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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. 17, Iss. 10 — Oct. 1, 2000
  • pp: 1755–1762

Flatland optics: fundamentals

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


JOSA A, Vol. 17, Issue 10, pp. 1755-1762 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001755


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Abstract

“Flatland” is the title of a 120-year-old science fiction story. It describes the life of creatures living in a two-dimensional (2D) Flatland. A superior creature living in the three-dimensional (3D) spaceland, as we do, can easily inspect, for example, the inside of a Flatland house, as well as the content of a flat man’s stomach without leaving any trace. Furthermore, the 3D person has supernatural powers that enable him to change the laws of physics in Flatland. We present here the concept of a 2D Flatland optics with one transversal coordinate x and one longitudinal coordinate z. The other transversal coordinate y allows total inspection of Flatland optics, and the freedom to change the wavelength, without using something like nonlinear optics or a Doppler shift. Monochromatic 3D light can be converted reversibly into polychromatic 2D light. A large variety of 2D systems and 2D effects will be presented here and in follow-up contributions. An epilogue faces the question, how “real” is Flatland optics?

© 2000 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, Avi Pe'er, Dayong Wang, and Asher A. Friesem, "Flatland optics: fundamentals," J. Opt. Soc. Am. A 17, 1755-1762 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-10-1755


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References

  1. E. A. Abbott, Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952).
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  6. A. W. Lohmann, A. Pe’er, Dayong Wang, and A. A. Friesem, “Flatland optics: basic experiments,” available from the authors.
  7. A. W. Lohmann, A. Pe’er, Dayong Wang, A. A. Friesem, “Flatland optics: achromatic diffraction,” available from the authors.
  8. H. E. Talbot, “Facts relating to optical science, No. IV,” Philos. Mag. 9, 401–407 (1836).
  9. W. Klaus, Y. Arimoto, and K. Kodate, “High-performance Talbot illuminators,” Appl. Opt. 37, 4357–4365 (1998).
  10. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967).

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