TY - JOUR
T1 - The phase retrieval problem
T2 - A spectral parameter power series approach
AU - Barrera-Figueroa, Víctor
AU - Blancarte, Herminio
AU - Kravchenko, Vladislav V.
N1 - Funding Information:
Acknowledgments V.B.F. acknowledges the support by COTEBAL-IPN for all the facilities given in the realization of this work. V.K. acknowledges the support by CONACyT via Project 166141.
PY - 2014/4
Y1 - 2014/4
N2 - This paper presents the application of the spectral parameter power series method [Pauli, Math Method Appl Sci 33:459-468 (2010)] for constructing the Green's function for the elliptic operator ∇ · I ∇ in a rectangular domain Ω ⊂ ℝ2, where I admits separation of variables. This operator appears in the transport-of-intensity equation (TLE) for undulatory phenomena, which relates the phase of a coherent wave with the axial derivative of its intensity in the Fresnel regime. We present a method for solving the TIE with Dirichlet boundary conditions. In particular, we discuss the case of an inhomogeneous boundary condition, a problem that has not been addressed specifically in other works, under the restricted assumption that the intensity I admits separation of variables. Several simulations show the validity of the method.
AB - This paper presents the application of the spectral parameter power series method [Pauli, Math Method Appl Sci 33:459-468 (2010)] for constructing the Green's function for the elliptic operator ∇ · I ∇ in a rectangular domain Ω ⊂ ℝ2, where I admits separation of variables. This operator appears in the transport-of-intensity equation (TLE) for undulatory phenomena, which relates the phase of a coherent wave with the axial derivative of its intensity in the Fresnel regime. We present a method for solving the TIE with Dirichlet boundary conditions. In particular, we discuss the case of an inhomogeneous boundary condition, a problem that has not been addressed specifically in other works, under the restricted assumption that the intensity I admits separation of variables. Several simulations show the validity of the method.
KW - Fresnel diffraction
KW - Green's function
KW - Phase retrieval problem
KW - Spectral parameter power series (SPPS)
KW - Transport-of-intensity equation (TIE)
UR - http://www.scopus.com/inward/record.url?scp=84897704590&partnerID=8YFLogxK
U2 - 10.1007/s10665-013-9644-7
DO - 10.1007/s10665-013-9644-7
M3 - Artículo
SN - 0022-0833
VL - 85
SP - 179
EP - 209
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
ER -