Abstract

An imager and a spectrometric imager, which achieve multiplexing by the use of binary optical encoding masks, have been built and tested. The masks are based on orthogonal, pseudorandom digital codes derived from Hadamard matrices. The spatial (and/or spectral) data are therefore obtained in the form of a Hadamard transform of the spatial (and/or spectral) scene; computer algorithms are used to decode the data and reconstruct images of the original scene. The hardware, algorithms processing and display facility are described. A number of spatial and spatial/spectral images, obtained in the laboratory, are presented. We present an analysis of the situations for which the multiplex advantage may be gained and of the limitations of the technique. Potential applications of the spectrometric imager are discussed. The spectrometric imager is covered by U.S. Patent 3,720,469 assigned to Spectral Imaging Inc., Concord, Mass.

© 1976 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. E. D. Nelson, M. L. Fredman, J. Opt. Soc. Am. 60, 1664 (1971).
    [Crossref]
  8. N. J. A. Sloane, M. Harwit, “Masks for Hadamard Transform Optics and Weighing Designs,” Appl. Opt., to be published (1976).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]

1974 (2)

1972 (1)

1971 (4)

1970 (1)

1969 (2)

1968 (4)

1967 (1)

T. Namioka, M. Seya, Sci. Light 16, 169 (1967).

1964 (1)

1961 (1)

1949 (1)

Allemand, C. D.

Aspinall, D.

Baumert, L. D.

L. D. Baumert, in Digital Communications with Space Applications, S. W. Golomb, Ed. (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 17–32, 47–64, 165–195.

Briotta, D. A.

Decker, J. A.

Droppleman, LeA.

Fine, T.

Fredman, M. L.

Golay, M. J. E.

Gottlieb, P.

P. Gottlieb, IEEE Trans. Inf. Theory IT-14, 428 (1968).
[Crossref]

Grainger, J. F.

Hanel, R. A.

Harwit, M.

Ibbett, R. N.

King, L. W.

Megill, L. R.

Murty, M. V. R. K.

Namioka, T.

T. Namioka, M. Seya, Sci. Light 16, 169 (1967).

Nelson, E. D.

Phillips, P. G.

Reader, J.

Seya, M.

T. Namioka, M. Seya, Sci. Light 16, 169 (1967).

Shafer, A. B.

Sloane, N. J. A.

Stewart, J. E.

J. E. Stewart, Infrared Spectroscopy (Dekker, New York, 1970); this is a generally good reference on ir spectroscopy, including the design of spectrograph optical systems.

Wark, D. Q.

Appl. Opt. (9)

IEEE Trans. Inf. Theory (1)

P. Gottlieb, IEEE Trans. Inf. Theory IT-14, 428 (1968).
[Crossref]

J. Opt. Soc. Am. (6)

Rep. Prog. Opt. (1)

M. Harwit, J. A. Decker, Rep. Prog. Opt. 12, 102 (1974).

Sci. Light (1)

T. Namioka, M. Seya, Sci. Light 16, 169 (1967).

Other (3)

L. D. Baumert, in Digital Communications with Space Applications, S. W. Golomb, Ed. (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 17–32, 47–64, 165–195.

N. J. A. Sloane, M. Harwit, “Masks for Hadamard Transform Optics and Weighing Designs,” Appl. Opt., to be published (1976).
[Crossref]

J. E. Stewart, Infrared Spectroscopy (Dekker, New York, 1970); this is a generally good reference on ir spectroscopy, including the design of spectrograph optical systems.

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Figures (10)

Fig. 1
Fig. 1

Block diagram of the Hadamard transform imaging spectrometer system (For a full description see text).

Fig. 2
Fig. 2

(a) Drawing of the interior and (b) photograph showing the external view of the imaging spectrometer seen from opposite sides. The photograph shows the spatial encoding assembly and objective lens.

Fig. 3
Fig. 3

Entrance mask and field stop used both for the imager and the imaging spectrometer.

Fig. 4
Fig. 4

Imaging spectrometer exit mask and field stop.

Fig. 5
Fig. 5

Illustration of the overlap of spatial/spectral information (for a full discussion see text).

Fig. 6
Fig. 6

Photographs of the Hadamard transform imager, showing two views.

Fig. 7
Fig. 7

Optical path within the imager.

Fig. 8
Fig. 8

Twelve frames showing a scene containing a flame and a small (nearly point source) blackbody (see bright spot in upper left frame). The frames represent successive wavelength increments around the 4.3-μm carbon dioxide band. Outside the band, the flame emits very little light. Within the band its emission dominates that of the blackbody.

Fig. 9
Fig. 9

Display showing the ir image of the scene shown in Fig. 8, together with a gray scale and the spectrum of a point on the flame. The selected point is indicated by the cursor spot on the image. The wavelength extremes are 3.06 μm and 6.33 μm, and these two numbers are shown on the lower right of the display.

Fig. 10
Fig. 10

Thermal emission of a hand seen by the imager. For added clarity this image has been integrated over sixteen frame times, each frame lasting 25 msec. Note the wrist watch.

Tables (2)

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Table I Imaging Spectrometer Design Specifications

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Table II Signal-to-Noise Ratio Gain Relative to Single Element Scanning for n Spectral and m Spatial Elementsa

Equations (6)

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d β d α = - cos α cos β ,
λ = a ( sin α + sin β ) ,
element size = 0.1778 mm ( 0.960 ) ( 1.075 ) = 0.1723 mm .
exp ( - T / τ ) = 2 1 / 12 ,
τ T / 8.
f = 1 / ( 2 π τ ) .

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