  We consider the imaging of arbitrary shaped, arc-like perfectly conducting
cracks located in the two-dimensional homogeneous space via linear sampling
method. Based on the structure of eigenvectors of so-called Multi Static
Response (MSR) matrix, we discover the relationship between imaging functional
adopted in the linear sampling method and Bessel function of integer order of
the first kind. This relationship tells us that why linear sampling method
works for imaging of perfectly conducting cracks in either Transverse Magnetic
(Dirichlet boundary condition) and Transverse Electric (Neumann boundary
condition), and explains its certain properties. Furthermore, we suggest
multi-frequency imaging functional, which improves traditional linear sampling
method. Various numerical experiments are performed for supporting our
explores.
