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IX - The diffraction theory of aberrations

Max Born
Affiliation:
Georg-August-Universität, Göttingen, Germany and University of Edinburgh
Emil Wolf
Affiliation:
University of Rochester, New York
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Summary

IN Chapter V we studied the effects of aberrations on the basis of geometrical optics. In that treatment the image was identified with the blurred figure formed by the points of intersection of the geometrical rays with the image plane. Since geometrical optics gives an approximate model valid in the limit of very short wavelengths, it is to be expected that the geometrical theory gradually loses its validity as the aberrations become small. For example, in the limiting case of a perfectly spherical convergent wave issuing from a circular aperture, geometrical optics predicts for the focal plane an infinite intensity at the focus and zero intensity elsewhere, whereas, as has been shown in §8.5.2, the real image consists of a bright central area surrounded by dark and bright rings (the Airy pattern). In the neighbourhood of the focal plane the light distribution has also been seen to be of a much more complicated nature (see Fig. 8.41) than geometrical optics suggests. We are thus led to the study of the effects of aberrations on the basis of diffraction theory.

The first investigations in this field are due to Rayleigh. His main contribution was the formulation of a criterion (discussed in §9.3) which, in an extended form, has come to be widely used for determining the maximum amounts of aberrations that may be tolerated in optical instruments. The subject was carried further by the researches of many writers who investigated the effects of various aberrations, and we may mention, in particular, the more extensive treatments by Steward, Picht, and Born.

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Principles of Optics
Electromagnetic Theory of Propagation, Interference and Diffraction of Light
, pp. 517 - 553
Publisher: Cambridge University Press
Print publication year: 1999

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  • The diffraction theory of aberrations
  • Max Born, Georg-August-Universität, Göttingen, Germany and University of Edinburgh, Emil Wolf, University of Rochester, New York
  • Book: Principles of Optics
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139644181.018
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  • The diffraction theory of aberrations
  • Max Born, Georg-August-Universität, Göttingen, Germany and University of Edinburgh, Emil Wolf, University of Rochester, New York
  • Book: Principles of Optics
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139644181.018
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • The diffraction theory of aberrations
  • Max Born, Georg-August-Universität, Göttingen, Germany and University of Edinburgh, Emil Wolf, University of Rochester, New York
  • Book: Principles of Optics
  • Online publication: 05 April 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139644181.018
Available formats
×