On the convergence of the Rytov approximation for the reduced wave equation Export

@article{citeulike:3440326, abstract = {The reduced wave equation Deltau+k2n2(x)u=0 is treated where n(x) fluctuates about unity in a compact domain D, and is equal to unity in the region exterior to D. In the Rytov approximation the total field u(x) generated by an incident field ui(x) has the form u(x)\~{}ui(x)exp phi(x) where phi(x)ui(x)=(1/4pi)[integral]_D (eik||x−y||/||x−y||)k2(n2−1) ×ui(y)dtauy. It is shown that under suitable conditions on n(x) and restrictions on ui(x), the approximation is a leading term of a convergent expansion holding for all x in D. This is in contrast to previous theory, which treated the Rytov approximation as an asymptotic expansion valid in the forward-scattered direction.}, author = {Weston, V. H.}, citeulike-article-id = {3440326}, citeulike-linkout-0 = {http:// http://link.aip.org/link/?JMAPAQ/26/1979/1}, citeulike-linkout-1 = {http://dx.doi.org/10.1063/1.526867}, doi = {10.1063/1.526867}, journal = {J. Math. Phys.}, keywords = {born-approximation, direction, em, optics, physics, rytov-approximation, wave}, pages = {1979+}, posted-at = {2008-10-22 14:35:26}, priority = {2}, title = {On the convergence of the Rytov approximation for the reduced wave equation}, url = {http://dx.doi.org/10.1063/1.526867}, volume = {26}, year = {1985} }

TY - JOUR ID - citeulike:3440326 L3 - citeulike-article-id:3440326 N2 - The reduced wave equation Deltau+k2n2(x)u=0 is treated where n(x) fluctuates about unity in a compact domain D, and is equal to unity in the region exterior to D. In the Rytov approximation the total field u(x) generated by an incident field ui(x) has the form u(x)~ui(x)exp phi(x) where phi(x)ui(x)=(1/4pi)[integral]_D (eik||x−y||/||x−y||)k2(n2−1) ×ui(y)dtauy. It is shown that under suitable conditions on n(x) and restrictions on ui(x), the approximation is a leading term of a convergent expansion holding for all x in D. This is in contrast to previous theory, which treated the Rytov approximation as an asymptotic expansion valid in the forward-scattered direction. JF - J. Math. Phys. TI - On the convergence of the Rytov approximation for the reduced wave equation VL - 26 SP - 1979 KW - born-approximation KW - direction KW - em KW - optics KW - physics KW - rytov-approximation KW - wave AU - Weston, VH PY - 1985/// UR - http://dx.doi.org/10.1063/1.526867 ER -