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In this paper, direct sampling method is considered for determining thelocation of a set of small, linear perfectly conducting cracks from thecollected far-field data corresponding to an incident field. To show thefeasibility of the direct sampling method, this study proves that the indicatorfunction of the direct sampling method can be represented by the Besselfunction of order zero and the crack lengths. The results of the numericalsimulations are shown to support the fact that the imaging performance ishighly dependent on the crack lengths. To explain the fact that the imagingperformance is highly dependent on the rotation of the cracks, the directsampling method is further analyzed by establishing a representation usingBessel functions of orders zero and one. Based on the derived representation ofindicator function, we design improved direct sampling methods by applyingincident fields with multiple directions and multiple frequencies.Corresponding analysis of indicator functions and simulation results are shownfor demonstrating the effectiveness and improvements.

Direct sampling method for retrieving small perfectly conducting cracks