Abstract

The validity of the Debye approximation is reexamined. It is shown that for paraxial systems with strong aberrations the Debye approximation may not be valid, even for systems with a large Fresnel number. The particular case of spherical aberration is considered. Extension to high-aperture systems is discussed.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Li and E. Wolf, J. Opt. Soc. Am. A 1, 801 (1984).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993).
  3. C. J. R. Sheppard and P. Török, J. Opt. Soc. Am. A 15, 3016 (1998).
    [CrossRef]
  4. W. Hsu and R. Barakat, J. Opt. Soc. Am. A 11, 623 (1994).
    [CrossRef]
  5. P. Török, J. Opt. Soc. Am. A 15, 3009 (1998).
    [CrossRef]

1998 (2)

1994 (1)

1984 (1)

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 (1)

Fig. 1
Fig. 1

Intensity along the axis for a lens with 17.5 wavelengths of primary spherical aberration. The curves on the left show the results for an unapodized system b=0. The top left-hand curve, for a Fresnel number N of 10,000, is identical to that predicted by the Debye approximation. The middle and bottom left-hand curves, for N=100 and N=10, respectively, show pronounced asymmetry, demonstrating breakdown of the Debye approximation. The curves on the right are for an apodized lens, b=0.5. The apodization also introduces an asymmetry, which in the middle right-hand plot almost cancels that caused by the finite Fresnel number. An apodization with a value of b=0.25 would result from a lens with semiangle of convergence of 75°.

Equations (14)

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

Ur,z=-ika2f+zexpikr22f+zexpikz×01AρJ0kρraf+zexp-ikzρ2a22ff+zρdρ,
vN=kraf+z,uN=kra2ff+z,
N=a2λf,
Ur,z=-2πiN11-uN/2πN×expivN24πN1-uN/2πN×01J0vNρexp-12iuNρ2ρdρ.
kraf=vN1-uN/2πN,kra2f2=uN1-uN/2πN.
Ur,z=-2πiN01J0vNρexp-12iuρ2ρdρ,
v=kra/f, u=kza2/f2,
uN2πN
zf.
Aρ=1-bρ2exp-2πiA40ρ4.
z=-f1-N/4A40
uN=-8πA40.
A40N/4.
I0,z=2π2N2ff+22×01exp-iπNtzfff+z×exp-2πiA40t21-btdt.

Metrics