Solution to the Boundary problem for Fourier and Multigrid transport equation of intensity based solvers - Martinez-Carranza, Juan; Falaggis, Konstantinos; Kozacki, Tomasz (Photonics Letters of Poland, 2015)
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 References K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey", Phys. Today 54, 27 (2001). CrossRef 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 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 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 N. Streibl, "Phase imaging by the transport equation of intensity", Opt. Commun. 49(1984). DirectLink 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 J. Martinez-Carranza, K. Falaggis, and T. Kozacki, "Optimum plane selection for transport-of-intensity-equation-based solvers", Appl. Opt. 53, 7050(2014). CrossRef 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 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 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 F. Roddier and C. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics", Appl. Opt. 27, 1223 (1988). CrossRef 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 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 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 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 W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, Second (SIAM, 2000). CrossRef