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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23875–23886

Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams

Manuel Silva-López, José María Rico-García, and Javier Alda  »View Author Affiliations

Optics Express, Vol. 20, Issue 21, pp. 23875-23886 (2012)

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An experimental setup to measure the three-dimensional phase-intensity distribution of an infrared laser beam in the focal region has been presented. It is based on the knife-edge method to perform a tomographic reconstruction and on a transport of intensity equation-based numerical method to obtain the propagating wavefront. This experimental approach allows us to characterize a focalized laser beam when the use of image or interferometer arrangements is not possible. Thus, we have recovered intensity and phase of an aberrated beam dominated by astigmatism. The phase evolution is fully consistent with that of the beam intensity along the optical axis. Moreover, this method is based on an expansion on both the irradiance and the phase information in a series of Zernike polynomials. We have described guidelines to choose a proper set of these polynomials depending on the experimental conditions and showed that, by abiding these criteria, numerical errors can be reduced.

© 2012 OSA

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(100.5070) Image processing : Phase retrieval
(100.6950) Image processing : Tomographic image processing
(140.3295) Lasers and laser optics : Laser beam characterization

ToC Category:
Image Processing

Original Manuscript: June 20, 2012
Revised Manuscript: July 23, 2012
Manuscript Accepted: July 23, 2012
Published: October 3, 2012

Manuel Silva-López, José María Rico-García, and Javier Alda, "Measurement limitations in knife-edge tomographic phase retrieval of focused IR laser beams," Opt. Express 20, 23875-23886 (2012)

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  1. P. S. Carney, B. Deutsch, A. A. Govyadinov, and R. Hillenbrand, “Phase in nanooptics,” ACS Nano6, 8 – 12 (2012). [CrossRef] [PubMed]
  2. G. Volpe, S. Cherukulappurath, R. J. Parramon, G. Molina-Terriza, and R. Quidant, “Controlling the Optical Near Field of Nanoantennas with Spatial Phase-Shaped Beams,” Nano Lett.93608–3611 (2009). [CrossRef] [PubMed]
  3. E. C. Kinzel, J. C. Ginn, R. L. Olmon, D. J. Shelton, B. A. Lail, I. Brener, M. B. Sinclair, M. B. Raschke, and G. D. Boreman, “Phase resolved near-field mode imaging for the design of frequency-selective surfaces,” Opt. Express20, 11986–11993 (2012). [CrossRef] [PubMed]
  4. E. Cubukcu, N. Yu, E. J. Smythe, L. Diehl, K. B. Crozier, and F. Capasso, “Plasmonic Laser Antennas and Related Devices,” J. Sel. T. Q. Elec.14, 1448–1461 (2008). [CrossRef]
  5. L. Novotny and N. Van Hulst, “Antennas for light,” Nature Phot.5, 83–90 (2011). [CrossRef]
  6. J. Alda, J. M. Rico-García, J. M. López-Alonso, and G. D. Boreman, “Optical antennas for nanophotonics applications,” Nanotechnology16, S230, (2005). [CrossRef]
  7. M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antenna,” Science332, 702–704, (2011). [CrossRef] [PubMed]
  8. R. L. Olmon, P. M. Krenz, B. A. Lail, L. V. Saraf, G. D. Boreman, and M. B. Raschke, “Determination of electric-field, magnetic-field, and electric-current distributions of infrared optical antennas: A near-field optical vector network analyzer,” Phys. Rev. Lett.105, 167403 (2010). [CrossRef]
  9. C. Fumeaux, G. D. Boreman, W. Herrmann, F. K. Kneubhl, and H. Rothuizen, “Spatial impulse response of lithographic infrared antennas,” Appl. Opt.38, 37–46 (1999). [CrossRef]
  10. J. Alda, C. Fumeaux, L. Codreanu, J. A. Schaefer, and G. D. Boreman, “Deconvolution method for two dimensional spatial response mapping of lithographic infrared antennas,” Appl. Opt.383993–4000 (1999). [CrossRef]
  11. J. M. López-Alonso, B. Monacelli, J. Alda, and G. D. Boreman, “Uncertainty analysis in the measurement of the spatial responsivity of infrared antennas,” Appl. Opt.44, 4557–4568 (2005). [CrossRef] [PubMed]
  12. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).
  13. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21, 2758–2769 (1982). [CrossRef] [PubMed]
  14. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A15, 1662–1669 (1998). [CrossRef]
  15. W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt.50, 2008–2015 (2011). [CrossRef] [PubMed]
  16. H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. H. Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A23, 1179–1200(2006). [CrossRef]
  17. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nature Phys.2, 101–104 (2006). [CrossRef]
  18. A. H. Firester, M. E. Heller, and P. Sheng, “Knife-edge scanning measurements of subwavelength focused light beams,” Appl. Opt.16, 1971–1974 (1977). [CrossRef] [PubMed]
  19. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs “The focus of light - theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72, 109–113 (2001). [CrossRef]
  20. J. M. Rico-García, L. M. Sánchez-Brea, and J. Alda, “Application of tomographic techniques to the spatial-response mapping of antenna-coupled detectors in the visible,” Appl. Opt.47, 768–775 (2008). [CrossRef] [PubMed]
  21. P. Marchenko, S. Orlov, C. Huber, P. Banzer, S. Quabis, U. Peschel, and G. Leuchs, “Interaction of highly focused vector beams with a metal knife-edge,” Opt. Express19, 7244–7249 (2011). [CrossRef] [PubMed]
  22. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am.73, 1434–1441 (1983). [CrossRef]
  23. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt.29, 1402–1403 (1990). [CrossRef] [PubMed]
  24. T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A13(8), 1670–1682 (1996). [CrossRef]
  25. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am.66, 207–211 (1976). [CrossRef]
  26. J. Alda, J. Alonso, and E. Bernabéu, “Characterization of aberrated laser beams,” J. Opt. Soc. Am. A14, 2737–2747 (1997). [CrossRef]
  27. S. Barbero and L. N. Thibos, “Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation,” Opt. Eng.45, 094001 (2006). [CrossRef]
  28. M. Soto, E. Acosta, and S. Rios “Performance analysis of curvature sensors: optimum positioning of measurement planes,” Opt. Express11, 2577–2588 (2003). [CrossRef] [PubMed]
  29. P. Toft, “The Radon transform: theory and implementation,” Ph. D. dissertation (Technical University of Denmark, 1996), http://petertoft.dk/PhD .
  30. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, (Gatesmark Publishing2008).
  31. M. Born and E. Wolf, Principles of Optics, (Pergamon Press, 1980).
  32. G. M. Dai, “Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation,” Opt. Lett.31, 501–503 (2006). [CrossRef] [PubMed]
  33. S. V. Pinhasi, R. Alimi, S. Eliezer, and L. Perelmutter “Fast optical computerized topography,” Phys. Lett. A374, 2798–2800 (2006). [CrossRef]
  34. J. Alda, “Laser and Gaussian beam propagation and transformation,” in Encyclopedia of Optical Engineering (Marcel Dekker Inc. 2003), 999–1013.
  35. J. M. Braat, S. Van Haver, A. E. M. Janssen, and P. Dirksen, “Assessment of optical systems by means of point spread functions,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2008), 349–468. [CrossRef]

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