Abstract

A method of processing optical information is described in which the use of absorptive spatial filters is replaced by suitable mirrors with spatially varying reflectances. When these mirrors are made the terminal planes of a laser resonator, the light which is lost in conventional spatial filtering systems, is stored in the laser cavity. It is shown that shallowly modulated phase objects may be imaged outside the resonator without any appreciable effect on the modes of the resonator.

© 1967 Optical Society of America

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References

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  1. R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
    [CrossRef]
  2. R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
    [CrossRef]
  3. R. A. Myers, R. V. Pole, J. Opt. Soc. Am. 55, 1574 (1965).
    [CrossRef]
  4. R. V. Pole, J. Opt. Soc. Am. 55, 254 (1965).
    [CrossRef]
  5. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

1966 (2)

R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
[CrossRef]

R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
[CrossRef]

1965 (2)

R. A. Myers, R. V. Pole, J. Opt. Soc. Am. 55, 1574 (1965).
[CrossRef]

R. V. Pole, J. Opt. Soc. Am. 55, 254 (1965).
[CrossRef]

1960 (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

Leith, E. N.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

Myers, R. A.

R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
[CrossRef]

R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
[CrossRef]

R. A. Myers, R. V. Pole, J. Opt. Soc. Am. 55, 1574 (1965).
[CrossRef]

Palermo, C. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

Pole, R. V.

R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
[CrossRef]

R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
[CrossRef]

R. A. Myers, R. V. Pole, J. Opt. Soc. Am. 55, 1574 (1965).
[CrossRef]

R. V. Pole, J. Opt. Soc. Am. 55, 254 (1965).
[CrossRef]

Porcello, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

Wieder, H.

R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
[CrossRef]

R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
[CrossRef]

Appl. Phys. Letters (1)

R. V. Pole, H. Wieder, R. A. Myers, Appl. Phys. Letters 8, 229 (1966).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. A. Myers, H. Wieder, R. V. Pole, IEEE J. Quantum Electron. QE-2, 270 (1966).
[CrossRef]

Inst. Radio. Engrs. Trans. (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio. Engrs. Trans. IT-6, 386 (1960).

J. Opt. Soc. Am. (2)

R. V. Pole, J. Opt. Soc. Am. 55, 254 (1965).
[CrossRef]

R. A. Myers, R. V. Pole, J. Opt. Soc. Am. 55, 1574 (1965).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) and (b) show the Flat Field Conjugate resonator in its degenerate and multimode version. (c) and (d) show this resonator in its single mode form. These two forms are optically equivalent to the Concentric and Fabry-Perot resonators, respectively.

Fig. 2
Fig. 2

Schematic diagram of the reactive optical information processing system.

Equations (16)

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F ( x ) = e i A ( x ) ,             x < 1 = 0 , elsewhere
U ( x , y ) = e i δ ( a 2 / λ f ) - 1 1 - 1 1 exp [ i c ( x x 1 + y y 1 ) ] u ( x 1 , y 1 ) d x 1 d y 1 ,
δ = ( π / 2 ) - 2 k f , c = 2 π ( a b / λ f ) = 2 π N ( N = Fresnel number ) , k = 2 π / λ ( λ = wavelength of light in vacuum ) .
u ( x 2 , y 2 ) = e i δ b 2 / λ f - 1 1 - 1 1 F ( x ) U ( x , y ) exp [ i c ( x 2 x + y 2 y ) ] d x d y .
u ( x 2 , y 2 ) = e i 2 δ 4 π 2 c 2 - 1 1 - 1 1 { - 1 1 - 1 1 exp [ i c ( x x 1 + y y 1 ) ] u ( x 1 , y 1 ) × d x 1 d y 1 } [ F ( x ) exp [ - i c ( x 2 x + y 2 y ) ] d x d y = e i 2 δ c 2 π - 1 1 - 1 1 { - 1 1 exp [ i c ( x 1 - x 2 ) x ] F ( x ) d x } × sin c ( y 1 - y 2 ) π ( y 1 - y 2 ) × [ u ( x 1 , y 1 ) d x 1 d y 1 ] .
u x ( x 2 ) = e i δ c 2 π - 1 1 { - 1 1 exp [ i c ( x 1 - x 2 ) x ] F ( x ) d x } u x ( x 1 ) d x 1 .
u y ( y 2 ) = e i δ - 1 1 sin c ( y 1 - y 2 ) π ( y 1 - y 2 ) u y ( y 1 ) d y 1 .
σ i ψ i ( x 2 ) = e i δ - 1 1 K ( x 1 , x 2 ) ψ i ( x 1 ) d x 1 ,
K ( x 1 , x 2 ) = c 2 π - 1 1 exp [ i c ( x 1 - x 2 ) x ] F ( x ) d x .
A ( x ) = G ( x ) cos ω ( x ) x
F ( x ) 1 + i A ( x ) = 1 + i G ( x ) cos ω x ,
u ( x 2 ) = e i δ - 1 1 sin c ( x 1 - x 2 ) π ( x 1 - x 2 ) u ( x 1 ) d x 1 + i exp [ i ( δ / 2 ) ] b ( λ f ) 1 2 - 1 1 U ( x ) G ( x ) cos ω x exp [ - i e x 2 x ] d x ,
U ( x ) = exp [ i ( δ / 2 ) ] a ( λ f ) 1 2 - 1 1 exp [ i c x 1 x ) u ( x 1 ) d x 1 .
u ( x 2 ) = exp [ i ( δ / 2 ) ] b ( λ f ) 1 2 - 1 1 U ( x ) exp [ - i c x 2 x ] d x
g ( x 2 ) = - 1 1 G ( x ) exp [ - i c x 2 x ] d x ,
u ( x 2 ) = e i δ - 1 1 sin c ( x 1 - x 2 ) π ( x 1 - x 2 ) u ( x 1 ) d x 1 + i c 4 π - u ( x 2 ) g ( x 2 - ( ω / c ) - x 2 ) d x 2 + i c 4 π - u ( x 2 ) g ( x 2 + ( ω / c ) - x 2 ) d x 2 ,

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