Abstract

The influence of aperture stop position on the focusing properties of a lens is investigated. Expressions are obtained for the optical coordinates in terms of the system geometry. If the aperture stop is placed in the front focal plane of the lens, the effective Fresnel number is infinite. For other positions, the effective Fresnel number can be made either positive or negative, corresponding to focal shift either toward or away from the lens and a resulting coordinate rescaling.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957).
    [CrossRef]
  2. A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Opt. Acta 23, 245–250 (1976).
    [CrossRef]
  3. J. Erkkila, M. Rogers, “Diffracted fields in the focal region of a convergent wave,” J. Opt. Soc. Am. 71, 904–905 (1981).
    [CrossRef]
  4. J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981).
    [CrossRef]
  5. Y. Li, E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A 1, 801–808 (1984).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).
  7. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  8. W. Hsu, R. Barakat, “Stratton–Chu vectorial diffraction of electromagnetic fields by apertures with application to small-Fresnel-number systems,” J. Opt. Soc. Am. A 11, 623–629 (1994).
    [CrossRef]
  9. V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997).
    [CrossRef]
  10. H. Ling, S. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. 59, 559–567 (1984).
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  12. R. G. Wenzel, “Effect of the aperture–lens separation on the focal shift in large-F-number systems,” J. Opt. Soc. Am. A 4, 340–345 (1987).
    [CrossRef]
  13. I. S. Gradstein, I. M. Ryshik, Tables of Series, Products, and Integrals (Deutsch, Frankfurt, Germany, 1981).

1997 (1)

V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997).
[CrossRef]

1994 (1)

1987 (1)

1984 (2)

1981 (2)

J. Erkkila, M. Rogers, “Diffracted fields in the focal region of a convergent wave,” J. Opt. Soc. Am. 71, 904–905 (1981).
[CrossRef]

J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981).
[CrossRef]

1976 (1)

A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

1966 (1)

1957 (1)

G. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957).
[CrossRef]

Arimoto, A.

A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

Barakat, R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).

Dhayalan, V.

V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997).
[CrossRef]

Erkkila, J.

Farnell, G.

G. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gradstein, I. S.

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products, and Integrals (Deutsch, Frankfurt, Germany, 1981).

Hsu, W.

Kogelnik, H.

Lee, S.

Li, T.

Li, Y.

Ling, H.

Rogers, M.

Ryshik, I. M.

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products, and Integrals (Deutsch, Frankfurt, Germany, 1981).

Spejelkavik, B.

J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981).
[CrossRef]

Stamnes, J.

V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997).
[CrossRef]

J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981).
[CrossRef]

Wenzel, R. G.

Wolf, E.

Appl. Opt. (1)

Can. J. Phys. (1)

G. Farnell, “Calculated intensity and phase distribution in the image space of a microwave lens,” Can. J. Phys. 35, 777–783 (1957).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

A. Arimoto, “Intensity distribution of aberration-free diffraction patterns due to circular apertures in large f-number optical systems,” Opt. Acta 23, 245–250 (1976).
[CrossRef]

Opt. Commun. (1)

J. Stamnes, B. Spejelkavik, “Focusing at small angular apertures in the Debye and Kirchhoff approximations,” Opt. Commun. 40, 81–85 (1981).
[CrossRef]

Pure Appl. Opt. (1)

V. Dhayalan, J. Stamnes, “Focusing of mixed-dipole waves,” Pure Appl. Opt. 6, 317–345 (1997).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1975).

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products, and Integrals (Deutsch, Frankfurt, Germany, 1981).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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 (4)

Fig. 1
Fig. 1

Geometry of the optical system. Light divergent from a point is incident on an aperture stop, placed a distance f+d from a lens of focal length f.

Fig. 2
Fig. 2

Exit pupil of the system is in this case the virtual image of the aperture stop formed by the lens.

Fig. 3
Fig. 3

Contours of constant intensity in the meridional plane for the case in which a=500 µm, f=1000 µm, λ=632.8 nm, and R0, for values of d of 0 and 20 mm. The contours are plotted every 2.5 dB.

Fig. 4
Fig. 4

Contours of constant intensity in the meridional plane for the case in which a=500 µm, f=1000 µm, λ=632.8 nm, and R0=100 mm, for values of d of 0 and 20 mm. The contours are plotted every 2.5 dB.

Equations (25)

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

N0=a2λf=(a/f)2(f/λ),
U(r0)=2π exp(ikz0)iλz0 expikr022z0×0a expikr1221R0+1z0J0kr0r1z0r1dr1,
U(r0)=U(r0)exp-ikr022 f
U(r, z)=-4π2 exp[ik(z0+z)]λ2z0z×00aJ0kr0r1z0J0krr0z×expikr22zexpik2 r021z0+1z-1f+r121R0+1z0r1dr1r0dr0.
0 exp(-ibx2)J0(αx)J0(βx)xdx=i2b expi(α2+β2)4bJ0αβ2b.
d=z0-f,
ζ=z-f,
ρ=r1/a,
U(r, z)=ikfa22(f2-ζd) exp[ik(z+z0)]expikdr22(f2-ζd)×012 exp-12iuρ2J0(vρ)ρdρ,
v=kraff2-ζd,
u=ka2ζf2-ζd-1R0.
v=2πN0(f/a) rf+ζ,
u=2πN0 ζf+ζ,
N0=a2λf,
v=kr(a/f),
u=kζ(a/f)2,
u0=ka2R0,
S=f2f2-ζd,
U(r, z)=iπNS exp[ik(z+z0)]expi dζf2 v22(u+u0)×012 exp-12iuρ2J0(vρ)ρdρ,
v=2πN0S ra,
u=2πN0Sζ-u0.
N=-a2λd,
S=11+N0/N(ζ/f).
ζd=f2,
v0=2π raN01-N0N fR0,

Metrics