Abstract

We propose the use of a phase-shifting apodizers to increase focal depth, and we study the axial and radial behavior of this kind of apodizer under the condition that the axial intensity distribution is optimized for high focal depth.

© 2002 Optical Society of America

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References

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  1. W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
    [CrossRef]
  2. J. T. McCrickerd, “Coherent processing and depth of focus of annular aperture imagery,” Appl. Opt. 10, 2226–2231 (1971).
    [CrossRef] [PubMed]
  3. J. Ojeda-Castaneda, P. Andres, A. Diaz, “Annular apodizers for low sensitivity to defocus and to spherical aberration,” Opt. Lett. 11, 487–489 (1986).
    [CrossRef] [PubMed]
  4. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Spatial filter for increasing the depth of focus,” Opt. Lett. 10, 520–522 (1985).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castaneda, L. R. Berriel Valdos, “Arbitrarily high focal depth with finite apertures,” Opt. Lett. 13, 183–185 (1988).
    [CrossRef] [PubMed]
  6. G. Indebetouw, H. Bai, “Imaging with Fresnel zone pupil masks: extended depth of field,” Appl. Opt. 23, 4299–4302 (1984).
    [CrossRef] [PubMed]
  7. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. L. Montes, “Line-spread function relatively insensitive to defocus,” Opt. Lett. 8, 458–460 (1983).
    [CrossRef] [PubMed]
  8. J. Ojeda-Castaneda, A. Diaz, “High focal depth by quasibifocus,” Appl. Opt. 27, 4163–4165 (1988).
    [CrossRef]
  9. S. Sanyal, A. Ghosh, “High focal depth with a quasi-bifocus birefringent lens,” Appl. Opt. 39, 2321–2325 (2000).
    [CrossRef]
  10. G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Comm. 6, 38–42 (1972).
    [CrossRef]
  11. R. J. Pieper, A. Korpel, “Image processing for extended depth of field,” Appl. Opt. 22, 1449–1453 (1983).
    [CrossRef] [PubMed]
  12. H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
    [CrossRef]
  13. H. Wang, F. Gan, “High focal depth with pure-phase apodizers,” Appl. Opt. 40, 5658–5662 (2001).
    [CrossRef]

2001 (1)

2000 (1)

1992 (1)

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

1988 (2)

1986 (1)

1985 (1)

1984 (1)

1983 (2)

1972 (1)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Comm. 6, 38–42 (1972).
[CrossRef]

1971 (1)

1960 (1)

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Ando, H.

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

Andres, P.

Bai, H.

Berriel Valdos, L. R.

Berriel-Valdos, L. R.

Diaz, A.

Gan, F.

Ghosh, A.

Hausler, G.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Comm. 6, 38–42 (1972).
[CrossRef]

Indebetouw, G.

Korpel, A.

McCrickerd, J. T.

Montes, E.

Montes, E. L.

Ojeda-Castaneda, J.

Pieper, R. J.

Sanyal, S.

Wang, H.

Welford, W. T.

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

W. T. Welford, “Use of annular aperture to increase focal depth,” J. Opt. Soc. Am. A 50, 749–753 (1960).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

Opt. Comm. (1)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Comm. 6, 38–42 (1972).
[CrossRef]

Opt. Lett. (4)

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Figures (9)

Fig. 1
Fig. 1

Structure of the apodizer.

Fig. 2
Fig. 2

System setup.

Fig. 3
Fig. 3

Outer radius a versus inner radius b for the axial-optimized condition.

Fig. 4
Fig. 4

Axial intensity distribution of the optimized and original optical systems.

Fig. 5
Fig. 5

Corresponding radial intensity distribution of each curve in Fig. 4.

Fig. 6
Fig. 6

Formation of bifocus for some pairs of b and a in curve 1 of Fig. 3.

Fig. 7
Fig. 7

HWR and the Strehl ratio versus inner radius b for the axial-optimized apodizers in curve 1 of Fig. 3.

Fig. 8
Fig. 8

HWR and the Strehl ratio versus inner radius b for the axial-optimized apodizers in curve 2 of Fig. 3.

Fig. 9
Fig. 9

Axial intensity distribution of the original system and the calculated, tested, and expected results.

Equations (5)

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HWR=1-2a2-b21-2a4-b41/2,
S=1-2a2-b22,
Gu=2 j=1Nexp iϕjrj-1rjr exp-1/2iur2dr=20bexp-1/2iur2dr-baexp-1/2iur2dr+a1exp-1/2iur2dr=2iuexp-1/2iu-1-2 exp[-1/2iua2-exp-1/2iub2,
Iu=10+16 sinu4a2-b2×sinu4cosu41-a2-b2-8 cosu2a2-b2-2 cosu24u2=sinc2u4+4a2-b22sinc2a2-b24 u+2 1-a22sinc21-a24 u-2 1-b22sinc21-b24 u-2a4sinc2a24 u+2b4sinc2b24 u.
d2Iudu2=-12-2 a2-b24- 1-a24+ 1-b24+a8-b8=0.5

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