Abstract

An advanced coded imaging system is described, and some results of phantom experiments are presented. The advanced method uses a pair of coherent codes (+1 and −1 codes) and has many advantages compared with conventional ones. One of the greatest advantages is that there are no sidelobes in the focal plane and only a few in other planes. Therefore, when an object can be regarded as two-dimensional, it is perfectly reconstructed with high detecting efficiency, and this is successfully simulated by a thyroid phantom with 99mTc. Moreover, this system has an ability to reconstruct tomograms, which is also shown by using ring phantoms piled on one another with some cold spots in their shells. From these experimental results it may be concluded that the new system is useful for practical applications, for example, to nuclear medicine.

© 1983 Optical Society of America

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  1. H. H. Barrett, F. A. Horrigan, Appl. Opt. 12, 2686 (1973).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
    [CrossRef]

1981 (1)

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
[CrossRef]

1978 (2)

C. Chou, H. H. Barrett, Opt. Lett. 3, 187 (1978).
[CrossRef] [PubMed]

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 27, 339 (1978).
[CrossRef]

1977 (2)

D. Rosenfeld, A. Macovski, IEEE Trans. Nucl. Sci. NS-24, 570 (1977).
[CrossRef]

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

1974 (2)

1973 (1)

1969 (1)

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Akcasu, Z.

Barrett, H. H.

Brown, C.

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

Chou, C.

Hayat, G. S.

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Honda, T.

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
[CrossRef]

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 27, 339 (1978).
[CrossRef]

Hoover, R. B.

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Horrigan, F. A.

Klotz, E.

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Knoll, G. F.

Linde, R.

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Macovski, A.

D. Rosenfeld, A. Macovski, IEEE Trans. Nucl. Sci. NS-24, 570 (1977).
[CrossRef]

May, R. S.

Ohyama, N.

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
[CrossRef]

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 27, 339 (1978).
[CrossRef]

N. Ohyama, “New Coded Aperture Methods for Reconstructing Tomograms and Applications to Nuclear Medicine,” Ph.D. Thesis, Imaging Science and Engineering Laboratory, Tokyo Institute of Technology (1982), p. 51.

Rabe, G.

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Rosenfeld, D.

D. Rosenfeld, A. Macovski, IEEE Trans. Nucl. Sci. NS-24, 570 (1977).
[CrossRef]

Stroke, G. W.

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Tiemens, U.

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Tsujiuchi, J.

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
[CrossRef]

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 27, 339 (1978).
[CrossRef]

Underwood, J. H.

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Weiss, H.

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Nucl. Sci. (1)

D. Rosenfeld, A. Macovski, IEEE Trans. Nucl. Sci. NS-24, 570 (1977).
[CrossRef]

J. Appl. Phys. (1)

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

Opt. Acta (1)

H. Weiss, E. Klotz, R. Linde, G. Rabe, U. Tiemens, Opt. Acta 24, 305 (1977).
[CrossRef]

Opt. Commun. (3)

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 27, 339 (1978).
[CrossRef]

N. Ohyama, T. Honda, J. Tsujiuchi, Opt. Commun. 36, 434 (1981).
[CrossRef]

G. W. Stroke, G. S. Hayat, R. B. Hoover, J. H. Underwood, Opt. Commun. 1, 138 (1969).
[CrossRef]

Opt. Lett. (1)

Other (1)

N. Ohyama, “New Coded Aperture Methods for Reconstructing Tomograms and Applications to Nuclear Medicine,” Ph.D. Thesis, Imaging Science and Engineering Laboratory, Tokyo Institute of Technology (1982), p. 51.

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of system operation. This system uses four kinds of shutter to realize a pair of coherent codes.

Fig. 2
Fig. 2

(a) Basic pair of 2 × 1 codes; (b) their autocorrelations. An upward arrow is a plus pinhole, and a downward one is a minus one

Fig. 3
Fig. 3

(a) Pair of 2 × 2 codes; (b) their matrix expressions; (c) their autocorrelations.

Fig. 4
Fig. 4

(a) Pair of 4 × 4 codes used in this experiment and their derivations; (b) their autocorrelations. Notice that sidelobes are completely cleared away by adding them to each other.

Fig. 5
Fig. 5

Multipinhole collimator and aperture. This aperture has sixteen pinholes of 3-mm diam arranged like a square grid at 15-mm intervals. On this aperture is set a shutter plate to close some pinholes according to the codes.

Fig. 6
Fig. 6

(a) Pair of recorded images of a thyroid phantom with 99mTc. (b) Correlated images by corresponding codes, P and G. There still remains a strong ghost caused by the insuppressible sidelobes.

Fig. 7
Fig. 7

Multipinhole images of the thyroid phantom reconstructed in different conditions: (a) energy gate off, without scatter plate; (b) energy gate on, without scatter plate; (c) energy gate off, with scatter plate; (d) energy gate on, with scatter plate. Total counts of the contributed events to reconstruction are, respectively, (a) 349,171, (b) 274,296, (c) 206,148, (d) 127,676.

Fig. 8
Fig. 8

Single-pinhole images recorded under the same conditions as shown in Fig. 7: (a) energy gate off, without scatter plate; (b) energy gate on, without scatter plate; (c) energy gate off, with scatter plate; (d) energy gate on, with scatter plate. Total counts of each image are, respectively, (a) 60,000, (b) 40,643, (c) 29,560, (d) 17,920.

Fig. 9
Fig. 9

Sampled areas for evaluating the deviations and SNRs.

Fig. 10
Fig. 10

Experimental geometry for tomogram reconstruction and shapes of ring phantoms on the detector.

Fig. 11
Fig. 11

Obtained records of the ring phantoms coded by P and G. Total recording time is 200 sec, and detected events are ∼4,890,000.

Fig. 12
Fig. 12

Initial guesses of seven-layer reconstruction. These images are not good enough to recognize the regions of interest.

Fig. 13
Fig. 13

Reconstructed images after five iterations. Images become much better than the initials, so we can easily find the defects (cold spots) of ring phantoms.

Tables (1)

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Table 1 Signal-to-Noise Ratios of Obtained Images by Multipinhole and Single-pinhole Collimator

Equations (22)

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

R = O * P ,
R = i = 1 n O i * P i ,
O k = R P k = i = 1 n O i * O i P k ,
P k P k = δ
P k P m = 0 ( k m ) ,
P P + G G = 2 N δ ,
P = δ ( x a ) + δ ( x + a ) ;
G = δ ( x a ) + δ ( x + a ) .
P = P + G ,
G = P G ,
P P = P P + G G + P G + G P ,
G G = P P + G G P G G P .
P P + G G = 2 ( P P + G G ) .
P P + G G = 4 N δ .
P k P m + G k G m = 0 ( k m ) .
O k 0 = R 1 P k + R 2 G k = i = 1 n O i * ( P i P k + G i G k ) ,
O k 0 = O k + i = 1 n O i ʹ * ( P i P k + G i G k ) .
O k 0 = O k + g k 0 .
R 1 = i = 1 n g i 0 * P i ;
R 2 = i = 1 n g i 0 G i .
C k 0 = g k 0 + i = 1 n g i 0 ʹ * ( P i P k + G i G k ) = g k 0 + g k 1 .
O k 1 = O k 0 C k 0 = O k g k 1 .

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