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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 51, Iss. 2 — Feb. 1, 1961
  • pp: 152–157

Total Illumination in a Diffraction Image Containing Spherical Aberration

RICHARD BARAKAT  »View Author Affiliations

JOSA, Vol. 51, Issue 2, pp. 152-157 (1961)

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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.

RICHARD BARAKAT, "Total Illumination in a Diffraction Image Containing Spherical Aberration," J. Opt. Soc. Am. 51, 152-157 (1961)

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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).

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