Abstract

The increasing popularity of optical communication has also brought a demand for a broader bandwidth. The trend, naturally, was to implement methods from traditional electronic communication. One of the most effective traditional methods is Code Division Multiple Access. In this research, we suggest the use of this approach for spatial coding applied to images. The approach is to multiplex several filters into one plane while keeping their mutual orthogonality. It is shown that if the filters are limited by their bandwidth, the output of all the filters can be sampled in the original image resolution and fully recovered through an all-optical setup. The theoretical analysis of such a setup is verified in an experimental demonstration.

© 2003 Optical Society of America

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References

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  1. A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1995).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2001

1997

1992

1964

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Chen, J.

De Nicola, S.

Ferraro, P.

Finizio, A.

Garcia, J.

Girilli, S.

Goodman, J.

J. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996).

Mendlovic, D.

Meucci, R.

Pierattini, G.

Sheng, Y.

Szu, H.

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Viterbi, A. J.

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1995).

Zalevsky, Z.

Appl. Opt.

IEEE Trans. Inf. Theory

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Opt. Express

Other

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, Reading, Mass., 1995).

J. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, New York, 1996).

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Figures (5)

Fig. 1
Fig. 1

One of the filter’s discrete spectrums.

Fig. 2
Fig. 2

CDMA filter with illustrated colors.

Fig. 3
Fig. 3

Input mask.

Fig. 4
Fig. 4

Ideal output of the different filters.

Fig. 5
Fig. 5

Retrieved output from the experiment.

Equations (13)

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

Sx, y=n=14 Fnx, yMnx, y.
Ox, y=n=14 Ix, yFnx, yMnx, y.
Rix, y=Ox, yFix, yMix, y =n=14 Ix, yFnx, yMnx, y×Fix, yMix, y =n=14 Ix, yFnx, yMnx, y×Fix, yMix, y.
Rix, y=Ix, yFi2x, yMi2x, y.
Rix, y=Ix, y.
order_0n=α0an+β0bn+χ0cn+δ0dn, order_1n=α1an+β1bn+χ1cn+δ1dn, order_2n=α2an+β2bn+χ2cn+δ2dn, order_3n=α3an+β3bn+χ3cn+δ3dn.
α0β0χ0δ0α1β1χ1δ1α2β2χ2δ2α3β3χ3δ3a0aNb0bNc0cNd0dN =A·a0aNb0bNc0cNd0dN =order00order0Norder10order1Norder20order2Norder30order3N.
A-1·order00order0Norder10order1Norder20order2Norder30order3N =a0aNb0bNc0cNd0dN.
order_in=αian+αi,-1an-1+αi,1an+1αi,2an+2+βibn+βi,-1b×n-1+βi,1bn+1+βi,2bn+2+χicn+χi.,-1cn-1+χi.,1cn+1+χi.,2cn+2+δidn+δi,-1dn-1+δi,1dn+1+δi,2dn+2.
order_in=αian+βibn+χicn+δidn+αi,-1αian-1+βibn-1+χic×n-1+δidn-1+αi,1αian+1+βibn+1+χicn+1+δidn+1+αi,2αian+2+βibn+2+χicn+2+δidn+2=orig_order_in+αi,-1×orig_order_i×n-1+αi,1×orig_order_in+1+αi,2×orig_order_in+2,
orig_order_in=αian+βibn+χicn+δidn.
000αiαi,-100αi,1αiαi,-100αi,2αi,1αi00orig_order_i0orig_order_iN =B·orig_order_i0orig_order_iN =order_i0order_iN.
B-1·order_i0order_iN =orig_order_i0orig_order_iN.

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