Abstract

Processes that are analogous to the neural process of recurrent lateral inhibition can be found in optical systems that consist of a shift-invariant system and a Fabry–Perot cavity. The properties of the optical recurrent system are derived and demonstrated by computer simulation. The simulation shows that optical lateral inhibition can be used to enhance the outline of an amplitude object and to make phase-only objects directly detectable and visible. The optical recurrent system is compared with frequency-plane spatial filtering. Requirements and practical limitations for the design of an optical recurrent system are also discussed.

© 1994 Optical Society of America

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References

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  1. H. K. Hartline, F. Ratliff, “Inhibitory interaction of receptor units in the eye of Limulus,” J. Gen. Physiol. 40, 357–376 (1957).
    [CrossRef] [PubMed]
  2. F. Ratliff, H. K. Hartline, W. H. Miller, “Spatial and temporal aspects of retinal inhibitory interaction,” J. Opt. Soc. Am. 53, 110–120 (1963).
    [CrossRef] [PubMed]
  3. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.7, p. 48.
  4. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 7.6, p. 323.
  5. F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
    [CrossRef]
  6. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 6.8, p. 279.

1969 (1)

F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
[CrossRef]

1963 (1)

1957 (1)

H. K. Hartline, F. Ratliff, “Inhibitory interaction of receptor units in the eye of Limulus,” J. Gen. Physiol. 40, 357–376 (1957).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 7.6, p. 323.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.7, p. 48.

Graham, N.

F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
[CrossRef]

Hartline, H. K.

F. Ratliff, H. K. Hartline, W. H. Miller, “Spatial and temporal aspects of retinal inhibitory interaction,” J. Opt. Soc. Am. 53, 110–120 (1963).
[CrossRef] [PubMed]

H. K. Hartline, F. Ratliff, “Inhibitory interaction of receptor units in the eye of Limulus,” J. Gen. Physiol. 40, 357–376 (1957).
[CrossRef] [PubMed]

Knight, B. W.

F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
[CrossRef]

Miller, W. H.

Ratliff, F.

F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
[CrossRef]

F. Ratliff, H. K. Hartline, W. H. Miller, “Spatial and temporal aspects of retinal inhibitory interaction,” J. Opt. Soc. Am. 53, 110–120 (1963).
[CrossRef] [PubMed]

H. K. Hartline, F. Ratliff, “Inhibitory interaction of receptor units in the eye of Limulus,” J. Gen. Physiol. 40, 357–376 (1957).
[CrossRef] [PubMed]

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 6.8, p. 279.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 7.6, p. 323.

J. Gen. Physiol. (1)

H. K. Hartline, F. Ratliff, “Inhibitory interaction of receptor units in the eye of Limulus,” J. Gen. Physiol. 40, 357–376 (1957).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Proc. Natl. Acad. Sci. (USA) (1)

F. Ratliff, B. W. Knight, N. Graham, “On tuning and amplification by lateral inhibition,” Proc. Natl. Acad. Sci. (USA) 62, 737–740 (1969).
[CrossRef]

Other (3)

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 6.8, p. 279.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.7, p. 48.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975), Chap. 7.6, p. 323.

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Figures (4)

Fig. 1
Fig. 1

(a) Geometry for optical coherent propagation in free space. The Fabry–Perot cavity with interfaces I1 and I2 is between P1 and P2. (b) A basic optical recurrent system.

Fig. 2
Fig. 2

Distribution of the amplitude-only object (arbitrary units) and the phase-only object (unit is π/ 10) used in the simulations.

Fig. 3
Fig. 3

Intensity distribution (arbitrary units) of the response of T(r/F) to the amplitude-only test input for R = 0.64 and N π = 1.

Fig. 4
Fig. 4

Intensity distribution (arbitrary units) of the response of T(r/F) to the phase-only test input for R = 0.64 and N π = 1.

Tables (1)

Tables Icon

Table 1 Edge Enhancement by Optical Lateral Inhibition

Equations (12)

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r ( x ) = s ( x ) i ( x ) .
r ( x ) = s ( x ) + k ( x x ) s ( x ) d x ,
r ( x ) = s ( x ) + k ( x x ) r ( x ) d x ,
H ( f x , f y ) = exp ( j 2 π z γ / λ ) .
T ( f x , f y ) = T / [ 1 R exp ( j 4 π n Δ γ / λ ) ] .
U 2 ( f x , f y ) = H 12 ( f x , f y ) T ( f x , f y ) U 1 ( f x , f y ) ,
u 2 ( x , y ) = h 12 ( x , y ) * t ( x , y ) * u 1 ( x , y ) ,
H ( f x ) = R ( f x ) / S ( f x ) = 1 / [ 1 + K ( f x ) ] ,
T ( f x , f y ) = T ( r / F ) = T / { 1 R exp [ j ϕ ( r / F ) ] } ,
ϕ ( r / F ) = 2 π m [ 1 ( r / F ) 2 / 2 ] ,
r max / F = ( N π / m ) 1 / 2 .
A FPC A i + 2 d tan θ + 2 ( 2 N + 1 ) × Δ sin θ / ( n 2 sin 2 θ ) 1 / 2 ,

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