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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 5 — May. 1, 1983
  • pp: 707–719

Aberration-free nonparaxial self-imaging

Y. Cohen-Sabban and D. Joyeux  »View Author Affiliations

JOSA, Vol. 73, Issue 5, pp. 707-719 (1983)

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The fields diffracted by planar one- or two-dimensional periodic objects, and in particular their Fourier and Fresnel self-images, can be computed with the aid of a ray-tracing technique based on the Fermat principle. This method (geometrical self-imaging) yields accurate results for any numerical aperture and image field. An analytical study of the image formation, carried out in the fourth-order approximation for the phase, leads to the definition of selfimaging aberrations. These aberrations are strongly dependent on spatial frequency and render the well-known relationships derived by Rayleigh for the location and magnification of self-images approximate at best. The aberrations can be described graphically by a phase diagram and a magnification diagram, which permit interpretation of the properties of high-aperture, large-field self-images and the prediction of optimal imaging conditions. In the case of large magnifications (10OX and larger), we present a simple method to eliminate all fourth-order aberrations completely and even sixth-order ones partially. This method consists of introducing a compensating spherical aberration to the incident wave, e.g., by the insertion of a glass plate of appropriate index and thickness just before the object. Thus object spatial frequencies up to about 800 m-1 can be imaged almost without aberration for several image periods.

© 1983 Optical Society of America

Y. Cohen-Sabban and D. Joyeux, "Aberration-free nonparaxial self-imaging," J. Opt. Soc. Am. 73, 707-719 (1983)

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