On a numerical minimization problem for a new class of nonlinear partial differential equations arising in nonspherical geometrical optics and beamforming lenticular antennas. II (Q1094847)

An improved mixed numerical and analytical procedure for solving the problem of determining the surfaces \({\mathcal S}\) and \({\mathcal S}'\) of a three-dimensional, aperture or volume extremized and ellipticized, bifocal, nonspherical, singlet optical, radar or sonar lens antenna defined by a system of four nonlinear partial differential equations with specified symmetry and boundary conditions subject to a minimizing side condition on the antenna focal length, of f-number, is presented. The index of refraction \(n_ 0\), the maximum lens diameter \(2b_ 0\) and the bifocal off-axis angle \(\psi_ 0\) are assumed given. The results obtained are of approximately twice the accuracy of those computed in Part I [the authors and \textit{D. R. Childs}, ibid. 12/13, 591-607 (1985; Zbl 0576.65127)].