Science in China Series A: Mathematics

, Volume 51, Issue 6, pp 1059–1070 | Cite as

Reconstruction of the shape of object with near field measurements in a half-plane

  • HePing DongEmail author
  • FuMing Ma


We consider a mathematical problem modelling some characteristics of near field optical microscope. We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem. Some numerical examples to show the feasibility of the method are presented.


Helmholtz equation inverse problem mixed reciprocity relation factorization method 


35J05 78A46 


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Copyright information

© Science in China Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Institute of MathematicsJilin UniversityChangchunChina

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