Abstract

We present a procedure for designing rotationally symmetric pupil-plane masks to control the three-dimensional light-intensity distribution near focus. Our method is based on the use of a series of figures of merit that are properly defined to describe the effect of general complex pupil functions. As a practical implementation, we have applied our method to obtain superresolving continuous smoothly varying phase-only filters. The advantages of these kinds of filters are that they do not produce energy absorption and they are easy to build with a phase-controlling device such as a deformable mirror. Results of comparisons between the performance of our method and that of other phase-filter designs are provided.

© 2003 Optical Society of America

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References

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  1. G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
    [CrossRef]
  2. C. J. R. Sheppard, Optik 48, 329 (1977).
  3. I. J. Cox, C. J. R. Sheppard, and T. Wilson, J. Opt. Soc. Am. 72, 1287 (1982).
  4. T. R. M. Sales and G. M. Morris, Opt. Lett. 22, 582 (1997).
    [CrossRef] [PubMed]
  5. T. R. M. Sales and G. M. Morris, J. Opt. Soc. Am. 14, 1637 (1997).
    [CrossRef]
  6. H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
    [CrossRef]
  7. H. Wang, Z. Chen, and F. Gan, Appl. Opt. 40, 5658 (2001).
    [CrossRef]
  8. J. Zhai, Y. Yan, D. Huang, M. Wu, and G. Jin, Proc. SPIE 3429, 177 (1998).
    [CrossRef]
  9. C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. 5, 643 (1988).
    [CrossRef]
  10. J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, (Argonne National Laboratory, Argonne, Ill., 1980).

2001

H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
[CrossRef]

H. Wang, Z. Chen, and F. Gan, Appl. Opt. 40, 5658 (2001).
[CrossRef]

1998

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

1997

T. R. M. Sales and G. M. Morris, Opt. Lett. 22, 582 (1997).
[CrossRef] [PubMed]

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

1988

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

1982

1977

C. J. R. Sheppard, Optik 48, 329 (1977).

1952

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Chen, Z.

H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
[CrossRef]

H. Wang, Z. Chen, and F. Gan, Appl. Opt. 40, 5658 (2001).
[CrossRef]

Cox, I. J.

Gan, F.

H. Wang, Z. Chen, and F. Gan, Appl. Opt. 40, 5658 (2001).
[CrossRef]

H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
[CrossRef]

Garbow, B. S.

J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, (Argonne National Laboratory, Argonne, Ill., 1980).

Hegedus, Z. S.

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

Hillstrom, K. E.

J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, (Argonne National Laboratory, Argonne, Ill., 1980).

Huang, D.

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

Jin, G.

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

More, J. J.

J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, (Argonne National Laboratory, Argonne, Ill., 1980).

Morris, G. M.

T. R. M. Sales and G. M. Morris, Opt. Lett. 22, 582 (1997).
[CrossRef] [PubMed]

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

Sales, T. R. M.

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

T. R. M. Sales and G. M. Morris, Opt. Lett. 22, 582 (1997).
[CrossRef] [PubMed]

Sheppard, C. J. R.

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

I. J. Cox, C. J. R. Sheppard, and T. Wilson, J. Opt. Soc. Am. 72, 1287 (1982).

C. J. R. Sheppard, Optik 48, 329 (1977).

Toraldo di Francia, G.

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Wang, H.

H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
[CrossRef]

H. Wang, Z. Chen, and F. Gan, Appl. Opt. 40, 5658 (2001).
[CrossRef]

Wilson, T.

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]

Zhai, J.

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

Appl. Opt.

J. Opt. Soc. Am.

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

I. J. Cox, C. J. R. Sheppard, and T. Wilson, J. Opt. Soc. Am. 72, 1287 (1982).

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

Nuovo Cimento Suppl.

G. Toraldo di Francia, Nuovo Cimento Suppl. 9, 426 (1952).
[CrossRef]

Opt. Eng.

H. Wang, Z. Chen, and F. Gan, Opt. Eng. 40, 991 (2001).
[CrossRef]

Opt. Lett.

Optik

C. J. R. Sheppard, Optik 48, 329 (1977).

Proc. SPIE

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

Other

J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, (Argonne National Laboratory, Argonne, Ill., 1980).

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Figures (2)

Fig. 1
Fig. 1

Illustration of the notation used in determining the structure of the focal region. Point Q is located on a converging spherical wave front centered on F and passing through the center, O, of the pupil; P is a point near the focus, F; f is the focal length; and a is the pupil radius. The coordinates r and z of P are taken from the geometrical focus of the pupil.

Fig. 2
Fig. 2

Normalized transverse PSF produced by the superresolving phase filter with parameters a and b given in the legend (solid curve) compared with the Airy PSF (dashed curve).

Tables (2)

Tables Icon

Table 1 Performance of Phase Filters with the Form ϕρ,a,b=a sin2πbr

Tables Icon

Table 2 Comparison of the Performance of Phase Filters Obtained with Three Methods

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Uv,u=201PρJ0vρexpjuρ2/2ρdρ,
v=kNAr,
u=kNA2z,
Iv,0=I02-12ReI0I1*v2,
I0,u=I02-ImI0*I1u-14ReI2*I0-I12u2,
In=01Pttndt.
uF=-2ImI0*I1ReI2*I0-I12.
GT=2ReI0I1*-uFImI0*I2I02-uFImI0*I1,
GA=12ReI2*I0-I12I02-uFImI0*I1.
S=I02-uFImI0*I1.
uFa,buF0,
GTa,b-GT0=0,
Sa,b-S0=0,

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