Abstract

Multispectral images that have spectral resolution as high as their spatial resolution may be called supermultispectral images or simply spectral images. The principle of an interferometric method of supermultispectral imaging has been developed by unifying the principles of incoherent holography and Fourier spectroscopy. The method is expected to inherit the multiplex and throughput advantages from Fourier spectroscopy. We present our first experimental results of the method applied to diffusely illuminated objects and self-radiating thermal objects along with a simplified theory and brief discussion on the signal-to-noise ratios.

© 1990 Optical Society of America

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References

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  1. K. Itoh, Y. Ohtsuka, “Interferometric Spectral Imaging,” in Conference Digest of ICO-13 on Optics in Modern Science and Technology (Organization Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.
  2. K. Itoh, Y. Ohtsuka, “Fourier-Transform Spectral Imaging: Retrieval of Source Information from 3-D Spatial Coherence,” J. Opt. Soc. Am. A 3, 94–99 (1986).
    [CrossRef]
  3. G. Vane, Ed., imaging Spectroscopy II, Proc. Soc. Photo-Opt. Instrum. Eng.834 (1988).
  4. J. M. Mariotti, S. T. Ridgway, “Double Fourier Spatio-Spectral Interferometry: Combining High Spectral and High Spatial Resolution in the Near Infrared,” Astron. Astrophys. 195, 350–363 (1988).
  5. L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.
  6. O. Bryngdahl, A. W. Lohmann, “Variable Magnification in Incoherent Holography,” Appl. Opt. 9, 231–232 (1970).
    [CrossRef] [PubMed]
  7. Ref. 5, Chaps. 1 and 2.
  8. G. A. Vanasse, H. Sakai, “Fourier Spectroscopy,” Prog. Opt. 6, 261–327 (1967).
  9. A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, NJ, 1962), Chap. 3.
  10. S. W. Lang, T. L. Marzetta, “Image Spectral Estimation,” in Digital Image Processing, M. P. Ekstrom, Ed. (Academic, Orlando, FL, 1984), Chap. 6.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.
  12. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.
  13. J. W. Goodman, Introduction to Fourier Optics (Wiley, New York, 1968), Chap. 2.
  14. W. H. Carter, E. Wolf, “Coherence and Radiometry with Quasihomogeneous Planar Sources,” J. Opt. Soc. Am. 67, 785–796 (1977).
    [CrossRef]
  15. K. Itoh, T. Inoue, Y. Ichioka, “Fourier-Transform Spectral Imaging with Variable Magnification,” in Proceedings, Fourteenth Congress of ICO, H. H. Arsenault, Ed. (Publication Committee of ICO, Quebec, Canada, 1987), pp. 519–520.
  16. K. Itoh, T. Inoue, Y. Ichioka, “Interferometric Spectral Imaging in the Visible and Near-Infrared Regions,” in Technical Digest, Topical Meeting on Space Optics for Astronomy and Earth and Planetary Remote Sensing (Optical Society of America, Washington, DC, 1988), pp. 76–78.
  17. C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
    [CrossRef]

1988

J. M. Mariotti, S. T. Ridgway, “Double Fourier Spatio-Spectral Interferometry: Combining High Spectral and High Spatial Resolution in the Near Infrared,” Astron. Astrophys. 195, 350–363 (1988).

1986

1977

1970

1967

G. A. Vanasse, H. Sakai, “Fourier Spectroscopy,” Prog. Opt. 6, 261–327 (1967).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.

Bryngdahl, O.

Carter, W. H.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.

J. W. Goodman, Introduction to Fourier Optics (Wiley, New York, 1968), Chap. 2.

Ichioka, Y.

K. Itoh, T. Inoue, Y. Ichioka, “Interferometric Spectral Imaging in the Visible and Near-Infrared Regions,” in Technical Digest, Topical Meeting on Space Optics for Astronomy and Earth and Planetary Remote Sensing (Optical Society of America, Washington, DC, 1988), pp. 76–78.

K. Itoh, T. Inoue, Y. Ichioka, “Fourier-Transform Spectral Imaging with Variable Magnification,” in Proceedings, Fourteenth Congress of ICO, H. H. Arsenault, Ed. (Publication Committee of ICO, Quebec, Canada, 1987), pp. 519–520.

Inoue, T.

K. Itoh, T. Inoue, Y. Ichioka, “Fourier-Transform Spectral Imaging with Variable Magnification,” in Proceedings, Fourteenth Congress of ICO, H. H. Arsenault, Ed. (Publication Committee of ICO, Quebec, Canada, 1987), pp. 519–520.

K. Itoh, T. Inoue, Y. Ichioka, “Interferometric Spectral Imaging in the Visible and Near-Infrared Regions,” in Technical Digest, Topical Meeting on Space Optics for Astronomy and Earth and Planetary Remote Sensing (Optical Society of America, Washington, DC, 1988), pp. 76–78.

Itoh, K.

K. Itoh, Y. Ohtsuka, “Fourier-Transform Spectral Imaging: Retrieval of Source Information from 3-D Spatial Coherence,” J. Opt. Soc. Am. A 3, 94–99 (1986).
[CrossRef]

K. Itoh, T. Inoue, Y. Ichioka, “Interferometric Spectral Imaging in the Visible and Near-Infrared Regions,” in Technical Digest, Topical Meeting on Space Optics for Astronomy and Earth and Planetary Remote Sensing (Optical Society of America, Washington, DC, 1988), pp. 76–78.

K. Itoh, T. Inoue, Y. Ichioka, “Fourier-Transform Spectral Imaging with Variable Magnification,” in Proceedings, Fourteenth Congress of ICO, H. H. Arsenault, Ed. (Publication Committee of ICO, Quebec, Canada, 1987), pp. 519–520.

K. Itoh, Y. Ohtsuka, “Interferometric Spectral Imaging,” in Conference Digest of ICO-13 on Optics in Modern Science and Technology (Organization Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.

Lang, S. W.

S. W. Lang, T. L. Marzetta, “Image Spectral Estimation,” in Digital Image Processing, M. P. Ekstrom, Ed. (Academic, Orlando, FL, 1984), Chap. 6.

Lohmann, A. W.

Mariotti, J. M.

J. M. Mariotti, S. T. Ridgway, “Double Fourier Spatio-Spectral Interferometry: Combining High Spectral and High Spatial Resolution in the Near Infrared,” Astron. Astrophys. 195, 350–363 (1988).

Marzetta, T. L.

S. W. Lang, T. L. Marzetta, “Image Spectral Estimation,” in Digital Image Processing, M. P. Ekstrom, Ed. (Academic, Orlando, FL, 1984), Chap. 6.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.

Ohtsuka, Y.

K. Itoh, Y. Ohtsuka, “Fourier-Transform Spectral Imaging: Retrieval of Source Information from 3-D Spatial Coherence,” J. Opt. Soc. Am. A 3, 94–99 (1986).
[CrossRef]

K. Itoh, Y. Ohtsuka, “Interferometric Spectral Imaging,” in Conference Digest of ICO-13 on Optics in Modern Science and Technology (Organization Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.

Ridgway, S. T.

J. M. Mariotti, S. T. Ridgway, “Double Fourier Spatio-Spectral Interferometry: Combining High Spectral and High Spatial Resolution in the Near Infrared,” Astron. Astrophys. 195, 350–363 (1988).

Roddier, C.

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Roddier, F.

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Sakai, H.

G. A. Vanasse, H. Sakai, “Fourier Spectroscopy,” Prog. Opt. 6, 261–327 (1967).

Vanasse, G. A.

G. A. Vanasse, H. Sakai, “Fourier Spectroscopy,” Prog. Opt. 6, 261–327 (1967).

Wolf, E.

Yaglom, A. M.

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, NJ, 1962), Chap. 3.

Appl. Opt.

Astron. Astrophys.

J. M. Mariotti, S. T. Ridgway, “Double Fourier Spatio-Spectral Interferometry: Combining High Spectral and High Spatial Resolution in the Near Infrared,” Astron. Astrophys. 195, 350–363 (1988).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Prog. Opt.

G. A. Vanasse, H. Sakai, “Fourier Spectroscopy,” Prog. Opt. 6, 261–327 (1967).

Other

A. M. Yaglom, An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, NJ, 1962), Chap. 3.

S. W. Lang, T. L. Marzetta, “Image Spectral Estimation,” in Digital Image Processing, M. P. Ekstrom, Ed. (Academic, Orlando, FL, 1984), Chap. 6.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), Chap. 10.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.

J. W. Goodman, Introduction to Fourier Optics (Wiley, New York, 1968), Chap. 2.

G. Vane, Ed., imaging Spectroscopy II, Proc. Soc. Photo-Opt. Instrum. Eng.834 (1988).

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.

K. Itoh, Y. Ohtsuka, “Interferometric Spectral Imaging,” in Conference Digest of ICO-13 on Optics in Modern Science and Technology (Organization Committee of ICO-13, Sapporo, Japan, 1984), pp. 600–601.

K. Itoh, T. Inoue, Y. Ichioka, “Fourier-Transform Spectral Imaging with Variable Magnification,” in Proceedings, Fourteenth Congress of ICO, H. H. Arsenault, Ed. (Publication Committee of ICO, Quebec, Canada, 1987), pp. 519–520.

K. Itoh, T. Inoue, Y. Ichioka, “Interferometric Spectral Imaging in the Visible and Near-Infrared Regions,” in Technical Digest, Topical Meeting on Space Optics for Astronomy and Earth and Planetary Remote Sensing (Optical Society of America, Washington, DC, 1988), pp. 76–78.

C. Roddier, F. Roddier, “Imaging with a Coherence Interferometer in Optical Astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, Ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Ref. 5, Chaps. 1 and 2.

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Figures (10)

Fig. 1
Fig. 1

Rotational shear volume interferometer. Rotational shear is introduced by tilting the two right angle prisms around the optical axis. Longitudinal shear is created by shifting one of the prisms along the optical axis.

Fig. 2
Fig. 2

Picture of the rotational shear volume interferometer. The two right angle prisms are rotated by 0.6° around the optical axis. The IR vidicon camera (at the left of the interferometer) is focused on the apexes of the prisms.

Fig. 3
Fig. 3

Object is a live flower. The central gray region is red and is surrounded by a white area. Green leaves are visible near the flower.

Fig. 4
Fig. 4

Series of interference patterns detected by an image sensor (CCD camera). Each pattern has a different longitudinal shear. The image sensor is focused on the detection plane that includes the apexes of the prisms.

Fig. 5
Fig. 5

Slices of the spectral image of the live flower shown in Fig. 3. Cross sections perpendicular to the kz axis are shown. The number attached to each cross section denotes the wavelength corresponding to the kz component.

Fig. 6
Fig. 6

Object is a postage stamp.

Fig. 7
Fig. 7

Slices of the spectral image of the postage stamp shown in Fig. 6. Cross sections perpendicular to the kz axis are shown. The number attached to each cross section denotes the wavelength corresponding to the kz component.

Fig. 8
Fig. 8

Spectra extracted from the spectral image of the postage stamp shown in Fig. 7. Each spectrum stands for a particular location in the object of a distinct color.

Fig. 9
Fig. 9

Object under illumination of visible light (solder iron tip).

Fig. 10
Fig. 10

Slice of an infrared spectral image of the solder iron tip shown in Fig. 9. Cross sections perpendicular to the kz axis are shown. The number attached to each cross section denotes the wavelength corresponding to the kz component.

Equations (15)

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J A ( r ¯ ) = V A ( r ¯ + r ¯ ) V A * ( r ¯ ) ,
J A ( r ¯ ) = K G A ( k ¯ ) exp ( i k ¯ · r ¯ ) d k ¯ ,
V A ( r ¯ ) = K a A ( k ¯ ) exp ( i k ¯ · r ¯ ) d k ¯ ,
J A ( r ¯ 1 , r ¯ 2 ) = V A ( r ¯ 1 ) V A * ( r ¯ 2 ) = K a A ( k ¯ 1 ) a A * ( k ¯ 2 ) exp [ i ( k ¯ 1 - k ¯ 2 ) · r ¯ + / 2 + ( k ¯ 1 + k ¯ 2 ) · r ¯ / 2 ] d k ¯ 1 d k ¯ 2 ,
a A ( k ¯ 1 ) a A * ( k ¯ 2 ) = G A ( k ¯ 1 ) δ ( k ¯ 1 - k ¯ 2 ) .
I A ( x , y , d ) = J A ( r ¯ θ ) + J A * ( r ¯ θ ) + ( const bias ) ,
r ¯ θ = 2 sin θ ( - y e ¯ x + x e ¯ y ) + 2 d e ¯ z .
δ k x = δ k y = π / ( L 1 sin θ ) ,
δ k z = π / L 3 .
Δ k x = Δ k y = π / ( l 1 sin θ ) ,
Δ k z = π / l 3 .
Δ ϕ = λ / ( 2 l 1 sin θ )
ρ 1 = N t / 2 .
ρ 2 = ρ 1 ( sin θ 1 / sin θ ) 2 .
ρ 3 = ρ 1 [ sin 2 θ 1 / ( sin θ sin θ 2 ) ] .

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