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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 1 — Jan. 13, 2014
  • pp: 311–324

Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory

A. P. Konijnenberg, L. Wei, N. Kumar, L. Couto Correa Pinto Filho, L. Cisotto, S. F. Pereira, and H. P. Urbach  »View Author Affiliations

Optics Express, Vol. 22, Issue 1, pp. 311-324 (2014)

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In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM).

© 2014 Optical Society of America

OCIS Codes
(110.1220) Imaging systems : Apertures
(260.1960) Physical optics : Diffraction theory
(110.7348) Imaging systems : Wavefront encoding
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Physical Optics

Original Manuscript: October 14, 2013
Revised Manuscript: November 21, 2013
Manuscript Accepted: November 26, 2013
Published: January 2, 2014

A. P. Konijnenberg, L. Wei, N. Kumar, L. Couto Correa Pinto Filho, L. Cisotto, S. F. Pereira, and H. P. Urbach, "Demonstration of an optimised focal field with long focal depth and high transmission obtained with the Extended Nijboer-Zernike theory," Opt. Express 22, 311-324 (2014)

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  1. G. B. Airy, “On the diffraction of an annular aperture,” Philos. Mag. 18, 1–10 (1841).
  2. J. Durnin, J. J. Miceli, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef] [PubMed]
  3. Y. Xu, J. Singh, C. Sheppard, N. Chen, “Ultra long high resolution beam by multi-zone rotationally symmetrical complex pupil filter,” Opt. Express 15, 6409–6413 (2007). [CrossRef] [PubMed]
  4. H. Wang, C. J. R. Sheppard, K. Ravi, S. T. Ho, G. Vienne, “Fighting against diffraction: apodization and near field diffraction structures,” Laser Photonics Rev. 6, 354–392 (2012). [CrossRef]
  5. B. J. Thompson, “Diffraction by semitransparent and phase annuli,” J. Opt. Soc. Am. 55, 145–148 (1965). [CrossRef]
  6. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento 9, 426–438 (1952). [CrossRef]
  7. H. Wang, F. Gan, “High focal depth with a pure-phase apodizer,” Appl. Opt. 40, 5658–5662 (2001). [CrossRef]
  8. C. J. R. Sheppard, “Synthesis of filters for specified axial properties,” J. Mod. Opt. 43, 525–536 (1996). [CrossRef]
  9. J. Ojeda-Castañeda, L. R. Berriel-Valdos, “Arbitrarily high focal depth with finite apertures,” Opt. Lett. 13, 183–185 (1988). [CrossRef] [PubMed]
  10. H. Wang, G. Yuan, W. Tan, L. Shi, T. Chong, “Spot size and depth of focus in optical data storage system,” Opt. Eng. 46, 065201 (2007). [CrossRef]
  11. L. Wei, “Evaluation of Extended Nijboer-Zernike theory as a tool for complex point spread function calculation,” Master thesis (Delft University of Technology, 2012).
  12. J. J. M. Braat, A. J. E. M. Janssen, P. Dirksen, S. van Haver, “Assessment of optical systems by means of point spread functions,” Prog. Opt. 51, 349–468 (2008).
  13. C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011). [CrossRef]
  14. A. J. E. M. Janssen, “ENZ approach for the computation of optical point spread function,” J. Opt. Soc. Am. A 19, 849–857 (2002). [CrossRef]
  15. A. J. E. M. Janssen, J. J. M. Braat, P. Dirksen, “On the computation of the Nijboer-Zernike aberration integrals at arbitrary defocus,” J. Mod. Opt. 51, 687–703 (2004). [CrossRef]
  16. S. van Haver, A. J. E. M. Janssen, “Advanced analytic treatment and efficient computation of the diffraction integrals in the Extended Nijboer-Zernike theory,” J. Eur. Opt. Soc. Rap. Publ. 8, 13044 (2013). [CrossRef]
  17. Holoeye, “PLUTO Phase Only Spatial Light Modulator (Reflective),” http://holoeye.com/spatial-light-modulators/slm-pluto-phase-only/ , June 24, 2013.
  18. O. El Gawhary, A. Wiegmann, N. Kumar, S. F. Pereira, H. P. Urbach, “Through-focus phase retrieval and its connection to the spatial correlation for propagating fields,” Opt. Express 21, 5550–5560 (2013). [CrossRef] [PubMed]
  19. H. Zhang, J. Xie, J. Liu, Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. 48, 5834–5841 (2009). [CrossRef] [PubMed]

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