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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2095–2097

Flatland optics. III. Achromatic diffraction

Adolf W. Lohmann, Avi Pe’er, Dayong Wang, and Asher A. Friesem  »View Author Affiliations

JOSA A, Vol. 18, Issue 9, pp. 2095-2097 (2001)

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In the previous two sections of “Flatland optics” [J. Opt. Soc. Am. A 17, 1755 (2000); J. Opt. Soc. Am. A 18, 1056 (2001)] we described the basic principles of two-dimensional (2D) optics and showed that a wavelength λ in three-dimensional (3D) space (x, y, z) may appear in Flatland (x, z) as a wave with another wavelength Λ=λ/cos α. The tilt angle α can be modified by a 3D-Spaceland individual, who then is able to influence the 2D optics in a way that must appear to be magical to 2D-Flatland individuals—in the spirit of E. A. Abbott’s science fiction story of 1884 [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)]. Here we show how the light from a white source can be perceived in Flatland as perfectly monochromatic, so diffraction with white light will be free of color blurring and the contrast of interference fringes can be 100%. The basic considerations for perfectly achromatic diffraction are presented, along with experimental illustration of Talbot self-imaging performed with broadband illumination.

© 2001 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(050.1960) Diffraction and gratings : Diffraction theory

Original Manuscript: October 23, 2000
Revised Manuscript: February 14, 2001
Manuscript Accepted: February 14, 2001
Published: September 1, 2001

Adolf W. Lohmann, Avi Pe’er, Dayong Wang, and Asher A. Friesem, "Flatland optics. III. Achromatic diffraction," J. Opt. Soc. Am. A 18, 2095-2097 (2001)

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  1. E. A. Abbot, Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952).
  2. A. W. Lohmann, A. Pe’er, D. Wang, A. A. Friesem, “Flatland optics. I. Fundamentals,” J. Opt. Soc. Am. A 17, 1755–1762 (2000). [CrossRef]
  3. A. W. Lohmann, D. Wang, A. Pe’er, A. A. Friesem, “Flatland optics. II. Basic experiments,” J. Opt. Soc. Am. A 18, 1056–1061 (2000). [CrossRef]
  4. B. Packross, R. Eschbach, O. Bryngdahl, “Achromatization of the self-imaging (Talbot) effect,” Opt. Commun. 50, 205–209 (1984). [CrossRef]
  5. E. E. Sicre, N. Bolognini, M. Garavaglia, “Partial achromatization of the self-imaging phenomenon,” Appl. Opt. 24, 929–930 (1985). [CrossRef]
  6. G. Indebetouw, “Polychromatic self-imaging,” J. Mod. Opt. 35, 243–252 (1988). [CrossRef]
  7. P. Andres, J. Lancis, E. E. Sicre, E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104, 39–45 (1993). [CrossRef]
  8. E. Tajahuerce, P. Andres, M. Fernandez-Alonso, V. Climent, “White-light array generation with a diffractive lenslet array,” J. Mod. Opt. 46, 49–63 (1999). [CrossRef]
  9. N. Guerineau, J. Primot, “Nondiffracting array generation using an N-wave interferometer,” J. Opt. Soc. Am. A 16, 293–298 (1999). [CrossRef]

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