Abstract

In the formation of multiplexed filters, the phase-only and binary phase-only operations result in spurious cross terms and a nonlinear scaling. We use complementary random binary patterns having different pattern densities to encode the various functions within the multiplexed function. The orthogonality of these complementary masks permits separability of the phase-only or binary phase-only operations. By changing the pixel density of the random pattern, we can easily change the relative weights of the functions that compose the multiplexed filter. Experimental results are shown that demonstrate the effectiveness of this approach.

© 1994 Optical Society of America

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References

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1992

J. L. Horner, B. Javidi, J. Wang, Opt. Commun. 91, 189 (1992).
[CrossRef]

1990

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, Opt. Eng. 29, 1094 (1990).
[CrossRef]

1989

1986

1985

1984

1983

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

1970

1969

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Bach, G. W.

Bunch, R. M.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, Opt. Eng. 29, 1094 (1990).
[CrossRef]

Casasent, D.

Casasent, D. P.

D. P. Casasent, W. T. Chang, Appl. Opt. 24, 2343 (1986).
[CrossRef]

D. P. Casasent, Appl. Opt. 23, 1620 (1984).
[CrossRef] [PubMed]

Caulfield, H. J.

Chang, W. T.

D. P. Casasent, W. T. Chang, Appl. Opt. 24, 2343 (1986).
[CrossRef]

Connely, S. W.

Cottrell, D. M.

Davis, J. A.

Ennis, D. J.

Gianino, P. D.

Horner, J. L.

Jarad, D. A.

Javidi, B.

J. L. Horner, B. Javidi, J. Wang, Opt. Commun. 91, 189 (1992).
[CrossRef]

Kallman, R. R.

Leger, J. R.

Lilly, R. A.

Maloney, W. T.

Merrill, E. A.

J. A. Davis, E. A. Merrill, D. M. Cottrell, R. M. Bunch, Opt. Eng. 29, 1094 (1990).
[CrossRef]

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, Opt. Eng. 22, 485 (1983).

Rozzi, W. A.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, Opt. Eng. 23, 698 (1984).

Wang, J.

J. L. Horner, B. Javidi, J. Wang, Opt. Commun. 91, 189 (1992).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Composite lens functions focusing light simultaneously to two locations: (a) Analytical lens formed by multiplying each lens function by scaling factor and then adding. (b) Lens formed by multiplying the lens function by complementary random patterns having different numbers of pixels.

Fig. 2
Fig. 2

Intensities of the two focused spots by use of (a) the lens of Fig. 1(a) and (b) the lens of Fig. 1(b). The output intensities in (a) do not follow the intended design ratio, and a spurious peak is introduced. In (b) the output intensities follow the intended ratio.

Equations (7)

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M ( u ) = α G ( u ) + β H ( u ) .
M ˜ ( u ) = α G ( u ) + β H ( u ) α G ( u ) + β H ( u ) = α G ( u ) α G ( u ) + β H ( u ) + β H ( u ) α G ( u ) + β H ( u ) .
M ˜ ( u ) = α G ( u ) + β H ( u ) α G ( u ) + β H ( u ) + α * G * ( u ) + β * H * ( u ) + α * G * ( u ) + β * H * ( u ) α G ( u ) + β H ( u ) + α * G * ( u ) + β * H * ( u ) .
M ( u ) = R ( u ) G ( u ) + R ¯ ( u ) H ( u ) .
M ˜ ( u ) = R ( u ) G ( u ) + R ¯ ( u ) H ( u ) R ( u ) G ( u ) + R ¯ ( u ) H ( u ) = R ( u ) G ( u ) G ( u ) + R ¯ ( u ) H ( u ) H ( u ) .
M ˜ ( u ) = 2 π [ R ( u ) G ( u ) G ( u ) + R ( u ) G * ( u ) G * ( u ) + R ¯ ( u ) H ( u ) H ( u ) + R ¯ ( u ) H * ( u ) H * ( u ) ] + higher - order terms .
M ( u ) = α Z * ( u - a ) + β Z * ( u - b ) ,

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