Abstract

The derivation of the point spread function in general uses the mathematical theory of diffraction in detail. This derivation uses geometric relations of the incoming and diffracted wave front to establish the diffraction integral, which is equal to the Hankel integral for the Bessel function of the first kind of order one.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Morgan, Geometrical and Physical Optics (McGraw-Hill, New York, 1953).
  2. F. A. Jenkins, H. E. White, Fundamentals of Optics, (McGraw Hill, New York, 1976).
  3. G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).
  4. E. Lommel, Z. Math. Phys. 15, 141 (1870).
  5. F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 98.
  6. N. G. Watson, A Treatise of the Theory of Bessel Functions (Cambridge U.P., London, 1944), p. 48.
  7. D. Hilbert, Anschauliche Geometrie (Springer-Verlag, Berlin, 1932); English translation: Geometry and imagination (Chelsea, New York, 1952).

1870

E. Lommel, Z. Math. Phys. 15, 141 (1870).

1835

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Airy, G. B.

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Bowman, F.

F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 98.

Hilbert, D.

D. Hilbert, Anschauliche Geometrie (Springer-Verlag, Berlin, 1932); English translation: Geometry and imagination (Chelsea, New York, 1952).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics, (McGraw Hill, New York, 1976).

Lommel, E.

E. Lommel, Z. Math. Phys. 15, 141 (1870).

Morgan, J.

J. Morgan, Geometrical and Physical Optics (McGraw-Hill, New York, 1953).

Watson, N. G.

N. G. Watson, A Treatise of the Theory of Bessel Functions (Cambridge U.P., London, 1944), p. 48.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics, (McGraw Hill, New York, 1976).

Trans. Cambridge Philos. Soc.

G. B. Airy, Trans. Cambridge Philos. Soc. 5, 283 (1835).

Z. Math. Phys.

E. Lommel, Z. Math. Phys. 15, 141 (1870).

Other

F. Bowman, Introduction to Bessel Functions (Dover, New York, 1958), pp. 98.

N. G. Watson, A Treatise of the Theory of Bessel Functions (Cambridge U.P., London, 1944), p. 48.

D. Hilbert, Anschauliche Geometrie (Springer-Verlag, Berlin, 1932); English translation: Geometry and imagination (Chelsea, New York, 1952).

J. Morgan, Geometrical and Physical Optics (McGraw-Hill, New York, 1953).

F. A. Jenkins, H. E. White, Fundamentals of Optics, (McGraw Hill, New York, 1976).

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

Geometry of wave fronts for the generation of image points. The left-hand side shows the cosines of the phase differences xt between OA and OA′.

Equations (5)

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

A = 0 1 cos ( x t ) d t = sin x / x .
I = A 2 = ( sin x / x ) 2 .
A = ( 4 / π ) 0 1 ( 1 t 2 ) 0.5 cos ( x t ) · d t .
A = ( 2 / x ) [ ( 2 x / π ) 0 1 ( 1 t 2 ) 0.5 cos ( x t ) · d t ] .
I = A 2 = [ 2 J 1 x / x ] 2 .

Metrics