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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 10 — Oct. 1, 2000
  • pp: 1864–1869

General linear optical coordinate transformations

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

JOSA A, Vol. 17, Issue 10, pp. 1864-1869 (2000)

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New optical configurations for performing general coordinate transformation operations of shear, rotation, and their combination are presented. These configurations consist of refractive spherical and cylindrical lenses that are readily available. Typically, high-resolution imagery can be obtained, depending on the size of the input object, the illumination wavelength, and the f-number of the lenses. Basic and more general configurations are presented, along with experimental results clearly showing image shearing, rotation, and a combination of these with high-quality output imagery.

© 2000 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6110) Fourier optics and signal processing : Spatial filtering
(100.0100) Image processing : Image processing
(100.1160) Image processing : Analog optical image processing

Original Manuscript: August 18, 1999
Revised Manuscript: May 10, 2000
Manuscript Accepted: May 10, 2000
Published: October 1, 2000

Dayong Wang, Avi Pe’er, Asher A. Friesem, and Adolf W. Lohmann, "General linear optical coordinate transformations," J. Opt. Soc. Am. A 17, 1864-1869 (2000)

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  1. A. Sawchuk, “Space-variant image restoration by coordinate transformation,” J. Opt. Soc. Am. 64, 138–144 (1974). [CrossRef]
  2. D. Casasent, D. Psaltis, “Deformation invariant, space variant optical pattern recognition,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 289–356.
  3. Ji-Hong Feng, Min-Xian Wu, Guo-Fan Jin, “Invariant joint transform correlator using coordinate transformation,” Opt. Eng. 35, 3392–3399 (1996). [CrossRef]
  4. G. Häusler, N. Streibl, “Optical compensation of geometrical distortion by deformable mirror,” Opt. Commun. 42, 381–385 (1982). [CrossRef]
  5. A. W. Lohmann, N. Streibl, “Map transformations by optical anamorphic processing,” Appl. Opt. 22, 780–783 (1983). [CrossRef] [PubMed]
  6. D. Mendlovic, H. M. Ozaktas, “Optical-coordinate transformation methods and optical-interconnection architecture,” Appl. Opt. 32, 5119–5124 (1993). [CrossRef] [PubMed]
  7. B. Braunecker, O. Bryngdahl, B. Schnell, “Optical system for image rotation and magnification,” J. Opt. Soc. Am. 70, 137–141 (1980). [CrossRef]
  8. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64, 1092–1099 (1974). [CrossRef]
  9. O. Bryngdahl, “Optical map transformations,” Opt. Commun. 10, 164–168 (1974). [CrossRef]
  10. J. N. Cederquist, A. M. Tai, “Computer-generated holograms for geometric transformations,” Appl. Opt. 23, 3099–3104 (1984). [CrossRef] [PubMed]
  11. W. J. Hossack, A. M. Darling, A. Dahdouh, “Coordinate transformations with multiple computer-generated optical elements,” J. Mod. Opt. 34, 1235–1250 (1987). [CrossRef]
  12. M. A. Stuff, J. N. Cederquist, “Coordinate transformations realizable with multiple holographic optical elements,” J. Opt. Soc. Am. A 7, 977–981 (1990). [CrossRef]
  13. N. Davidson, A. A. Friesem, E. Hasman, “Optical coordinate transformations,” Appl. Opt. 31, 1067–1073 (1992). [CrossRef] [PubMed]
  14. S. K. Case, P. R. Haugen, O. J. Loberge, “Multifacet holographic optical elements for wave front transformations,” Appl. Opt. 20, 2670–2675 (1981). [CrossRef] [PubMed]
  15. J. W. Goodman, P. Kellman, E. W. Hansen, “Linear space-variant optical processing of 1-D signals,” Appl. Opt. 16, 733–738 (1977). [CrossRef] [PubMed]
  16. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993). [CrossRef]
  17. K. G. Larkin, M. A. Oldfield, H. Klemm, “Fast Fourier method for the accurate rotation of sampled images,” Opt. Commun. 139, 99–106 (1997). [CrossRef]

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