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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 5 — May. 1, 2001
  • pp: 1056–1061

Flatland optics. II. Basic experiments

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


JOSA A, Vol. 18, Issue 5, pp. 1056-1061 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001056


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Abstract

In “Flatland optics: fundamentals” [J. Opt. Soc. Am. A 17, 1755 (2000)] 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/cosα. 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 [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)] of 1884. We now want to establish the reality or objectivity of the 2D wavelength Λ by some basic experiments similar to those that demonstrated roughly 200 years ago the wave nature of light. Specifically, we describe how to measure the 2D wavelength Λ by mean of five different arrangements that involve Young’s biprism configuration, Talbot’s self-imaging effect, measuring the focal length of a Fresnel zone plate, and letting light be diffracted by a double slit and by a grating. We also performed experiments with most of these arrangements. The results reveal that the theoretical wavelength, as predicted by our Flatland optics theory, does indeed coincide with the wavelength Λ as measured by Flatland experiments. Finally, we present an alternative way to understand Flatland optics in the spatial frequency domains of Flatland and Spaceland.

© 2001 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(100.1160) Image processing : Analog optical image processing
(110.2990) Imaging systems : Image formation theory
(200.3050) Optics in computing : Information processing
(260.1960) Physical optics : Diffraction theory

Citation
Adolf W. Lohmann, Dayong Wang, Avi Pe'er, and Asher A. Friesem, "Flatland optics. II. Basic experiments," J. Opt. Soc. Am. A 18, 1056-1061 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-5-1056


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