A Radon Transform Interpretation of Contour Integral in Time-Domain Equivalent Edge Currents

Time-domain equivalent edge currents (TD-EEC) require the calculation of an integral of the input pulse over the edge contour and thereby yield finite results at the caustics of diffracted rays. Generally, the edge contour is subdivided into a series of straight segments, and the contour integral is evaluated as a sum of the integration over each segment. However, the length of each straight segment should be small enough in order to satisfy the accuracy of integration. In this letter, this integration is interpreted as a Radon transform, on the basis of which an exact closed-form expression is obtained. The accuracy of the derived closed-form expression is not dependent on the length of the integration line of interest. Hence, the need for subdivision can be eliminated for any straight diffracting edge. Some numerical examples are provided to demonstrate the validity and applicability of the proposed approach .