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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 22 — Aug. 1, 2008
  • pp: 4061–4067

Convex objective function-based design method developed for minimizing side lobe

Jian Liu, Jiubin Tan, and Chenguang Zhao  »View Author Affiliations

Applied Optics, Vol. 47, Issue 22, pp. 4061-4067 (2008)

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The existence of multiple local solutions makes it very difficult to search for filter parameters to achieve a desired side lobe level during the design of superresolution pupil filters. To deal with the difficult issue of side lobe control in the designing process, a convex objective function-based design method is developed through phase rotation and variable replacement to transform the complicated solving process with multiextreme subintervals into a simple optimization process with a convex interval. A group of constant annular complex superresolving filters are designed using the developed method. The comparison of the superresolving filters designed in this way with the well-known continuous phase filter and 3-zone multiphase diffractive superresolution filters proves the validity of the developed method.

© 2008 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(220.1230) Optical design and fabrication : Apodization

ToC Category:
Image Processing

Original Manuscript: April 15, 2008
Revised Manuscript: June 16, 2008
Manuscript Accepted: July 7, 2008
Published: July 25, 2008

Jian Liu, Jiubin Tan, and Chenguang Zhao, "Convex objective function-based design method developed for minimizing side lobe," Appl. Opt. 47, 4061-4067 (2008)

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  1. J. Jia, C. Zhou, and L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271-278(2003). [CrossRef]
  2. G. Boyer, “New class of axially apodizing filters for confocal scanning microscopy,” J. Opt. Soc. Am. A 19, 584-589 (2002). [CrossRef]
  3. M. T. Caballero, P. Andrés, A. Pons, J. Lancis, and M. Martínez-Corral, “Axial resolution in two-color excitation fluorescence microscopy by phase-only apodization,” Opt. Commun. 246, 313-321 (2005). [CrossRef]
  4. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Transverse or axial superresolution in a 4Pi confocal microscope by phase-only filters,” J. Opt. Soc. Am. A 20, 2172-2178 (2003). [CrossRef]
  5. X. Zhao, C. Li, and H. Ruan, “New approach for improving transverse superresolution in optical data storage,” Opt. Eng. 44, 125202-1-125202-4 (2005). [CrossRef]
  6. C. J. R. Sheppard and Z. S. Hegedus, “Axial behavior of pupil-plane filters,” J. Opt. Soc. Am. A 5, 643-647 (1988). [CrossRef]
  7. T. R. M. Sales and G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637-1646 (1997). [CrossRef]
  8. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607-609 (2003). [CrossRef] [PubMed]
  9. S. Ledesma, J. Campos, and J. C. Escalera, “Simple expressions for performance parameters of complex filters, with application to super-Gaussian phase filters,” Opt. Lett. 29, 932-934 (2004). [CrossRef] [PubMed]
  10. H. Liu, Y. Yan, and G. Jin, “Design theories and performance limits of diffractive superresolution elements with the highest side lobe suppressed,” J. Opt. Soc. Am. A 22, 828-838 (2005). [CrossRef]
  11. W. Zhao and L. Qiu, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14, 7024-7036 (2006). [CrossRef] [PubMed]
  12. C. Liu and S.-H. Park, “Numerical analysis of an annular-aperture solid immersion lens,” Opt. Lett. 29, 1742-1744(2004). [CrossRef] [PubMed]
  13. V. F. Canales, J. E. Oti, and M. P. Cagigal, “Three-dimensional control of the focal light intensity distribution by analytically designed phase masks,” Opt. Commun. 247, 11-18 (2005). [CrossRef]
  14. M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun. 241, 249-253 (2004). [CrossRef]
  15. V. F. Canales, “Pupil filter design by using a Bessel functions basis at the image plane,” Opt. Express 14, 10393-10402(2006). [CrossRef] [PubMed]
  16. C. J. R. Sheppard, “Filter performance parameters for high-aperture focusing,” Opt. Lett. 32, 1653-1655 (2007). [CrossRef] [PubMed]

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