On the closed-form evaluation of the PO integral using the Radon transform interpretation for linear triangles

This letter presents the complete mathematical formulation for the closed-form evaluation of the time domain physical optics (PO) integral on linear triangular patches using Radon transform (RT) interpretation. The incident field is assumed to be an impulsively excited plane wave and scattered fields are observed at far-zone. The PO integral is evaluated in closed-form as the intersection of the triangle and the plane formed by the incident and observation directions. In addition, a formula is suggested for the special case, which occurs if there is no intersection of the plane and all scatterer. Accuracy of the closed-form expressions is demonstrated via numerical examples.

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