Abstract

A temporally and spatially nonscanning imaging spectrometer is described in terms of computed-tomography concepts, specifically the central-slice theorem. A sequence of three transmission sinusoidal-phase gratings rotated in 60° increments achieves dispersion in multiple directions and into multiple orders. The dispersed images of the system’s field stop are interpreted as two-dimensional projections of a three-dimensional (x, y, λ) object cube. Because of the size of the finite focal-plane array, this imaging spectrometer is an example of a limited-view-angle tomographic system. The imaging spectrometer’s point spread function is measured experimentally as a function of wavelength and position in the field of view. Reconstruction of the object cube is then achieved through the maximum-likelihood, expectation-maximization algorithm under the assumption of a Poisson likelihood law. Experimental results indicate that the instrument performs well in the case of broadband and narrow-band emitters.

© 1995 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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1993 (2)

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

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

1991 (2)

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

T. Okamoto, I. Yamaguchi, “Simultaneous acquisition of spectral image information,” Opt. Lett. 16, 1277–1279 (1991).
[CrossRef] [PubMed]

1990 (1)

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

1988 (1)

G. Vane, A. F. H. Goetz, “Terrestrial imaging spectroscopy,” Remote Sensing Environ. 24, 1–29 (1988).
[CrossRef]

1982 (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–122 (1982).
[CrossRef]

1979 (1)

1973 (1)

1969 (1)

Aarsvold, J. N.

J. N. Aarsvold, “Multiple-pinhole transaxial tomography: a model and analysis,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1993), Chap. 2.

Arendt, J. W.

Barrett, H. H.

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

M. Y. Chiu, H. H. Barrett, R. G. Simpson, C. Chou, J. W. Arendt, G. R. Rindi, “Three-dimensional radiographic imaging with a restricted view angle,” J. Opt. Soc. Am. 69, 1323–1333 (1979).
[CrossRef]

H. H. Barrett, “Image reconstruction and the solution of inverse problems in medical imaging,” in The Formation, Handling, and Evaluation of Medical Images, A. Todd-Pokropek, M. A. Viergever, eds. (Springer-Verlag, Berlin, 1991), pp. 3–42.

H. H. Barrett, W. Swindell, Radiological Imaging/The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vol. 2.

Bétrémieux, Y.

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

Blyleven, W.

W. Blyleven, DALSA CCD Image Sensors Inc. Waterloo, Ontario, Canada N2V 2E9 (personal communication, 1994).

Bulygin, F. V.

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

Chakrabarti, S.

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

Chiu, M. Y.

Chou, C.

Cook, T. A.

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

Descour, M. R.

M. R. Descour, “Non-scanning imaging spectrometry,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994), Chap. 2.

Fine, T.

Frieden, B. R.

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1991), Chap. 17.

Goetz, A. F. H.

G. Vane, A. F. H. Goetz, “Terrestrial imaging spectroscopy,” Remote Sensing Environ. 24, 1–29 (1988).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 69– 70.

Harwit, M.

Hedler, R. A.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

Karpukhin, D. V.

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

Levin, G. G.

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

Maninger, L. L.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

Momberger, R. A.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

Mooney, J. M.

J. M. Mooney, “Spectral imaging via computed tomography,” in Proceedings of Infrared Information Symposia (IRIS) Specialty Group on Passive Sensors [Environmental Research Institute of Michigan (ERIM), Ann Arbor, Mich., 1994], Vol. 1, pp. 203–215.

Okamoto, T.

Phillips, P. G.

Radon, J.

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” in Gesammelte Abhandlungen/Collected Works (Birkhäuser Verlag, Vienna, 1987), Vol. 2, pp. 11–26.

Rindi, G. R.

Robbins, J. D.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

Rowe, R. K.

R. K. Rowe, “A system for three-dimensional SPECT without motion,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1991), Chap. 5.

Say, D. L.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

Shepp, L. A.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–122 (1982).
[CrossRef]

Simpson, R. G.

Sloane, N. J. A.

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging/The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vol. 2.

Takahashi, A.

Vane, G.

G. Vane, A. F. H. Goetz, “Terrestrial imaging spectroscopy,” Remote Sensing Environ. 24, 1–29 (1988).
[CrossRef]

Vardi, Y.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–122 (1982).
[CrossRef]

Vishnyakov, G. N.

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

Wyant, J. C.

Yamaguchi, I.

Appl. Opt. (2)

Appl. Spectrosc. (1)

IEEE Trans. Med. Imaging (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–122 (1982).
[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)

Opt. Eng. (1)

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

Opt. Lett. (1)

Opt. Spectrosc. (USSR) (1)

F. V. Bulygin, G. N. Vishnyakov, G. G. Levin, D. V. Karpukhin, “Spectrotomography—a new method of obtaining spectrograms of 2-D objects,” Opt. Spectrosc. (USSR) 71, 561–563 (1991).

Remote Sensing Environ. (1)

G. Vane, A. F. H. Goetz, “Terrestrial imaging spectroscopy,” Remote Sensing Environ. 24, 1–29 (1988).
[CrossRef]

Other (11)

W. Blyleven, DALSA CCD Image Sensors Inc. Waterloo, Ontario, Canada N2V 2E9 (personal communication, 1994).

J. M. Mooney, “Spectral imaging via computed tomography,” in Proceedings of Infrared Information Symposia (IRIS) Specialty Group on Passive Sensors [Environmental Research Institute of Michigan (ERIM), Ann Arbor, Mich., 1994], Vol. 1, pp. 203–215.

H. H. Barrett, “Image reconstruction and the solution of inverse problems in medical imaging,” in The Formation, Handling, and Evaluation of Medical Images, A. Todd-Pokropek, M. A. Viergever, eds. (Springer-Verlag, Berlin, 1991), pp. 3–42.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 4, pp. 69– 70.

M. R. Descour, “Non-scanning imaging spectrometry,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994), Chap. 2.

R. K. Rowe, “A system for three-dimensional SPECT without motion,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1991), Chap. 5.

H. H. Barrett, W. Swindell, Radiological Imaging/The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vol. 2.

J. N. Aarsvold, “Multiple-pinhole transaxial tomography: a model and analysis,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1993), Chap. 2.

B. R. Frieden, Probability, Statistical Optics, and Data Testing (Springer-Verlag, Berlin, 1991), Chap. 17.

D. L. Say, R. A. Hedler, L. L. Maninger, R. A. Momberger, J. D. Robbins, “Monochrome and color image-display devices,” in Television Engineering Handbook, K. B. Benson, ed. (McGraw-Hill, New York, 1992), Chap. 12.

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” in Gesammelte Abhandlungen/Collected Works (Birkhäuser Verlag, Vienna, 1987), Vol. 2, pp. 11–26.

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