Abstract

Interferometric tomography in the presence of an opaque object has been investigated. In principle the developed iterative algorithm does not need to augment the missing information. It is based on the successive reconstruction of the difference field, the difference between the object field to be reconstructed and its estimate, in the defined region only. The application of the algorithm results in stable convergence.

© 1989 Optical Society of America

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References

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  1. D. W. Sweeney, C. M. Vest, Int. J. Heat Mass Transfer 17, 1443 (1974).
    [CrossRef]
  2. H. Tan, D. Modarress, Opt. Eng. 24, 435 (1985).
  3. S. Cha, Opt. Eng. 27, 557 (1988).
  4. B. P. Medoff, W. R. Brody, M. Nassi, A. Macovski, J. Opt. Soc. Am. 73, 1493 (1983).
    [CrossRef]
  5. G. N. Ramachandran, A. V. Lakshminarayanan, Indian J. Pure Appl. Phys. 9, 997 (1971).
  6. P. B. Heffernan, R. A. Robb, Appl. Opt. 24, 4105 (1985).
    [CrossRef] [PubMed]
  7. C. M. Vest, I. Prikryl, Appl. Opt. 23, 2433 (1984).
    [CrossRef] [PubMed]
  8. S. Darenfed, P. V. Farrell, Opt. Lett. 10, 203 (1985).
    [CrossRef] [PubMed]
  9. T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
    [CrossRef]
  10. S. Cha, Ph.D. thesis (University of Michigan, Ann Arbor, Mich., 1980).
  11. R. M. Lewitt, R. H. T. Bates, Optik 50, 269 (1978).
  12. J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
    [CrossRef]
  13. R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).
  14. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  15. L. A. Shepp, B. F. Logan, IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

1988 (1)

S. Cha, Opt. Eng. 27, 557 (1988).

1985 (3)

1984 (1)

1983 (1)

1982 (1)

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

1978 (1)

R. M. Lewitt, R. H. T. Bates, Optik 50, 269 (1978).

1975 (1)

T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
[CrossRef]

1974 (2)

L. A. Shepp, B. F. Logan, IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

D. W. Sweeney, C. M. Vest, Int. J. Heat Mass Transfer 17, 1443 (1974).
[CrossRef]

1971 (1)

G. N. Ramachandran, A. V. Lakshminarayanan, Indian J. Pure Appl. Phys. 9, 997 (1971).

Bates, R. H. T.

R. M. Lewitt, R. H. T. Bates, Optik 50, 269 (1978).

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Brody, W. R.

Cha, S.

S. Cha, Opt. Eng. 27, 557 (1988).

S. Cha, Ph.D. thesis (University of Michigan, Ann Arbor, Mich., 1980).

Choi, J. S.

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

Darenfed, S.

Farrell, P. V.

Gonzalez, R. C.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Heffernan, P. B.

Lakshminarayanan, A. V.

G. N. Ramachandran, A. V. Lakshminarayanan, Indian J. Pure Appl. Phys. 9, 997 (1971).

Lewitt, R. M.

R. M. Lewitt, R. H. T. Bates, Optik 50, 269 (1978).

Logan, B. F.

L. A. Shepp, B. F. Logan, IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

Macovski, A.

Medoff, B. P.

Modarress, D.

H. Tan, D. Modarress, Opt. Eng. 24, 435 (1985).

Nakajima, M.

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

Nassi, M.

Ogawa, K.

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

Prikryl, I.

Ramachandran, G. N.

G. N. Ramachandran, A. V. Lakshminarayanan, Indian J. Pure Appl. Phys. 9, 997 (1971).

Rapsdale, W. C.

T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
[CrossRef]

Robb, R. A.

Shepp, L. A.

L. A. Shepp, B. F. Logan, IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

Spring, W. C.

T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
[CrossRef]

Sweeney, D. W.

D. W. Sweeney, C. M. Vest, Int. J. Heat Mass Transfer 17, 1443 (1974).
[CrossRef]

Tan, H.

H. Tan, D. Modarress, Opt. Eng. 24, 435 (1985).

Vest, C. M.

C. M. Vest, I. Prikryl, Appl. Opt. 23, 2433 (1984).
[CrossRef] [PubMed]

D. W. Sweeney, C. M. Vest, Int. J. Heat Mass Transfer 17, 1443 (1974).
[CrossRef]

Wintz, P.

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

Yata, S.

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

Zien, T. F.

T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
[CrossRef]

AIAA J. (1)

T. F. Zien, W. C. Rapsdale, W. C. Spring, AIAA J. 13, 841 (1975).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Nucl. Sci. (1)

L. A. Shepp, B. F. Logan, IEEE Trans. Nucl. Sci. NS-21, 21 (1974).

IEEE Trans. Sonics Ultrason. (1)

J. S. Choi, K. Ogawa, M. Nakajima, S. Yata, IEEE Trans. Sonics Ultrason. SU-29, 143 (1982).
[CrossRef]

Indian J. Pure Appl. Phys. (1)

G. N. Ramachandran, A. V. Lakshminarayanan, Indian J. Pure Appl. Phys. 9, 997 (1971).

Int. J. Heat Mass Transfer (1)

D. W. Sweeney, C. M. Vest, Int. J. Heat Mass Transfer 17, 1443 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

H. Tan, D. Modarress, Opt. Eng. 24, 435 (1985).

S. Cha, Opt. Eng. 27, 557 (1988).

Opt. Lett. (1)

Optik (1)

R. M. Lewitt, R. H. T. Bates, Optik 50, 269 (1978).

Other (3)

R. C. Gonzalez, P. Wintz, Digital Image Processing (Addison-Wesley, Reading, Mass., 1977).

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

S. Cha, Ph.D. thesis (University of Michigan, Ann Arbor, Mich., 1980).

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Figures (4)

Fig. 1
Fig. 1

Projection of an object field with an opaque object.

Fig. 2
Fig. 2

Profile of the test object field.

Fig. 3
Fig. 3

Reconstruction errors for two different iteration methods.

Fig. 4
Fig. 4

Profile of the reconstructed field after 12 iterations.

Equations (4)

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f r ( x , y ) = h ( x , y ) * * f ( x , y ) ,
E = - - f ( x , y ) - f r ( x , y ) 2 d x d y = - - [ 1 - H ( u , v ) ] F ( u , v ) 2 d u d v ,
E = - - [ 1 - H ( u , v ) ] [ F ( u , v ) - F a ( u , v ) ] 2 d u d v .
f ( x , y ) = 3.0 exp { - 6 [ ( x - 0.6 ) 2 + y 2 ] 1 - ( x 2 + y 2 ) } + 1.5 exp { - 6 [ ( x + 0.6 ) 2 + y 2 ] 1 - ( x 2 + y 2 ) } + 3.0 exp { - 6 [ x 2 + ( y - 0.6 ) 2 ] 1 - ( x 2 + y 2 ) } + 1.5 exp { - 6 [ x 2 + ( y + 0.6 ) 2 ] 1 - ( x 2 + y 2 ) } .

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