Abstract

A common problem associated with x-ray imaging using coded apertures is the reconstruction of low-intensity extended objects. In the decoding of such objects, the overlapping images from the multiple pinholes give rise to noise cross talk and, in many cases, also to signal cross talk. In this paper, we propose an alternate approach based on the principle used in our earlier laboratory device for the real-time viewing of x-ray objects. It is shown that with this approach, the nonoverlapping redundant array, the sidelobes in the point spread function are not eliminated but merely displaced through a suitable choice of geometry. In this manner, the sidelobes no longer contribute to the background in the vicinity of a reconstructed image, and both signal and noise cross talks are completely eliminated. It may now be possible to reconstruct extended x-ray objects in 3-D by simple optical correlation and tomographically by a computer.

© 1983 Optical Society of America

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  1. L. Mertz, N. O. Young, in Proceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London, 1961).
  2. R. H. Dicke, Astrophys. J. 153, L101 (1968).
    [CrossRef]
  3. J. G. Ables, Proc. Astron. Soc. Aust. 1, No. 4, 172 (1968).
  4. H. H. Barrett, F. A. Horrigan, Appl. Opt. 12, 2686 (1973).
    [CrossRef] [PubMed]
  5. T. M. Palmieri, Astrophys. Space Sci. 26, 431 (1974); Astrophys. Space Sci. 28, 277 (1974).
    [CrossRef]
  6. C. Brown, J. Appl. Phys. 45, 1806 (1974).
    [CrossRef]
  7. B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).
  8. R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
    [CrossRef]
  9. F. Gunsen, B. Polychronopulos, Mon. Not. R. Astron. Soc. 177, 485 (1976).
  10. L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).
  11. L. T. Chang, Ph.D. Thesis, U. California, Berkeley (1976).
  12. E. E. Fenimore, T. M. Cannon, Appl. Opt. 17, 337 (1978); Appl. Opt. 18, 1052 (1979).
    [CrossRef] [PubMed]
  13. E. E. Fenimore, Appl. Opt. 17, 3562 (1978).
    [CrossRef] [PubMed]
  14. E. E. Fenimore, Appl. Opt. 19, 2465 (1980).
    [CrossRef] [PubMed]
  15. E. E. Fenimore, T. M. Cannon, Appl. Opt. 20, 1858 (1981).
    [CrossRef] [PubMed]
  16. E. E. Fenimore, G. S. Weston, Appl. Opt. 20, 3058 (1981).
    [CrossRef] [PubMed]
  17. R. G. Simpson, H. H. Barrett, in Imaging for Medicine, Vol. 1, Nudelman, D. D. Patton, Eds. (Plenum, New York, 1980), Chap. 8.
  18. L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).
  19. L. Yin, J. I. Trombka, S. M. Seltzer, Appl. Opt. 19, 2952 (1980).
    [CrossRef] [PubMed]
  20. R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).
  21. L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
    [CrossRef]
  22. L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 172, 471 (1980).
    [CrossRef]

1981 (4)

E. E. Fenimore, T. M. Cannon, Appl. Opt. 20, 1858 (1981).
[CrossRef] [PubMed]

E. E. Fenimore, G. S. Weston, Appl. Opt. 20, 3058 (1981).
[CrossRef] [PubMed]

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).

1980 (3)

1979 (1)

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
[CrossRef]

1978 (2)

1976 (2)

F. Gunsen, B. Polychronopulos, Mon. Not. R. Astron. Soc. 177, 485 (1976).

L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).

1975 (1)

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

1974 (3)

T. M. Palmieri, Astrophys. Space Sci. 26, 431 (1974); Astrophys. Space Sci. 28, 277 (1974).
[CrossRef]

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

1973 (1)

1968 (2)

R. H. Dicke, Astrophys. J. 153, L101 (1968).
[CrossRef]

J. G. Ables, Proc. Astron. Soc. Aust. 1, No. 4, 172 (1968).

Ables, J. G.

J. G. Ables, Proc. Astron. Soc. Aust. 1, No. 4, 172 (1968).

Barrett, H. H.

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

H. H. Barrett, F. A. Horrigan, Appl. Opt. 12, 2686 (1973).
[CrossRef] [PubMed]

R. G. Simpson, H. H. Barrett, in Imaging for Medicine, Vol. 1, Nudelman, D. D. Patton, Eds. (Plenum, New York, 1980), Chap. 8.

Bielefeld, M.

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

Brown, C.

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

Brown, D. G.

R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).

Cannon, T. M.

Chang, L. T.

L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

L. T. Chang, Ph.D. Thesis, U. California, Berkeley (1976).

Dicke, R. H.

R. H. Dicke, Astrophys. J. 153, L101 (1968).
[CrossRef]

Fenimore, E. E.

Fisher, H. D.

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

Gunsen, F.

F. Gunsen, B. Polychronopulos, Mon. Not. R. Astron. Soc. 177, 485 (1976).

Horrigan, F. A.

MacDonald, B.

L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

Mertz, L.

L. Mertz, N. O. Young, in Proceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London, 1961).

Metz, E. C.

R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).

Palmieri, T. M.

T. M. Palmieri, Astrophys. Space Sci. 26, 431 (1974); Astrophys. Space Sci. 28, 277 (1974).
[CrossRef]

Perez-Mendez, V.

L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

Polychronopulos, B.

F. Gunsen, B. Polychronopulos, Mon. Not. R. Astron. Soc. 177, 485 (1976).

Schmadebeck, R.

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

Seltzer, S.

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 172, 471 (1980).
[CrossRef]

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
[CrossRef]

Seltzer, S. M.

Shiraishi, L.

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

Simpson, R. G.

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

R. G. Simpson, H. H. Barrett, in Imaging for Medicine, Vol. 1, Nudelman, D. D. Patton, Eds. (Plenum, New York, 1980), Chap. 8.

Suback, J. A.

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

Trombka, J.

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 172, 471 (1980).
[CrossRef]

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
[CrossRef]

Trombka, J. I.

Wagner, R. F.

R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).

Weston, G. S.

Yin, L.

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

L. Yin, J. I. Trombka, S. M. Seltzer, Appl. Opt. 19, 2952 (1980).
[CrossRef] [PubMed]

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 172, 471 (1980).
[CrossRef]

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
[CrossRef]

Young, N. O.

L. Mertz, N. O. Young, in Proceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London, 1961).

Appl. Opt. (7)

Astrophys. J. (1)

R. H. Dicke, Astrophys. J. 153, L101 (1968).
[CrossRef]

Astrophys. Space Sci. (1)

T. M. Palmieri, Astrophys. Space Sci. 26, 431 (1974); Astrophys. Space Sci. 28, 277 (1974).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

B. MacDonald, L. T. Chang, V. Perez-Mendez, L. Shiraishi, IEEE Trans. Nucl. Sci. NS-21, 672 (1974).

J. Appl. Phys. (1)

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

F. Gunsen, B. Polychronopulos, Mon. Not. R. Astron. Soc. 177, 485 (1976).

Nucl. Instrum. Methods (2)

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 158, 175 (1979).
[CrossRef]

L. Yin, J. Trombka, S. Seltzer, Nucl. Instrum. Methods 172, 471 (1980).
[CrossRef]

Opt. Eng. (1)

R. G. Simpson, H. H. Barrett, J. A. Suback, H. D. Fisher, Opt. Eng. 14, 490 (1975).
[CrossRef]

Proc. Astron. Soc. Aust. (1)

J. G. Ables, Proc. Astron. Soc. Aust. 1, No. 4, 172 (1968).

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

L. T. Chang, B. MacDonald, V. Perez-Mendez, Proc. Soc. Photo-Opt. Instrum. Eng. 89, 9 (1976).

R. F. Wagner, D. G. Brown, E. C. Metz, Proc. Soc. Photo-Opt. Instrum. Eng. 314, 72 (1981).

L. Yin, J. Trombka, R. Schmadebeck, S. Seltzer, M. Bielefeld, Proc. Soc. Photo-Opt. Instrum. Eng. 268, 97 (1981).

Other (3)

L. Mertz, N. O. Young, in Proceedings, International Conference on Optical Instruments and Techniques, K. J. Habell, Ed. (Chapman & Hall, London, 1961).

R. G. Simpson, H. H. Barrett, in Imaging for Medicine, Vol. 1, Nudelman, D. D. Patton, Eds. (Plenum, New York, 1980), Chap. 8.

L. T. Chang, Ph.D. Thesis, U. California, Berkeley (1976).

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Figures (6)

Fig. 1
Fig. 1

Simplified multiple-pinhole system with nonoverlapping images. An aperture screen S consists of three pinholes P1,P2,P3 with different separations. A,B are point x-ray sources. Detector D is an image intensifier with unity magnification, whose visible-light output is viewed through an identical screen S placed in registration at the same distance from the detector output as the input screen is from D. That is, optical correlation is used in the reconstruction method. Light rays a1, b1, etc. going through neighboring pinholes in the reconstruction process give rise to a distributed background in the image plane I in addition to the images of A and B. Here the separations between S and D, and between pinholes, are chosen carefully so that the background a and b values are displaced from the vicinity of the reconstructed images of A and B. In this way, if the space between A and B is filled with point sources to make AB an extended x-ray object, and a1b1, a2b2, a3b3 are the nonoverlapping mini-images of the object, there would be neither signal cross talk nor noise cross talk in the reconstructed image AB.

Fig. 2
Fig. 2

Schematic sketch illustrating the NORA principle of 3-D imaging of an extended x-ray object. The object ABC is reproduced as a real but pseudoscopic image ABC′ to the viewer.

Fig. 3
Fig. 3

Schematic sketch illustrating the method to present an orthoscopic virtual imageABC″ of the x-ray object ABC to the viewer.

Fig. 4
Fig. 4

Laboratory model of real-time 3-D viewing device for x-ray objects using the NORA design.

Fig. 5
Fig. 5

Square array of 121 mini-images of a large trigonal pyramid generated by a computer for orthoscopic analog optical reconstruction.

Fig. 6
Fig. 6

Reconstructed 3-D images of a trigonal pyramid through a screen of 121 square array of pinholes using a negative transparency of the mini-images shown in Fig. 5 mounted on a light box. (A) Frontal (normal) view of the central reconstructed image. The apex of the pyramid is toward the viewer. (B) Central image as viewed from slightly right of normal. Because of parallax, the apex has shifted leftward relative to the triangular base. (C) First-order image as viewed from ~50° left of normal.

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