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In the conventional time-domain physical optics (PO) method, the far fields scattered by a metallic plate S of arbitrary shape have been given by a surface integral. However, the numerical evaluation of such a surface integral is time-consuming, which becomes the crux of time-domain PO technique. In this letter, a time-domain PO integral is formulated under the incidence of plane waves and observation in the far-field region. Then, the surface integral over S is reduced to a line integral around the boundary of S . When S is a polygon, the line integral is further reduced to a closed-form expression, which is very similar to the well-known Gordon formula in the evaluation of PO integral in the frequency domain. When S is arbitrarily shaped, the integral evaluation is also efficient once the polygon mesh is given. The efficiency and accuracy of the closed-form expression in the time domain are demonstrated through a number of numerical examples.