The version of the “linear sampling” method introduced in D. Colton, A. Kirsch, Inverse Problems,

It consists into the attempt to recover a scatterer's contour by determining an

We show that the far field equation to solve does not have (almost anywhere) a solution for two classes of objects: Perfectly conducting cylinders and homogeneous dielectric cylinders having circular cross section. It thus follows that the indicator function is “infinite” (almost) everywhere both inside and outside the scatterer and, consequently, does not represent the shape of the object. UR - http://www.ingentaconnect.com/content/urban/541/2003/00000057/00000001/art00142 M3 - doi:10.1078/1434-8411-54100142 UR - http://dx.doi.org/10.1078/1434-8411-54100142 ER -