersson, “Ectomography—a new radiographic reconstruction method—I. Theory and error estimates,” IEEE Trans. Biomed. Eng. BME-27, 640–648 (1980).
[CrossRef]

C. Petersson, P. Edholm, G. Granlund, H. Knutsson, “Ectomography—a new radiographic reconstruction method—II. Computer simulated experiments,” IEEE Trans. Biomed. Eng. BME-27, 649–655 (1980).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

A. Papoulis, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975).
[CrossRef]

J. Nucl. Med. (1)

H. H. Barrett, “Editorial: Limited-angle tomography for the nineties,” J. Nucl. Med. 31, 1688–1692 (1990).
[PubMed]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

G. G. Levin, G. N. Vishnyakov, “On the possibilities of chronotomography of high-speed processes,” Opt. Commun. 56, 231–234 (1985).
[CrossRef]

Opt. Eng. (2)

Y. Betremieux, T. A. Cook, D. M. Cotton, S. Chakrabarti, “SPINR: two-dimensional spectral imaging through tomographic reconstruction,” Opt. Eng. 32, 3133–3138 (1993).
[CrossRef]

J. Mooney, F. Shepherd, W. Ewing, J. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staringcameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Other (13)

R. Basedow, D. Carmer, M. Anderson, “Hydice systems, implementation and performance,” in Imaging Spectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

J. M. Mooney, “Spectral imaging via computed tomography,” in Proceedings of the 1994 Meeting of the Infrared Information Symposia Specialty Group on Passive Sensors (Defense Technical Information Center, Alexandria, Va., 1994), Vol. 1, pp. 203–215.

J. M. Mooney, “Angularly multiplexed spectral imager,” in ImagingSpectrometry I, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 65–77 (1995).
[CrossRef]

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 433–434.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 52–54.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, New York, 1988), pp. 60–72.

D. M. Lyons, K. Whitcomb, “Characterization of the DIOS prototype: a diffractive optic image spectrometer,”in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 206–217 (1996).
[CrossRef]

M. Hinnrichs, M. A. Massie, “Image multispectral sensing: a new and innovative instrument for hyperspectralimaging using dispersive techniques,” in Imaging SpectrometryI, M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 93–104 (1995).
[CrossRef]

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), Vol. 2, pp. 375–446.

A. K. Brodzik, J. M. Mooney, M. An, “Image restoration by convex projections: application to image spectrometry,”in Imaging Spectrometry II,M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 231–242 (1996).
[CrossRef]

R. Tolimieri, M. An, C. Lu, Algorithms for Discrete Fourier Transform and Convolution (Springer, New York, 1989).

I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).

J. W. Boardman, “Analysis, understanding and visualization of hyperspectral data asa convex set in n-space,” in Imaging Spectrometry I,M. R. Descour, J. M. Mooney, D. L. Perry, L. Illing, eds., Proc. SPIE2480, 14–22 (1995).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Schematic representation of the spectral imager and its operation. On the left, the direct-vision prism is shown spreading red, green, and blue light across the FPA. On the right, the effect of the prism rotation on the overlapping red, green, and blue images is illustrated. The circles and arrows represent the prism orientation.

Fig. 2
Fig. 2

Correspondence of our recorded data to Radon projections. The projection angle follows from the definition that adjacent spectral bands are displaced by one pixel on the FPA and the assumption that the object volume elements are equilateral. The spectral image can be reconstructed in the frequency domain by using the central slice theorem (shown in both two and three dimensions).

Fig. 3
Fig. 3

Illustration of the w i , i ( ξ , ζ ) values as a function of spatial frequency. Each of these images corresponds to a horizontal slice through the 3D representation of the spatial–spectral transform image on the right side of Fig. 2. Zero spatial frequency is in the center of each image. Bright and dark regions correspond to large and small values of w i , i ( ξ , ζ ) , respectively. The sequence from left to right, top to bottom corresponds to descending chromatic-frequency data. The lower right image corresponds to image features that change slowly as a function of wavelength (low chromatic frequencies). The upper-left image corresponds to image features that change rapidly as a function of wavelength (high chromatic frequencies). The dark region in the center of each image corresponds to the spatial–chromatic frequencies where information has been lost.

Fig. 4
Fig. 4

Schematic representation of how low-pass filtering, augmenting the data, and use of the field-stop prior knowledge can be used to reduce the fractional volume of the missing cone. Low-pass filtering reduces the chromatic resolution but preferentially filters out missing information, the augmentative data fills in the zero spatial-frequency axis information, and the field-stop prior knowledge broadens all of the data samples.

Fig. 5
Fig. 5

Visible image of the scene used for the demonstration. The reflective plate and differential source are illuminated by an incandescent lamp. Here the lamp intensity is much greater than when the experiment was performed so that the reflected light can be seen.

Fig. 6
Fig. 6

Broadband infrared image of the scene used for the demonstration. Here the field stop limits the field of view to the central 100 × 100   pixels .

Fig. 7
Fig. 7

One of the 80 projections. Here the blurring is due to the prism dispersion.

Fig. 8
Fig. 8

One of the 50 spectral reconstructions before filtering. This reconstruction corresponds to 3.8 μm.

Fig. 9
Fig. 9

A comparison of single-pixel spectral profiles from the reflective plate, `Solar', and a hot bar, Thermal, before filtering. The spectral profiles shown are measured relative to the field stop, which we have assumed to be spectrally flat.

Fig. 10
Fig. 10

Scatterplot of the spatial–spectral image data, made with the two leading terms of the SVD. The indicated display axis corresponds to the left image in Fig. 11.

Fig. 11
Fig. 11

Spatial display of the spectrally discriminated objects. The center image is a broadband image. On the left the display axis is oriented to map the plate and the background to the same level and therefore accentuate the bars. On the right the plate is accentuated.

Fig. 12
Fig. 12

Four largest and smallest singular values as a function of number of iterations. The decline of the third largest singular value for the first few iterations indicates the effectiveness of the iterative techniques for filling the missing cone.

Fig. 13
Fig. 13

Enlarged view of the spatial eigenvector corresponding to the third-largest singular value (artifact due to the missing cone) after five iterations. The ringing at the plate edges is indicative of lost information.

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

r 1 ( x ,   y ) = p 1 , 1 ( x ,   y ) * * c 1 ( x ,   y ) + p 1 , 2 ( x ,   y ) * * c 2 ( x ,   y ) + p 1 , 3 ( x ,   y ) * * c 3 ( x ,   y )
r 2 ( x ,   y ) = p 2 , 1 ( x ,   y ) * * c 1 ( x ,   y ) + p 2 , 2 ( x ,   y ) * * c 2 ( x ,   y ) + p 2 , 3 ( x ,   y ) * * c 3 ( x ,   y )
r 3 ( x ,   y ) = p 3 , 1 ( x ,   y ) * * c 1 ( x ,   y ) + p 3 , 2 ( x ,   y ) * * c 2 ( x ,   y ) + p 3 , 3 ( x ,   y ) * * c 3 ( x ,   y )
r 4 ( x ,   y ) = p 4 , 1 ( x ,   y ) * * c 1 ( x ,   y ) + p 4 , 2 ( x ,   y ) * * c 2 ( x ,   y ) + p 4 , 3 ( x ,   y ) * * c 3 ( x ,   y ) ,
p m , k ( x ,   y ) = δ [ x - ( k - k 0 ) Δ x   cos ( ϕ m ) , y - ( k - k 0 ) Δ x   sin ( ϕ m ) ] ,
R 1 ( ξ ,   ζ ) = P 1 , 1 ( ξ ,   ζ ) C 1 ( ξ ,   ζ ) + P 1 , 2 ( ξ ,   ζ ) C 2 ( ξ ,   ζ ) + P 1 , 3 ( ξ ,   ζ ) C 3 ( ξ ,   ζ ) ,
R 2 ( ξ ,   ζ ) = P 2 , 1 ( ξ ,   ζ ) C 1 ( ξ ,   ζ ) + P 2 , 2 ( ξ ,   ζ ) C 2 ( ξ ,   ζ ) + P 2 , 3 ( ξ ,   ζ ) C 3 ( ξ ,   ζ ) ,
R 3 ( ξ ,   ζ ) = P 3 , 1 ( ξ ,   ζ ) C 1 ( ξ ,   ζ ) + P 3 , 2 ( ξ ,   ζ ) C 2 ( ξ ,   ζ ) + P 3 , 3 ( ξ ,   ζ ) C 3 ( ξ ,   ζ ) ,
R 4 ( ξ ,   ζ ) = P 4 , 1 ( ξ ,   ζ ) C 1 ( ξ ,   ζ ) + P 4 , 2 ( ξ ,   ζ ) C 2 ( ξ ,   ζ ) + P 4 , 3 ( ξ ,   ζ ) C 3 ( ξ ,   ζ ) ,
R 1 ( ξ ,   ζ ) R 2 ( ξ ,   ζ ) R 3 ( ξ ,   ζ ) R 4 ( ξ ,   ζ ) = P 1 , 1 ( ξ ,   ζ ) P 1 , 2 ( ξ ,   ζ ) P 1 , 3 ( ξ ,   ζ ) P 2 , 1 ( ξ ,   ζ ) P 2 , 2 ( ξ ,   ζ ) P 2 , 3 ( ξ ,   ζ ) P 3 , 1 ( ξ ,   ζ ) P 3 , 2 ( ξ ,   ζ ) P 3 , 3 ( ξ ,   ζ ) P 4 , 1 ( ξ ,   ζ ) P 4 , 2 ( ξ ,   ζ ) P 4 , 3 ( ξ ,   ζ ) × C 1 ( ξ ,   ζ ) C 2 ( ξ ,   ζ ) C 3 ( ξ ,   ζ ) ,
R ( ξ ,   ζ ) = P ( ξ ,   ζ ) C ( ξ ,   ζ ) .
P m , k ( ξ ,   ζ ) = exp { - 2 π i [ ξ   cos ( ϕ m ) + ζ   sin ( ϕ m ) ] × ( k - k 0 ) Δ x } .
P m , k ( ξ ,   ζ ) = P m , k ( ν ) = exp ( - 2 π i ν ρ ) ,
P m , k ( ξ ,   ζ ) = ( exp { - 2 π i [ ξ   cos ( ϕ m ) + ζ   sin ( ϕ m ) ] Δ x } ) ( k - k 0 ) ,
R ( ξ ,   ζ ) = P ( ξ ,   ζ ) C ( ξ ,   ζ ) + N ( ξ ,   ζ ) ,
P = UWV .
U U = V V = 1 ,
1 / w 1 , 1 1 / w K , K   w 1 , 1 w K , K = 1 .
1 = VW - 1 U P .
C ˜ ( ξ ,   ζ ) = V ( ξ ,   ζ ) W - 1 ( ξ ,   ζ ) U ( ξ ,   ζ ) R ( ξ ,   ζ ) ,
w ˜ i , i ( ξ ,   ζ ) = w i , i ( ξ ,   ζ ) w i , i 2 ( ξ ,   ζ ) + 2 .
C ˜ = V [ W ˜ - 1 WV C + W ˜ - 1 U N ] .
r = F - 1 PF c + n ,
r = F - 1 UWV F c + n .
r = F - 1 UWV FS c + n ,
c ˜ 0 = F - 1 V W ˜ - 1 U F r .
c ˜ j = F - 1 V [ L W ˜ - 1 U F r + RV FT c ˜ j - 1 ] ,
L i , i ( ξ ,   ζ ) = w i , i 2 ( ξ ,   ζ ) w i , i 2 ( ξ ,   ζ ) + β 2 ,
R i , i ( ξ ,   ζ ) = 1 - L i , i ( ξ ,   ζ ) ,
P m , k ( ξ ,   ζ ) = P m , 2 k 0 - k * ( ξ ,   ζ ) P m + M / 2 , k * ( ξ ,   ζ ) P m , k * ( - ξ ,   - ζ ) P m + M / 4 , k ( ζ ,   - ξ ) P M / 2 - m , k ( - ξ ,   ζ ) .

Metrics