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Optics Letters

Optics Letters


  • Editor: Xi-Cheng Zhang
  • Vol. 39, Iss. 2 — Jan. 15, 2014
  • pp: 182–185

Optimum measurement criteria for the axial derivative intensity used in transport of intensity-equation-based solvers

J. Martinez-Carranza, K. Falaggis, and T. Kozacki  »View Author Affiliations

Optics Letters, Vol. 39, Issue 2, pp. 182-185 (2014)

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For several years, scientific, industrial, and biological fields have benefited from knowledge of phase information, which allows for the revealing of hidden features of various objects. An alternative to interferometry is single-beam phase retrieval techniques that are based on the transport of intensity equation, which describes the relation between the axial derivative of the intensity and the phase distribution for a given plane in the Fresnel region. The estimation of the axial intensity derivative is obtained from a series of intensity measurements, where the accuracy is subject to an optimum separation between the measurement planes depending on the number of planes, the level of noise, and the actual object phase distribution. In this Letter, a quantitative analysis of the error in estimated axial derivative is carried out and a model is reported that describes the interdependence between these parameters. The results of this work allow for estimation of the optimum separation between measurement planes with minimal error in the axial derivative.

© 2014 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: September 24, 2013
Revised Manuscript: November 15, 2013
Manuscript Accepted: November 29, 2013
Published: January 3, 2014

Virtual Issues
Vol. 9, Iss. 3 Virtual Journal for Biomedical Optics

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, "Optimum measurement criteria for the axial derivative intensity used in transport of intensity-equation-based solvers," Opt. Lett. 39, 182-185 (2014)

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  1. M. P. Allen and L. J. Oxley, Opt. Commun. 199, 65 (2001). [CrossRef]
  2. G. Pedrini, W. Osten, and Y. Zhang, Opt. Lett. 30, 833 (2005). [CrossRef]
  3. K. Falaggis, T. Kozacki, and M. Kujawinska, Opt. Lett. 38, 1660 (2013). [CrossRef]
  4. E. J. Candes, T. Strohmer, and V. Voroninski, Commun. Pure Appl. Math. 66, 1241 (2013). [CrossRef]
  5. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983). [CrossRef]
  6. T. E. Gureyev, A. Roberts, and K. A. Nugent, J. Opt. Soc. Am. A 12, 1942 (1995). [CrossRef]
  7. J. C. Petruccelli, L. Tian, and G. Barbastathis, Opt. Express 21, 14430 (2013). [CrossRef]
  8. D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, J. Microsc. 214, 51 (2004). [CrossRef]
  9. T. Gureyev and S. Wilkins, Opt. Commun. 147, 229 (1998). [CrossRef]
  10. S. Bajt, A. Barty, K. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000). [CrossRef]
  11. M. Soto and E. Acosta, Appl. Opt. 46, 7978 (2007). [CrossRef]
  12. C. Zuo, Q. Chen, Y. Yu, and A. Asundi, Opt. Express 21, 5346 (2013). [CrossRef]
  13. L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010). [CrossRef]
  14. L. Tian, J. C. Petruccelli, and G. Barbastathis, Opt. Lett. 37, 4131 (2012). [CrossRef]
  15. L. Tian, J. C. Petruccelli, Q. Miao, H. Kudrolli, V. Nagarkar, and G. Barbastathis, Opt. Lett. 38, 3418 (2013). [CrossRef]
  16. R. Bie, X.-H. Yuan, M. Zhao, and L. Zhang, Opt. Express 20, 8186 (2012). [CrossRef]
  17. S. Huang, F. Xi, C. Liu, and Z. Jiang, J. Mod. Opt. 59, 35 (2012). [CrossRef]
  18. C. Zuo, Q. Chen, W. Qu, and A. Asundi, Opt. Lett. 38, 3538 (2013). [CrossRef]

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