Abstract

The focal depth of an arbitrary image is extended by optimization of the amplitude and phase distributions over the entire image. We propose a general method that takes advantage of a detector’s (possibly nonlinear) response to incident intensity. We demonstrate the method by computer simulations and experimentally, using computer-generated holograms.

© 1995 Optical Society of America

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References

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    [CrossRef] [PubMed]
  6. B. Salik, J. Rosen, A. Yariv, J. Opt. Soc. Am. A 12, 1702 (1995).
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    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 45.
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  15. R. A. Ferguson, Proc. Soc. Photo-Opt. Instrum. Eng. 2197, 130 (1994).
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  17. D. J. Elliott, Integrated Circuit Fabrication Technology (McGraw-Hill, New York, 1989), p. 232.

1995 (2)

1994 (6)

1992 (1)

Y. Liu, A. K. Pfau, A. Zakhor, Proc. Soc. Photo-Opt. Instrum. Eng. 1674, 14 (1992).

1990 (1)

1987 (1)

Berriel-Valdos, L. R.

Dartnall, H. J. A.

A. Knowles, H. J. A. Dartnall, in The Eye IIB, H. Davidson, ed. (Academic, Orlando, Fla., 1977), pp. 461–469.

Durnin, J.

Elliott, D. J.

D. J. Elliott, Integrated Circuit Fabrication Technology (McGraw-Hill, New York, 1989), p. 232.

Ferguson, R. A.

R. A. Ferguson, Proc. Soc. Photo-Opt. Instrum. Eng. 2197, 130 (1994).

Foulds, L. R.

L. R. Foulds, Optimization Techniques (Springer-Verlag, New York, 1981), pp. 329–335.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 45.

Hall, D. G.

Jordan, R. H.

Kailath, T.

Knowles, A.

A. Knowles, H. J. A. Dartnall, in The Eye IIB, H. Davidson, ed. (Academic, Orlando, Fla., 1977), pp. 461–469.

Levenson, M. D.

M. D. Levenson, Jpn. J. Appl. Phys. 33, 6765 (1994).
[CrossRef]

Liu, H. K.

Liu, Y.

Y. Liu, A. K. Pfau, A. Zakhor, Proc. Soc. Photo-Opt. Instrum. Eng. 1674, 14 (1992).

Ojeda-Castaneda, J.

Pati, Y. C.

Pfau, A. K.

Y. Liu, A. K. Pfau, A. Zakhor, Proc. Soc. Photo-Opt. Instrum. Eng. 1674, 14 (1992).

Piestun, R.

Rosen, J.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 665–681.

Salik, B.

B. Salik, J. Rosen, A. Yariv, J. Opt. Soc. Am. A 12, 1702 (1995).
[CrossRef]

J. Rosen, B. Salik, A. Yariv, H. K. Liu, Opt. Lett. 20, 423 (1995).
[CrossRef] [PubMed]

J. Rosen, B. Salik, A. Yariv, “Pseudonondiffracting beam generated by radial harmonic function,” submitted toJ. Opt. Soc. Am. A.

Shamir, J.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 665–681.

Yariv, A.

B. Salik, J. Rosen, A. Yariv, J. Opt. Soc. Am. A 12, 1702 (1995).
[CrossRef]

J. Rosen, B. Salik, A. Yariv, H. K. Liu, Opt. Lett. 20, 423 (1995).
[CrossRef] [PubMed]

J. Rosen, B. Salik, A. Yariv, “Pseudonondiffracting beam generated by radial harmonic function,” submitted toJ. Opt. Soc. Am. A.

Zakhor, A.

Y. Liu, A. K. Pfau, A. Zakhor, Proc. Soc. Photo-Opt. Instrum. Eng. 1674, 14 (1992).

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

Jpn. J. Appl. Phys. (1)

M. D. Levenson, Jpn. J. Appl. Phys. 33, 6765 (1994).
[CrossRef]

Opt. Lett. (4)

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. A. Ferguson, Proc. Soc. Photo-Opt. Instrum. Eng. 2197, 130 (1994).

Y. Liu, A. K. Pfau, A. Zakhor, Proc. Soc. Photo-Opt. Instrum. Eng. 1674, 14 (1992).

Other (6)

A. Knowles, H. J. A. Dartnall, in The Eye IIB, H. Davidson, ed. (Academic, Orlando, Fla., 1977), pp. 461–469.

D. J. Elliott, Integrated Circuit Fabrication Technology (McGraw-Hill, New York, 1989), p. 232.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 45.

L. R. Foulds, Optimization Techniques (Springer-Verlag, New York, 1981), pp. 329–335.

J. Rosen, B. Salik, A. Yariv, “Pseudonondiffracting beam generated by radial harmonic function,” submitted toJ. Opt. Soc. Am. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 665–681.

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Figures (6)

Fig. 1
Fig. 1

Typical detector response versus exposure intensity.

Fig. 2
Fig. 2

Relationship of critical planes to classical depth of focus σ.

Fig. 3
Fig. 3

Schematic diagram of a typical imaging system.

Fig. 4
Fig. 4

(a) Desired postthresholding image. (b) Simulated intensity pattern before thresholding at the image plane (z = 0) and the two critical planes z = 5pixels and z = 10pixels. (c) Simulated intensity pattern after thresholding at the image plane (z = 0) and the two critical planes z = 5pixels and z = 10pixels. Here one longitudinal pixel = (Δx)2/5λ = σ/5, or one fifth of the normal depth of focus.

Fig. 5
Fig. 5

Experimental configuration for realizing the mask function g(x, y).

Fig. 6
Fig. 6

(a) Measured intensity pattern before thresholding at the image plane (z = 0) and the critical planes z = 0.7 cm and z = 1.4 cm. (b) Measured intensity pattern after thresholding at the image plane (z = 0) and the critical planes z = 0.7 cm and z = 1.4 cm. Images were produced using setup of Fig. 5, with f = 100 cm, θ = 2.5 mrad, and illumination λ = 633 nm.

Equations (2)

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u ( x , y , z ) = u ( x 1 , y 1 ) z exp ( i k r ) i λ r 2 d x 1 d y 1 ,
G ( x 0 , y 0 ) = min ( Re { G ( x 0 , y 0 ) exp [ i 2 π u ( x 0 + y 0 ) ] } ) + Re { G ( x 0 , y 0 ) exp [ i 2 π u ( x 0 + y 0 ) ] } ,

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