Uniform asymptotics with respect to the aspect ratio in high-frequency diffraction by an elliptic cylinder

At high frequencies the scattered field from most bodies is maximal in the direction of incidence. For infinitely thin obstacles such as disks or strips at grazing or near grazing incidence the diffraction picture is different. Evidently that when the body becomes more and more slender, the scattered field can not abruptly change. Taking as an example the case of the elliptic cylinder, we trace the changes in the field of diffraction when the shape of the cylinder varies from a circle to a strip. The asymptotic approach is based on the results of (I. V. Andronov, “Strong elongation versus a large transverse curvature in the problems of high-frequency diffraction”, Antennas and Wireless Propag. Lett., 13, p. 826-827, 2014) and (I. V. Andronov, “High-frequency diffraction by an elliptic cylinder: the near field”, J. of Electromagnetic waves and applications, 28, DOI: 10.1080/09205071.2014.966860, 2014). It brings to the uniform expression for the scattering amplitude with respect to the rate of the elongation.