Abstract

The total illumination (or encircled energy) in a diffraction image containing spherical aberration is studied for various amounts of third- and fifth-order aberration. The Zernike polynomials are used to represent spherical aberration. The evaluation of the total illumination was done numerically, using double Gauss quadrature and 49 quadrature points. Contour maps of the total illumination were constructed and compared with the aberration-free case examined previously by E. Wolf.

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959), Chap. 9, p. 458. (This chapter contains an extensive survey of the field.)
  2. Lord Rayleigh, Phil. Mag. 11, 214 (1881).
  3. E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).
  4. See work cited in footnote 1, p. 463.
  5. G. N. Watson, Treatise on the Theory of Bessel Functions (Cambridge University Press, New York, 1944), p. 134.
  6. J. O. Irwin, On Quadrature and Cubature (Cambridge University Press, Cambridge, England, 1923), p. 21.
  7. G. Lansraux and G. Boivin, Can. J. Phys. 36, 1696 (1958).
  8. L. C. Martin, Trans. Opt. Soc. 23, 63 (1921).
  9. J. Focke, Optica Acta 3, 161 (1956).

Boivin, G.

G. Lansraux and G. Boivin, Can. J. Phys. 36, 1696 (1958).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959), Chap. 9, p. 458. (This chapter contains an extensive survey of the field.)

Focke, J.

J. Focke, Optica Acta 3, 161 (1956).

Irwin, J. O.

J. O. Irwin, On Quadrature and Cubature (Cambridge University Press, Cambridge, England, 1923), p. 21.

Lansraux, G.

G. Lansraux and G. Boivin, Can. J. Phys. 36, 1696 (1958).

Martin, L. C.

L. C. Martin, Trans. Opt. Soc. 23, 63 (1921).

Rayleigh, Lord

Lord Rayleigh, Phil. Mag. 11, 214 (1881).

Watson, G. N.

G. N. Watson, Treatise on the Theory of Bessel Functions (Cambridge University Press, New York, 1944), p. 134.

Wolf, E.

E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959), Chap. 9, p. 458. (This chapter contains an extensive survey of the field.)

Other (9)

M. Born and E. Wolf, Principles of Optics (Pergamon Press, London, 1959), Chap. 9, p. 458. (This chapter contains an extensive survey of the field.)

Lord Rayleigh, Phil. Mag. 11, 214 (1881).

E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

See work cited in footnote 1, p. 463.

G. N. Watson, Treatise on the Theory of Bessel Functions (Cambridge University Press, New York, 1944), p. 134.

J. O. Irwin, On Quadrature and Cubature (Cambridge University Press, Cambridge, England, 1923), p. 21.

G. Lansraux and G. Boivin, Can. J. Phys. 36, 1696 (1958).

L. C. Martin, Trans. Opt. Soc. 23, 63 (1921).

J. Focke, Optica Acta 3, 161 (1956).

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