OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

View Full Text Article

Enhanced HTML    Acrobat PDF (568 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

Original Manuscript: May 31, 2000
Revised Manuscript: September 13, 2000
Manuscript Accepted: November 1, 2000
Published: May 1, 2001

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)

Sort:  Author  |  Year  |  Journal  |  Reset  


Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited