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We apply the stationary phase method developed in (Assier, Shanin \&Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by aquarter-plane. The wave field is written as a double Fourier transform of anunknown spectral function. We make use of the analytical continuation resultsof (Assier \& Shanin, QJMAM, 72(1), 2018) to uncover the singularity structureof this spectral function. This allows us to provide a closed-form far-fieldasymptotic expansion of the field by estimating the double Fourier integralnear some special points of the spectral function. All the known results on thefar-field asymptotics of the quarter-plane problem are recovered, and newmathematical expressions are derived for the secondary diffracted waves in theplane of the scatterer.

A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem