Abstract

The three-dimensional (3-D) joint transform correlator is demonstrated with realistic targets. Three-dimensional objects observed by multiple cameras are correlated with a 3-D reference object. The number of cameras and their directions of observation are particularly considered.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964); B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
    [CrossRef]
  2. R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
    [CrossRef]
  3. Y. Karasik, “Evaluation of three-dimensional convolutions by two-dimensional filtering,” Appl. Opt. 36, 7397–7401 (1997).
    [CrossRef]
  4. J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964–966 (1997).
    [CrossRef] [PubMed]
  5. J. Rosen, “Three-dimensional electro-optical correlation,” J. Opt. Soc. Am. A 15, 430–436 (1998).
    [CrossRef]
  6. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966);F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992), Chap. 2, p. 34.
    [CrossRef] [PubMed]
  7. J. Rosen, U. Mahlab, J. Shamir, “Complex reference discriminant functions implemented iteratively on joint transform correlator,” Appl. Opt. 30, 5111–5115 (1991).
    [CrossRef] [PubMed]
  8. J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 31, 165–166 (1992).
    [CrossRef] [PubMed]

1998 (1)

1997 (2)

1992 (1)

1991 (1)

1982 (1)

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

1966 (1)

1964 (1)

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964); B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

Bamler, R.

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

Goodman, J. W.

Hofer-Alfeis, J.

R. Bamler, J. Hofer-Alfeis, “Three- and four-dimensional filter operations by coherent optics,” Opt. Acta 29, 747–757 (1982).
[CrossRef]

Horner, J. L.

Karasik, Y.

Mahlab, U.

Rosen, J.

Shamir, J.

VanderLugt, A. B.

A. B. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964); B. V. K. Vijaya Kumar, “Tutorial survey of composite filter designs for optical correlators,” Appl. Opt. 31, 4773–4801 (1992).
[CrossRef]

Weaver, C. S.

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

Illustration of the imaging system in the case of (a) parallel and (b) converging observations.

Fig. 2
Fig. 2

Schematic of the 3-D JTC.

Fig. 3
Fig. 3

Twelve projections out of 25 of the input scene as observed from different points of view along the baseline.

Fig. 4
Fig. 4

Intensity of the correlation results of the 3-D joint transform correlator (a) before and (b) after a threshold operation.

Fig. 5
Fig. 5

The peak-to-correlation energy (PCE) versus the number of cameras along the baseline.

Equations (12)

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

M z s = d L - z s = M 0 1 - z s / L .
O 3 u ,   v = M 0 2     o x s ,   y s ,   z s exp i k / f x i u + y i v d x s d y s d z s ,
O 3 u ,   v ,   D x = A   exp iM 0 kD x u / f ×   o x s ,   y s ,   z s exp i M 0 k / f x s u + y s v + z s D x u / L d x s d y s d z s ,
x i ,   y i = M 0 x s   cos   θ + z s   sin   θ ,   y s .
O 3 u ,   v ,   θ = A     o x s ,   y s ,   z s exp i kM 0 / f ux s   cos   θ + vy s + uz s   sin   θ d x s d y s d z s .
o x s ,   y s ,   z s = r x s ,   y s ,   z s + g x s + a ,   y s + b ,   z s + c .
I 3 u ,   v ,   θ = | O 3 u ,   v ,   θ | 2 = A     o x s ,   y s ,   z s exp i M 0 k / f x s u + y s v + z s D x u / L d x s d y s d z s 2 .
I 3 u ,   v ,   θ = | R u ,   v ,   θ + G u ,   v ,   θ exp i M 0 k / f × au + bv + cD x u / L | 2 ,
R G u ,   v ,   θ =   r g x s ,   y s ,   z s exp i M 0 k / f × x s u + y s v + z s D x u / L d x s d y s d z s .
Ĩ 3 u ,   v ,   uD x / L = | R ˜ u ,   v ,   uD x / L + G ˜ u ,   v ,   uD x / L exp i M 0 k / f × au + bv + cD x u / L | 2 = | R ˜ u ,   v ,   uD x / L | 2 + | G ˜ u ,   v ,   uD x / L | 2 + R ˜ u ,   v ,   uD x / L G ˜ * u ,   v ,   uD x / L × exp - i M 0 k / f au + bv + cD x u / L + G ˜ u ,   v ,   uD x / L × R ˜ * u ,   v ,   uD x / L exp i M 0 k / f × au + bv + cD x u / L ,
c x o ,   y o ,   z o =   Ĩ 3 f x ,   f y ,   f z × exp - i 2 π x o f x + y o f y + z o f z d f x d f y d f z = r r + g g + r g *   δ x o - a ,   y o - b ,   z o - c + g r   *   δ x o + a ,   y o + b ,   z o + c ,
g r x o ,   y o ,   z o =   g x ,   y ,   z × r x - x o ,   y - y o ,   z - z o d x d y d z .

Metrics