  In this paper, direct sampling method is considered for determining the
location of a set of small, linear perfectly conducting cracks from the
collected far-field data corresponding to an incident field. To show the
feasibility of the direct sampling method, this study proves that the indicator
function of the direct sampling method can be represented by the Bessel
function of order zero and the crack lengths. The results of the numerical
simulations are shown to support the fact that the imaging performance is
highly dependent on the crack lengths. To explain the fact that the imaging
performance is highly dependent on the rotation of the cracks, the direct
sampling method is further analyzed by establishing a representation using
Bessel functions of orders zero and one. Based on the derived representation of
indicator function, we design improved direct sampling methods by applying
incident fields with multiple directions and multiple frequencies.
Corresponding analysis of indicator functions and simulation results are shown
for demonstrating the effectiveness and improvements.
