Abstract

Superresolution phase-only pupil filters designed to utilize the degrees of freedom made available by diffractive optics technology are investigated theoretically. These so-called diffractive superresolution elements improve the quality of the superresolved diffraction pattern from the point of view of Strehl ratio, reduction of the spot size, control of the sidelobe effects, optimization procedures, and fabrication tolerances. The performance of these elements is studied, and the nature of the solutions obtainable with binary and multiple-phase structures is analyzed. Design considerations and solutions for applications such as confocal scanning microscopy and optical data storage are presented. Optimization of the degrees of freedom to satisfy desired constraints is discussed and compared with other methods.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. B. Marchant, Optical Recording: a Technical Overview (Addison-Wesley, Reading, Mass., 1990), Chap. 5, p. 101.
  2. K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.
  3. T. Wilson, Confocal Microscopy (Academic, London, 1990), Chap. 5, p. 171.
  4. T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.
  5. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [CrossRef]
  6. Z. S. Hegedus, “Annular pupil arrays. Applications to confocal scanning,” Opt. Acta 32, 815–826 (1985).
    [CrossRef]
  7. C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).
  8. Y. Yamanaka, Y. Hirose, H. Fujii, K. Kubota, “High density recording by superresolution in an optical disk memory system,” Appl. Opt. 29, 3046–3051 (1990).
    [CrossRef] [PubMed]
  9. I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
    [CrossRef]
  10. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  11. H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
    [CrossRef]
  12. T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
    [CrossRef] [PubMed]

1997 (1)

1992 (1)

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

1990 (1)

1986 (1)

1985 (1)

Z. S. Hegedus, “Annular pupil arrays. Applications to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

1982 (1)

1977 (1)

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

1952 (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Ando, H.

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

Cox, I. J.

Fujii, H.

Hegedus, Z. S.

Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
[CrossRef]

Z. S. Hegedus, “Annular pupil arrays. Applications to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

Hirose, Y.

Ichimura, I.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

Kubota, K.

Maeda, F.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

Marchant, A. B.

A. B. Marchant, Optical Recording: a Technical Overview (Addison-Wesley, Reading, Mass., 1990), Chap. 5, p. 101.

Morris, G. M.

T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
[CrossRef] [PubMed]

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Osato, K.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

Sales, T. R. M.

T. R. M. Sales, G. M. Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
[CrossRef] [PubMed]

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Sarafis, V.

Sheppard, C. J. R.

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
[CrossRef]

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

Toraldo di Francia, G.

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Watanabe, T.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

Wilson, T.

Yamamoto, K.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

Yamanaka, Y.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Jpn. J. Appl. Phys. (1)

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

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Opt. Acta (1)

Z. S. Hegedus, “Annular pupil arrays. Applications to confocal scanning,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

Opt. Lett. (1)

Optik (1)

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

Other (4)

A. B. Marchant, Optical Recording: a Technical Overview (Addison-Wesley, Reading, Mass., 1990), Chap. 5, p. 101.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “A 0.8 numerical aperture two element objective lens for the optical disk,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 345–347.

T. Wilson, Confocal Microscopy (Academic, London, 1990), Chap. 5, p. 171.

T. R. M. Sales, G. M. Morris, “Superresolution elements for high-density optical storage,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 290–292.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Phase function Φ of a binary DSE with maximum phase transmission ϕ0 and unit amplitude transmission. The aperture coordinate is normalized to 1.

Fig. 2
Fig. 2

Spot size G for a two-zone binary DSE (solid curve) as a function of zone-boundary position α. For comparison, the second-order approximation to G is also shown (dotted curve).

Fig. 3
Fig. 3

Strehl ratio S for a two-zone binary DSE as a function of zone-boundary position α for several values of phase transmission ϕ0.

Fig. 4
Fig. 4

Sidelobe intensity M for a two-zone binary DSE as a function of zone-boundary position α for several values of phase transmission ϕ0.

Fig. 5
Fig. 5

Space of solutions corresponding to all possible design configurations for a binary two-zone DSE such that the maximum sidelobe intensity M is 0.1 (off-white region).

Fig. 6
Fig. 6

Phase transmission ϕ0G that minimizes the spot size G subject to a sidelobe intensity M<0.1, as a function of zone boundary for a binary two-zone DSE. The corresponding values of spot size G, Strehl ratio S, and sidelobe intensity M are shown. The solid vertical line delimits the region in which the π-phase-shift element represents the best solution.

Fig. 7
Fig. 7

Diffraction pattern obtained with a binary DSE (solid curve) with ϕ0=π, α1=0.3, and α2=0.7. For comparison, the Airy disk pattern (dotted curve) is also shown. Spot size G=0.5, Strehl ratio S=0.04, sidelobe intensity M=1.65.

Fig. 8
Fig. 8

Space of solutions that satisfy the requirement of spot size G<0.5 and sidelobe intensity M<0.1 in the confocal imaging mode for a three-zone multiphase DSE with α1=0.3, and α2=0.7. Also, ϕ1=0. The black region indicates unacceptable solutions. The gray-level code applied to the solutions defines the Strehl ratio.

Fig. 9
Fig. 9

Illustration of a diffraction pattern (solid curve) belonging to the set of solutions shown in Fig. 8. For this case spot size G=0.44, Strehl ratio S=0.0273, and sidelobe intensity M=0.0875. The phase of each zone is given by ϕ1=0, ϕ2=0.74π, ϕ3=1.68π. Confocal imaging is assumed. For comparison, the result of a binary DSE with ϕ0=π (dashed curve) and the Airy disk pattern (dotted curve) are also shown.

Fig. 10
Fig. 10

Illustration of a diffraction pattern from a three-zone multiphase DSE with α1=0.3 and α2=0.7 satisfying G<0.8 and M<0.2. For this case spot size G=0.8, Strehl ratio S=0.42, and sidelobe intensity M=0.127. The phase of each zone is given by ϕ1=0, ϕ2=0.91π, ϕ3=1.32π. Conventional imaging is assumed. For comparison, the result obtained with ϕ0=π (dashed curve) and the Airy disk pattern (dotted curve) are also shown.

Fig. 11
Fig. 11

Diffraction pattern obtained from the design solution that one calculates by constraining the zeros for designs (a) 1 and (b) 3. The relevant data are shown in Table 2. The three curves compare the solutions obtained with a DSE (solid curve), a TFE (dashed curve), and the Airy disk pattern (dotted curve).

Fig. 12
Fig. 12

Normalized spot size as a function of the parameter β12 of the series expansion, so that the Strehl ratio has a value (a) S=0.8 and (b) S=0.5. Each curve in each case is labeled with a letter that refers to a particular value of phase transmittance and corresponding value of β02. In the case S=0.8 the following values are utilized: a: ϕ0=π, β02=0.0528; b: ϕ0=0.8π, β02=0.0587; c: ϕ0=0.6π, β02=0.0833; d: ϕ0=0.4π, β02=0.1755; e: ϕ0=0.3π, β02=0.4139. In the case of S=0.5 the following values are utilized: a: ϕ0=π, β02=0.1464; b: ϕ0=0.8π, β02=0.1656; c: ϕ0=0.75π, β02=0.1782; d: ϕ0=0.65π, β02=0.2206; e: ϕ0=0.55π, β02=0.3161. The calculation of G assumes a second-order approximation of the field.  

Tables (2)

Tables Icon

Table 1 Performance of Optimized Binary DSE’s a

Tables Icon

Table 2 Solutions Constraining the Zeros of the Diffraction Pattern a

Equations (11)

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

Ψ(η)=j=1N exp(iϕj)αj2 2J1(αjη)αjη-αj-12 2J1(αj-1η)αj-1η,
Ψ(η)=2J1(η)η-[1-exp(iϕ0)](-1)N+1j=1N-1(-1)j×αj2 2J1(αjη)αjη,
G=1-2(β02+β12-2β02β12)sin2(12ϕ0)1-4(1-β12)β12 sin2(12ϕ0)1/2,
S=1-4(1-β02)β02 sin2(12ϕ0),
Ψ(ηk)=j=1N exp(iϕj)ψj(ηk)=0,k=1,2,,K,
β02=12(1-|k0|),
k02=S+sin2 12ϕ0-1sin2 12ϕ0.
ϕ0m=2 arcsin 1-S.
(-1)N+1j=1N-1(-1)jαj2=β02,
(-1)N+1j=1N-1(-1)jαj4=β12.
Minimizeβ12-(-1)N+1j=1N-1(-1)jαj42subjecttoβ02-(-1)N+1j=1N-1(-1)jαj2=0.

Metrics