Abstract

A holographic technique by which two dissimilar optical fields can be subtracted to yield only their difference is presented. The principle underlying this technique is that of optical interference between a holographically reconstructed field and a direct real-time one. Experimental verification is presented for the three cases of image-plane, fourier-transform, and Fresnel side-band holograms. Also considered is the application of this concept to change detection between photographic transparencies of some scene taken at different times.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Vander Lugt, IEEE Trans. Inform. Theory. IT-10, 139 (1964).
    [CrossRef]
  2. K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
    [CrossRef]
  3. M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).
  4. P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Amer. 46, 825 (1956).
    [CrossRef]
  5. W. T. Cathey, J. G. Doidge, J. Opt. Soc. Amer. 56, 1139 (1966).
    [CrossRef]
  6. D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
    [CrossRef]
  7. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press, New York, 1966), p. 90.
  8. L. F. Collins, Appl. Opt. 7, 203 (1968).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 201.
  10. A. W. Lohmann, “The Space-Bandwidth Product,” IBM Research Paper RJ-438 (IBM San Jose Res. Lab., San Jose, Calif., 9May1967).
  11. G. B. Brandt, Appl. Opt. 8, 1421 (1969).
    [CrossRef] [PubMed]
  12. E. N. Leith, J. Upatnieks, Appl. Opt. 7, 2085 (1968).
    [CrossRef] [PubMed]
  13. A. A. Friesem, J. L. Walker, Appl. Opt. 8, 1504 (1969).
    [CrossRef] [PubMed]
  14. K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1693 (1970).

1970

K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1693 (1970).

1969

1968

1966

W. T. Cathey, J. G. Doidge, J. Opt. Soc. Amer. 56, 1139 (1966).
[CrossRef]

1965

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

1964

A. Vander Lugt, IEEE Trans. Inform. Theory. IT-10, 139 (1964).
[CrossRef]

1956

P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Amer. 46, 825 (1956).
[CrossRef]

Brandt, G. B.

Bromley, K.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).

Brumm, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Bryant, J. F.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).

Cathey, W. T.

W. T. Cathey, J. G. Doidge, J. Opt. Soc. Amer. 56, 1139 (1966).
[CrossRef]

Collins, L. F.

Doidge, J. G.

W. T. Cathey, J. G. Doidge, J. Opt. Soc. Amer. 56, 1139 (1966).
[CrossRef]

El-Sum, H. M. A.

P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Amer. 46, 825 (1956).
[CrossRef]

Friesem, A. A.

Funkhouser, A.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Gabor, D.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 201.

Harper, J. S.

K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1693 (1970).

Kirkpatrick, P.

P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Amer. 46, 825 (1956).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

A. W. Lohmann, “The Space-Bandwidth Product,” IBM Research Paper RJ-438 (IBM San Jose Res. Lab., San Jose, Calif., 9May1967).

Monahan, M. A.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).

Pennington, K. S.

K. S. Pennington, J. S. Harper, Appl. Opt. 9, 1693 (1970).

Restrick, R.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Stroke, G. W.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press, New York, 1966), p. 90.

Thompson, B. J.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).

Upatnieks, J.

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inform. Theory. IT-10, 139 (1964).
[CrossRef]

Walker, J. L.

Appl. Opt.

Appl. Phys. Lett.

K. Bromley, M. A. Monahan, J. F. Bryant, B. J. Thompson, Appl. Phys. Lett. 14, 67 (1969).
[CrossRef]

IEEE Trans. Inform. Theory.

A. Vander Lugt, IEEE Trans. Inform. Theory. IT-10, 139 (1964).
[CrossRef]

J. Opt. Soc. Amer.

P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Amer. 46, 825 (1956).
[CrossRef]

W. T. Cathey, J. G. Doidge, J. Opt. Soc. Amer. 56, 1139 (1966).
[CrossRef]

Phys. Lett.

D. Gabor, G. W. Stroke, R. Restrick, A. Funkhouser, D. Brumm, Phys. Lett. 18, 116 (1965).
[CrossRef]

Other

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press, New York, 1966), p. 90.

M. A. Monahan, K. Bromley, J. F. Bryant, B. J. Thompson, “The Use of Holographic Subtraction in the Optical Processing of Reconnaissance Data,” Reference 18 in North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development, Opto-Electronics Signal Processing Techniques (Advisory Group for Aerospace Research and Development, 1970), (AGARD Conference Proceedings No. 50).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 8, p. 201.

A. W. Lohmann, “The Space-Bandwidth Product,” IBM Research Paper RJ-438 (IBM San Jose Res. Lab., San Jose, Calif., 9May1967).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Double-wave reconstruction.

Fig. 2
Fig. 2

Experimental arrangement for performing holographic subtraction using A, image-plane, B, fourier-transform, and C, Fresnel side-band holograms.

Fig. 3
Fig. 3

(a) Input transparency of typical outdoor scene. (b) Magnified portion of image-plane hologram made of transparency in (a) (spatial frequency: 28 cycles mm−1). (c) Input transparency showing scene of (a) plus a jeep. (d) Output image showing transparancy of (a) subtracted from that of (c). (e) Magnified view of (d). (f) Magnified view of output image using hologram made with only 12 cycles mm−1.

Fig. 4
Fig. 4

(a) Array of circular apertures. (b) Zeroth order of fourier-transform hologram made of (a). (c) Different array of circular apertures. (d) Output image showing array of (a) subtracted from that of (c).

Fig. 5
Fig. 5

(a) Checkerboard pattern. (b) Magnified portion of Fresnel side-band hologram of pattern in (a). (c) Doubly exposed transparency showing one scene (checkerboard pattern) superimposed on another (naval officer). (d) Output image showing scene of (a) subtracted from that of (c).

Equations (7)

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

τ = τ 0 + S t e A S 2 ( x , y ) + S t e A R A S ( x , y ) × { e i [ k a x - ϕ ( x , y ) ] + e - i [ k a x - ϕ ( x , y ) ] } ,
Ψ ( x , y ) = [ A R τ 0 + S t e A R A S 2 ( x , y ) ] e i k a x + S t e A R A R A S ( x , y ) e i [ 2 k a x - ϕ ( x , y ) ] + S t e A R A R A S ( x , y ) e i ϕ ( x , y ) .
- S t e A R A R A S ( x , y ) e i [ ϕ ( x , y ) + π ] + [ τ 0 A S ( x , y ) + S t e A S ( x , y ) A S 2 ( x , y ) ] e i ϕ ( x , y ) .
S = - τ 0 / E 0 .
E 0 = t e A R 2 .
A R / A S ( x , y ) = A R / A S ( x , y ) - A S ( x , y ) / A R .
A R / A S ( x , y ) A R / A S ( x , y ) .

Metrics