This paper presents an extension over a novel, three dimensional high frequency method for the calculation of the scattered electromagnetic (EM) field from a Perfect Electric Conductor (PEC) plate, which is based on the Physical Optics (PO) approximation and the Stationary Phase Method (SPM). This extension defines a new analytical method which is proved to be very efficient in computer execution time and enhances the accuracy of its predecessor around the area of the main scattering lobe. This new analytical method accomplishes high accuracy through the use of higher order approximation terms, which imply the use of Fresnel functions (SPM-F method). By using higher order Fresnel approximation terms, no impact on the time efficiency of the SPM method appears to occur, since the extended SPM-F method just removes the troublesome vanishing denominators when the stationary point coincides with the edges of the scatterer. The SPM-F results are compared to other straightforward numerical and exact solution methods for the same problem in the far field, Fresnel zone and the near field area of the scatterer.
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