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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. 13, Iss. 1 — Jan. 1, 1996
  • pp: 97–103

Iterative optimization approach for designing an axicon with long focal depth and high transverse resolution

Bi-Zhen Dong, Guo-Zhen Yang, Ben-Yuan Gu, and Okan K. Ersoy  »View Author Affiliations


JOSA A, Vol. 13, Issue 1, pp. 97-103 (1996)
http://dx.doi.org/10.1364/JOSAA.13.000097


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Abstract

An iterative optimization approach for designing the phase of the uniform-intensity axicon is presented that is based on the general theory of amplitude-phase retrieval in optical systems. We extend previous theoretical formulas to deal with the linear imaging system with multiple output planes. We carry out numerical simulation calculations for designing the axicon for cases of both uniform and Gaussian beam illuminations. The numerical results are in good agreement with the desired performance of the axicon, for instance, with considerable uniformity and smoothness of the on-axis intensity and energy flow as well as with high lateral resolution. The influence of phase quantization on the designed result is also investigated.

© 1996 Optical Society of America

History
Original Manuscript: April 7, 1995
Revised Manuscript: August 8, 1995
Manuscript Accepted: August 17, 1995
Published: January 1, 1996

Citation
Bi-Zhen Dong, Okan K. Ersoy, Guo-Zhen Yang, and Ben-Yuan Gu, "Iterative optimization approach for designing an axicon with long focal depth and high transverse resolution," J. Opt. Soc. Am. A 13, 97-103 (1996)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-1-97


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References

  1. J. H. McLeod, “Axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954). [CrossRef]
  2. J. H. McLeod, “Axicons and their uses,” J. Opt. Soc. Am. 50, 166–169 (1960). [CrossRef]
  3. M. V. Pérez, C. Gómez-Reino, J. M. Cuadrado, “Diffraction pattern and zero plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986). [CrossRef]
  4. L. W. Casperson, M. S. Shekhani, “Air breakdown in a radial-mode focusing element,” Appl. Opt. 13, 104–108 (1974). [CrossRef] [PubMed]
  5. P. A. Bélanger, M. Rioux, “Ring pattern of a lens–axicon doublet illuminated by a Gaussian beam,” Appl. Opt. 17, 1080–1086 (1978). [CrossRef]
  6. M. Rioux, P. A. Bélanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17, 1532–1536 (1978). [CrossRef] [PubMed]
  7. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988). [CrossRef] [PubMed]
  8. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989). [CrossRef] [PubMed]
  9. G. Bickel, G. Häusler, M. Maul, “Triangulation with expanded range of depth,” Opt. Eng. 24, 975–977 (1985). [CrossRef]
  10. G. Häusler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988). [CrossRef] [PubMed]
  11. L. M. Soroko, “Axicons and meso-optical imaging devices,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1989), Vol. 27, pp. 109–160. [CrossRef]
  12. A. T. Friberg, S. Y. Popov, “Partially coherently illuminated uniform-intensity holographic axicons,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 224–227.
  13. Z. Jaroszewicz, J. F. R. Dopazo, “Polychromatic illumination of logarithmic annular-aperture diffractive axicon,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–231.
  14. N. Davidson, A. A. Friesem, E. Hasman, “Holographic axicon: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991). [CrossRef] [PubMed]
  15. J. Sochacki, S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17, 7–9 (1992). [CrossRef] [PubMed]
  16. J. Sochacki, A. Kołodziejczyk, Z. Jaroszewicz, S. Bará, “Nonparaxial design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992). [CrossRef] [PubMed]
  17. L. F. Staroński, J. Sochacki, Z. Jaroszewicz, A. Kołodziejczyk, “Lateral distribution and flow of energy in uniform-intensity axicons,” J. Opt. Soc. Am. A 9, 2091–2094 (1992). [CrossRef]
  18. J. Sochacki, Z. Jaroszewicz, L. R. Staroński, A. Kołodziejczyk, “Annular-aperture logarithmic axicon,” J. Opt. Soc. Am. A 10, 1765–1768 (1993). [CrossRef]
  19. Z. Jaroszewicz, J. Sochacki, A. Kołodziejczyk, L. R. Staroński, “Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions,” Opt. Lett. 18, 1893–1895 (1993). [CrossRef] [PubMed]
  20. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993). [CrossRef]
  21. R. Piestun, J. Shamir, “Control of wave-front propagation with diffractive elements,” Opt. Lett. 19, 771–773 (1994). [CrossRef] [PubMed]
  22. J. Rosen, A. Yariv, “Synsthesis of an arbitrary axial field profile by computer-generated holograms,” Opt. Lett. 19, 843–845 (1994). [CrossRef] [PubMed]
  23. J. Rosen, “Synsthesis of nondiffracting beams in free space,” Opt. Lett. 19, 369–371 (1994). [PubMed]
  24. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).
  25. B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981) (in Chinese).
  26. G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta. Phys. Sin. 30, 410–413 (1981) (in Chinese).
  27. G. Yang, L. Wang, B. Dong, B. Gu, “On the amplitude-phase retrieval problem in an optical system involving nonunitary transformation,” Optik (Stuttgart) 75, 68–74 (1987).
  28. G. Z. Yang, B. Y. Gu, B. Z. Dong, “Theory of the amplitude-phase retrieval in any linear transform system and its applications,” Int. J. Mod. Phys. B 7, 3153–3224 (1993). [CrossRef]
  29. G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994). [CrossRef] [PubMed]
  30. G. Z. Yang, B. Y. Gu, X. Tan, M. P. Chang, B. Z. Dong, O. K. Ersoy, “Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optical functions,” J. Opt. Soc. Am. 11, 1632–1640 (1994). [CrossRef]
  31. B. Y. Gu, G. Z. Yang, B. Z. Dong, M. P. Chang, O. K. Ersoy, “Diffractive-phase-element design that implements several optical functions,” Appl. Opt. 34, 2564–2570 (1995). [CrossRef] [PubMed]
  32. B. Dong, G. Yang, B. Gu, “Phase retardation for a uniform-intensity axicon: a new method of design,” submitted to Opt. Lett.
  33. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 13 and 63.

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