Abstract

To study the three-dimensional (3-D) behavior produced by complex filters, we have extended the expressions for the axial and the transverse gain to the case in which the best image plane is not near the paraxial focus. Super-Gaussian phase filters are proposed to control the 3-D image response of an optical system. Super-Gaussian phase filters depend on several parameters that modify the shape of the phase filter, producing tunable control of the 3-D response of the optical system. The filters are capable of producing a wide range of optical effects: transverse superresolution with high depth of focus, 3-D superresolution, and transverse apodization with different axial responses.

© 2004 Optical Society of America

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References

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  1. T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. A 14, 1637 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
    [CrossRef]

2003 (2)

2000 (1)

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

1998 (1)

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

1997 (2)

T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. A 14, 1637 (1997).
[CrossRef]

R. Hild, M. J. Yzuel, and J. C. Escalera, Microelectron. Eng. 34, 195 (1997).
[CrossRef]

1995 (1)

J. Ojeda-Castañeda, J. C. Escalera, and M. J. Yzuel, Opt. Commun. 114, 189 (1995).
[CrossRef]

1993 (1)

M. D. Levenson, Phys. Today 46(7), 28 (1993).
[CrossRef]

1991 (1)

M. Gu and C. J. R. Sheppard, J. Mod. Opt. 38, 2247 (1991).
[CrossRef]

1988 (1)

Cagigal, M. P.

Campos, J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

Canales, V. F.

de Juana, D. M.

Escalera, J. C.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

R. Hild, M. J. Yzuel, and J. C. Escalera, Microelectron. Eng. 34, 195 (1997).
[CrossRef]

J. Ojeda-Castañeda, J. C. Escalera, and M. J. Yzuel, Opt. Commun. 114, 189 (1995).
[CrossRef]

Gu, M.

M. Gu and C. J. R. Sheppard, J. Mod. Opt. 38, 2247 (1991).
[CrossRef]

Hegedus, Z. S.

Hild, R.

R. Hild, M. J. Yzuel, and J. C. Escalera, Microelectron. Eng. 34, 195 (1997).
[CrossRef]

Huang, D.

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

Ibáñez-López, C.

Jin, G.

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

Levenson, M. D.

M. D. Levenson, Phys. Today 46(7), 28 (1993).
[CrossRef]

Martínez-Corral, M.

Morris, G. M.

Ojeda-Castañeda, J.

J. Ojeda-Castañeda, J. C. Escalera, and M. J. Yzuel, Opt. Commun. 114, 189 (1995).
[CrossRef]

Oti, J. E.

Saavedra, G.

Sales, T. R. M.

Sheppard, C. J. R.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

M. Gu and C. J. R. Sheppard, J. Mod. Opt. 38, 2247 (1991).
[CrossRef]

C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
[CrossRef]

Wu, M.

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

Yan, Y.

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

Yzuel, M. J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

R. Hild, M. J. Yzuel, and J. C. Escalera, Microelectron. Eng. 34, 195 (1997).
[CrossRef]

J. Ojeda-Castañeda, J. C. Escalera, and M. J. Yzuel, Opt. Commun. 114, 189 (1995).
[CrossRef]

Zhai, J.

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

J. Mod. Opt. (2)

M. Gu and C. J. R. Sheppard, J. Mod. Opt. 38, 2247 (1991).
[CrossRef]

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, J. Mod. Opt. 47, 57 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Microelectron. Eng. (1)

R. Hild, M. J. Yzuel, and J. C. Escalera, Microelectron. Eng. 34, 195 (1997).
[CrossRef]

Opt. Commun. (1)

J. Ojeda-Castañeda, J. C. Escalera, and M. J. Yzuel, Opt. Commun. 114, 189 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Today (1)

M. D. Levenson, Phys. Today 46(7), 28 (1993).
[CrossRef]

Proc. SPIE (1)

J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Axial and transverse gain versus t0 for a=3, Ω=0.1, and α=2. (b) Phase transmission for filters with distributions centered at t0=0.2 and t0=0.4.

Fig. 2
Fig. 2

(a), (c) Axial intensities for t0=0.2 and t0=0.4, respectively. (b) Transverse intensity for t0=0.2, umax=2, S=0.49, GT=1.2, and GA=0.7. (d) Transverse intensity for t0=0.4, umax=0.5, S=0.44, GT=1.1, and GA=1.4.

Equations (11)

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φt=a exp-t-t0/Ω2α.
U0,u=01Qtexpiut/2dt,
U0,u01Qtexpiumaxt/21+it/2u-umax-t2/8u-umax2dt.
In=01Qttnexpiumaxt/2dt.
I0,uI02-ImI0*I1u+1/4×I12-ReI0I2*u2,
Uv,umax01Qt1-1/4v2texpiumaxtdt.
Iv,umaxI02-1/2ReI0I1*v2.
u0=2 ImI0*I1/I12-ReI0I2*.
GA=12ReI0I2*-I12I02-1/2u0 ImI0*I1,
GT=2 ReI0I1*/I02.
S=I02-u0 ImI0*I1.

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