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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 10 — Oct. 1, 2004
  • pp: 1875–1885

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

Jésus Lancis, Gladys Mı́nguez-Vega, Enrique Tajahuerce, Vicent Climent, Pedro Andrés, and José Caraquitena  »View Author Affiliations

JOSA A, Vol. 21, Issue 10, pp. 1875-1885 (2004)

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Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spatial domain, which is totally space variant, to the spectral domain, which is totally space invariant, with the chromatic correction remaining unaltered.

© 2004 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics

Original Manuscript: January 12, 2004
Revised Manuscript: May 7, 2004
Manuscript Accepted: May 7, 2004
Published: October 1, 2004

Jésus Lancis, Gladys Mı́nguez-Vega, Enrique Tajahuerce, Vicent Climent, Pedro Andrés, and José Caraquitena, "Chromatic compensation of broadband light diffraction: ABCD-matrix approach," J. Opt. Soc. Am. A 21, 1875-1885 (2004)

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  1. G. M. Morris, D. A. Zweig, “White-light Fourier transformations,” in Optical Signal Processing, J. L. Horner, ed. (Academic, New York, 1987), pp. 23–71.
  2. G. P. Behrmann, J. N. Mait, “Hybrid (refractive/diffractive) optics,” in Micro-Optics: Elements, systems and applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 259–292.
  3. G. M. Morris, K. J. McIntyre, “Optical system design with diffractive optics,” in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Akademie, Berlin, 1997), pp. 81–101.
  4. C. G. Wyne, “Extending the bandwidth of speckle interferometry,” Opt. Commun. 28, 21–25 (1979). [CrossRef]
  5. C. Brophy, “Design of an all-glass, achromatic, Fourier transform lens,” Opt. Commun. 47, 364–368 (1983). [CrossRef]
  6. G. M. Morris, “An ideal achromatic Fourier processor,” Opt. Commun. 39, 143–147 (1981). [CrossRef]
  7. G. M. Morris, “Diffraction theory for an achromatic Fourier transformation,” Appl. Opt. 20, 2017–2025 (1981). [CrossRef] [PubMed]
  8. R. H. Katyl, “Compensating optical systems. Part 3: achromatic Fourier transformation,” Appl. Opt. 11, 1255–1260 (1972). [CrossRef] [PubMed]
  9. S. Leon, E. N. Leith, “Optical processing and holography with polychromatic point source illumination,” Appl. Opt. 24, 3638–3642 (1985). [CrossRef] [PubMed]
  10. R. Ferrière, J. P. Goedgebuer, “Achromatic systems for far-field diffraction with broadband illumination,” Appl. Opt. 22, 1540–1545 (1983). [CrossRef]
  11. P. Andrés, J. Lancis, W. D. Furlan, “White-light Fourier transformer with low chromatic aberration,” Appl. Opt. 31, 4682–4687 (1992). [CrossRef] [PubMed]
  12. M. Schwab, N. Lindlein, J. Schwider, Y. Amitai, A. A. Friesem, S. Reinhorn, “Compensation of the wavelength dependence in diffractive star couplers,” J. Opt. Soc. Am. A 12, 1290–1297 (1995). [CrossRef]
  13. J. Schwider, “Achromatic design of holographic optical interconnects,” Opt. Eng. 35, 826–831 (1996). [CrossRef]
  14. J. Lancis, E. Tajahuerce, P. Andrés, G. Mı́nguez-Vega, M. Fernández-Alonso, V. Climent, “Quasi-wavelength-independent broadband optical Fourier transformer,” Opt. Commun. 172, 153–160 (1999). [CrossRef]
  15. D. Wang, A. Pe’er, A. W. Lohmann, A. A. Friesem, “Wigner algebra as a tool for the design of achromatic optical processing systems,” Opt. Eng. 39, 3014–3024 (2000). [CrossRef]
  16. J. Lancis, P. Andrés, W. D. Furlan, A. Pons, “All-diffractive achromatic Fourier-transform setup,” Opt. Lett. 19, 402–404 (1994). [PubMed]
  17. E. Tajahuerce, V. Climent, J. Lancis, M. Fernández-Alonso, P. Andrés, “Achromatic Fourier transforming properties of a separated diffractive lens doublet: theory and experiment,” Appl. Opt. 37, 6164–6173 (1998). [CrossRef]
  18. E. Tajahuerce, P. Andrés, J. Lancis, M. Fernández-Alonso, V. Climent, “White-light array generation with a diffractive lenslet array,” J. Mod. Opt. 46, 49–63 (1999). [CrossRef]
  19. G. M. Morris, N. George, “Frequency-plane filtering with an achromatic optical transform,” Opt. Lett. 5, 446–448 (1980). [CrossRef] [PubMed]
  20. R. Ferrière, C. Illueca, J. P. Goedgebuer, “Corrélateur achromatique bidimensionnel,” J. Opt. (Paris) 17, 153–159 (1986).
  21. E. Tajahuerce, J. Lancis, V. Climent, P. Andrés, “Hybrid #(refractive-diffractive) Fourier processor: a novel optical architecture for achromatic processing with broadband point-source illumination,” Opt. Commun. 151, 86–92 (1998). [CrossRef]
  22. M. Domingo, I. Arias, A. Garcı́a, “Achromatic Fourier processor with holographic optical lenses,” Appl. Opt. 40, 2267–2274 (2001). [CrossRef]
  23. D. Mendlovic, Z. Zalevsky, P. Andrés, “A novel device for achieving negative or positive dispersion and its applications,” Optik (Stuttgart) 110, 45–50 (1999).
  24. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 3–108 (1989).
  25. P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994). [CrossRef] [PubMed]
  26. P. Andrés, W. D. Furlan, G. Saavedra, A. W. Lohmann, “Variable fractional Fourier processor: a simple implementation,” J. Opt. Soc. Am. A 14, 853–858 (1997). [CrossRef]
  27. A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional transformations in optics,” Prog. Opt. 38, 265–342 (1998).
  28. H. M. Ozaktas, Z. Zalevsky, M. Alper Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, New York, 2000).
  29. A. Torre, “The fractional Fourier transform and some of its applications to optics,” Prog. Opt. 43, 531–596 (2002). [CrossRef]
  30. D. Mendlovic, Z. Zalevsky, H. M. Ozaktas, “Applications of the fractional Fourier transform to optical pattern recognition,” in Optical Pattern Recognition, F. T. S. Yu, S. Jutamulia, eds. (Cambridge U. Press, New York, 1998), pp. 89–125.
  31. J. A. Davis, D. M. Cottrell, N. Nestorovic, S. M. Highnote, “Space-variant Fresnel transform optical correlator,” Appl. Opt. 31, 6889–6893 (1992). [CrossRef] [PubMed]
  32. E. E. Sicre, N. Bolognini, M. Garavaglia, “Partial achromatization of the self-imaging phenomenon,” Appl. Opt. 24, 929–930 (1985). [CrossRef]
  33. G. Indebetouw, “Polychromatic self-imaging,” J. Mod. Opt. 35, 243–252 (1988). [CrossRef]
  34. R. H. Katyl, “Compensating optical systems. Part 2: generation of holograms with broadband light,” Appl. Opt. 11, 1248–1254 (1972). [CrossRef] [PubMed]
  35. B. Packross, R. Eschbach, O. Bryngdahl, “Achromatization of the self-imaging (Talbot) effect,” Opt. Commun. 50, 205–209 (1984). [CrossRef]
  36. P. Andrés, J. Lancis, E. E. Sicre, E. Bonet, “Achromatic Fresnel diffraction patterns,” Opt. Commun. 104, 39–45 (1993). [CrossRef]
  37. J. Lancis, E. E. Sicre, A. Pons, G. Saavedra, “Achromatic white-light self-imaging phenomenon: an approach using the Wigner distribution function,” J. Mod. Opt. 42, 425–434 (1995). [CrossRef]
  38. J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichin, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997). [CrossRef]
  39. J. Lancis, G. Mı́nguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, P. Andrés, “Wavelength-compensated Fourier and Fresnel transformers: a unified approach,” Opt. Lett. 27, 942–944 (2002). [CrossRef]
  40. E. Tajahuerce, G. Saavedra, W. D. Furlan, E. E. Sicre, P. Andrés, “White-light optical implementation of the fractional Fourier transform with adjustable order control,” Appl. Opt. 39, 238–245 (2000). [CrossRef]
  41. E. Tajahuerce, E. Bonet, P. Andrés, C. J. Zapata-Rodrı́guez, V. Climent, “White-light modified Talbot array illuminator with a variable density of light spots,” Appl. Opt. 37, 4366–4373 (1998). [CrossRef]
  42. E. Tajahuerce, E. Bonet, J. Lancis, M. T. Gale, P. Andrés, “Achromatic fan-out diffractive system for white-light free-space optical interconnects,” J. Mod. Opt. 48, 831–845 (2001). [CrossRef]
  43. G. Mı́nguez-Vega, J. Lancis, E. Tajahuerce, V. Climent, J. Caraquitena, P. Andrés, “Broadband space-variant Fresnel processor,” Opt. Lett. 27, 1926–1929 (2002). [CrossRef]
  44. J. Lancis, G. Mı́nguez-Vega, E. Tajahuerce, V. Climent, P. Andrés, Z. Jaroszewicz, “High-contrast white-light Lau fringes,” Opt. Lett. 29, 150–152 (2004). [CrossRef] [PubMed]
  45. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  46. A. Yariv, “Imaging of coherent fields through lenslike systems,” Opt. Lett. 19, 1607–1608 (1994). [CrossRef] [PubMed]

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