Abstract

Superresolution performance of a plano-convex lens made of absorbing glass is analyzed numerically. It was found that a reduction of the radius of the Airy disk depends solely on the center transmittance of the lens (a zero edge thickness is assumed) for any reasonable ratio of radius of curvature of the convex surface and the lens radius. The modest decrease in the size of the central diffraction peak is followed by a large decrease of its energy content and a rapid brightening of the diffraction rings. The most that can be achieved with such a lens is a reduction of the radius of the Airy disk to 71% of the corresponding clear aperture value, followed by approximately 78% of the energy being diverted into diffraction rings.

© 1997 Optical Society of America

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References

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1994 (1)

1988 (2)

1985 (1)

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

1983 (2)

1979 (1)

1978 (1)

1974 (2)

1971 (1)

1963 (1)

1962 (1)

1949 (1)

Andreic, Ž.

Barakat, R.

Hegedus, Z. S.

C. J. R. Sheppard, Z. S. Hegedus, “Axial behavior of pupil–plane filters,” J. Opt. Soc. Am. A 5, 643–647 (1988).
[CrossRef]

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

Levin, E.

Mino, M.

Okano, Y.

Osterberg, H.

Rivolta, C.

Sheppard, C. J. R.

Tschunko, H. F. A.

Wilkins, J. E.

Appl. Opt. (9)

J. Opt. Soc. Am. (3)

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

Opt. Acta (1)

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

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Figures (5)

Fig. 1
Fig. 1

Two possibilities for realizing a superresolution filter with an absorbing-glass positive lens: a, plano–parallel filter; b, achromatic objective. Gray glass is indicated by hatching.

Fig. 2
Fig. 2

Radius of the first diffraction minimum as a function of the lens center transmittance in units of the radius of the first diffraction minimum for a clear aperture.

Fig. 3
Fig. 3

Energy content in the central peak of the diffraction pattern as a function of the filter center transmittance. Filled circles indicate results of individual calculations.

Fig. 4
Fig. 4

Total (spatially integrated) energy content of the first four diffraction rings relative to the energy in the central peak of the diffraction pattern. The intensity of the higher-order rings is generally very small and drops smoothly with the increase of the ring order. The uppermost curve corresponds to the first diffraction ring and the lowermost curve to the fourth diffraction ring.

Fig. 5
Fig. 5

Integral transmittance of a lens with a zero center thickness as a function of the lens edge transmittance.

Equations (10)

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

x=rrl,
u=Rrl,
tc=exp-κrlu-u2-11/2,
txexp-κrlu2-x21/2-u2-11/2.
u1=u2 and κ1rl1=κ2rl2.
u1,
txexp-κrl1-x2/2u.
Aϑ=02π0r tρcos2πλ ρcos ϕsin ϑρdρdϕ,
Iϑ=AϑA02.
ϑo=1.22λr,

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