Abstract

For optical alignment, it may be convenient to use a three-dimensional diffraction pattern with zero irradiance along the optical axis. This pattern is created here by using annular screens in the form of a phase daisy, a daisy flower, or a pie, with an even number of slices of an equal central angle and with every other slice with a phase retardation of 180°. We recognize this form of angular variation as a particular solution of a wider set of functions that are able to produce zero axial irradiance.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. McLeod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, p. 592 (1954).
    [CrossRef]
  2. J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
    [CrossRef]
  3. A. C. S. van Heel, “Modern alignment devices,” in Progress in Optics, E. Wolf, ed. (Springer-Verlag, New York, 1961), Vol. 1, pp. 289–329.
    [CrossRef]
  4. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964).
    [CrossRef]
  5. K. G. Beauchamp, Walsh Functions and Their Applications (Academic, New York, 1975), pp. 6–7.

1964 (1)

1958 (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[CrossRef]

1954 (1)

Beauchamp, K. G.

K. G. Beauchamp, Walsh Functions and Their Applications (Academic, New York, 1975), pp. 6–7.

Dyson, J.

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[CrossRef]

McCutchen, C. W.

McLeod, J. H.

van Heel, A. C. S.

A. C. S. van Heel, “Modern alignment devices,” in Progress in Optics, E. Wolf, ed. (Springer-Verlag, New York, 1961), Vol. 1, pp. 289–329.
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. R. Soc. London Ser. A (1)

J. Dyson, “Circular and spiral diffraction gratings,” Proc. R. Soc. London Ser. A 248, 93–106 (1958).
[CrossRef]

Other (2)

A. C. S. van Heel, “Modern alignment devices,” in Progress in Optics, E. Wolf, ed. (Springer-Verlag, New York, 1961), Vol. 1, pp. 289–329.
[CrossRef]

K. G. Beauchamp, Walsh Functions and Their Applications (Academic, New York, 1975), pp. 6–7.

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 (3)

Fig. 1
Fig. 1

Image irradiance distribution at several parallel planes beyond the pupil plane when using 32 petals. The z coordinate, as defined in Fig. 2, takes the following values: (a) z = 1 m (paraxial focus plane), (b) z = 0.95 m, (c) z = 0.85 m, (d) z = 0.60 m.

Fig. 2
Fig. 2

Schematic diagram of the optical system that forms the image of a point source.

Fig. 3
Fig. 3

Polar variation of the complex amplitude in the pupil plane: (a) one-dimensional representation. The two curves shown are the Rademacher function m = 1, solid curve, and m = 3, dashed curve; (b) actual two-dimensional representation. The shaded portions have a transmission of −1.

Equations (4)

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

p ( r , ϕ ; W 20 ) = 0 2 π Ω Ω p ˜ ( ρ , θ ) × exp { i 2 π [ W 20 ( ρ / Ω ) 2 + r ρ cos ( ϕ - θ ) ] } ρ d ρ d θ ,
p ( W 20 ) = 0 2 π Ω Ω p ˜ ( ρ , θ ) exp [ i 2 π W 20 ( ρ / Ω ) 2 ] ρ d ρ d θ .
p ( W 20 ) = 2 π Ω Ω p ˜ av ( ρ ) exp [ i 2 π W 20 ( ρ / Ω ) 2 ] ρ d ρ ,
A ( θ ) = F m ( θ ) = sign [ sin ( 2 m - 1 θ ) ] ,

Metrics