Solution to the Boundary problem for Fourier and Multigrid transport equation of intensity based solvers

Juan Martinez-Carranza, Konstantinos Falaggis, Tomasz Kozacki


In this work we present a solution for the boundary problem for phase retrieval techniques based on the Transport of intensity Equation (TIE). The solution presented here is based on the Neumann Boundary condition and the mirror padding scheme of the captured intensities. The obtained results are derived for the widely used Fourier Transform based TIE solver, but it is shown that they can also be applied to Multigrid based techniques.

Full Text: PDF

  1. K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey", Phys. Today 54, 27 (2001). CrossRef
  2. R. Porras-Aguilar, M. Kujawinska, and W. Zaperty, "Capture and display mismatch compensation for real-time digital holographic interferometry", Appl. Opt. 53, 2870 (2014). CrossRef
  3. R. Porras-Aguilar, K. Falaggis, J. C. Ramirez-San-Juan, and R. Ramos-Garcia, "Self-calibrating common-path interferometry", Opt. Express 23, 3327 (2015). CrossRef
  4. I. A. Shevkunov, N. S. Balbekin, and N. V. Petrov, "Comparison of digital holography and iterative phase retrieval methods for wavefront reconstruction", Proc. SPIE 9271, 927128 (2014). CrossRef
  5. N. Streibl, "Phase imaging by the transport equation of intensity", Opt. Commun. 49(1984). DirectLink
  6. 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 (2014). CrossRef
  7. J. Martinez-Carranza, K. Falaggis, and T. Kozacki, "Optimum plane selection for transport-of-intensity-equation-based solvers", Appl. Opt. 53, 7050(2014). CrossRef
  8. K. Falaggis, T. Kozacki, and M. Kujawinska, "Optimum plane selection criteria for single-beam phase retrieval techniques based on the contrast transfer function", Opt. Lett. 39, 30(2014). CrossRef
  9. Z. Jingshan, R. Claus, J. Dauwels, and L. Tian, "Transport of Intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes", Opt. Express 22, 18125 (2014). CrossRef
  10. J. Martinez-Carranza, K. Falaggis, T. Kozacki, and M. Kujawinska, "Effect of imposed boundary conditions on the accuracy of transport of intensity equation based solvers", Proc. SPIE 8789, 87890N (2013). CrossRef
  11. F. Roddier and C. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics", Appl. Opt. 27, 1223 (1988). CrossRef
  12. C. Zuo, Q. Chen, and A. Asundi, "Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform", Opt. Express 22, 9220 (2014). CrossRef
  13. K. Falaggis, T. Kozacki, and M. Kujawinska, "Computation of highly off-axis diffracted fields using the band-limited angular spectrum method with suppressed Gibbs related artifacts", Appl. Opt. 52, 3288 (2013). CrossRef
  14. V. V. Volkov, Y. Zhu, and M. De Graef, "A new symmetrized solution for phase retrieval using the transport of intensity equation", Micron 33, 411 (2002). CrossRef
  15. K. Falaggis, T. Kozacki, and M. Kujawinska, "Accelerated single-beam wavefront reconstruction techniques based on relaxation and multiresolution strategies", Opt. Lett. 38, 1660(2013). CrossRef
  16. W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, Second (SIAM, 2000). CrossRef

Full Text:


Photonics Letters of Poland - A Publication of the Photonics Society of Poland
Published in cooperation with SPIE

ISSN: 2080-2242