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We examine the possibility of applying the baryonic acoustic oscillation reconstruction method to improve the neutrino mass Σm ν constraint. Thanks to the Gaussianization of the process, we demonstrate that the reconstruction algorithm could improve the measurement accuracy by roughly a factor of two. On the other hand, the reconstruction process itself becomes a source of systematic error. While the algorithm is supposed to produce the displacement field from a density distribution, various approximations cause the reconstructed output to deviate on intermediate scales. Nevertheless, it is still possible to benefit from this Gaussianized field, given that we can carefully calibrate the “transfer function” between the reconstruction output and theoretical displacement divergence from simulations. The limitation of this approach is then set by the numerical stability of this transfer function. With an ensemble of simulations, we show that such systematic error could become comparable to statistical uncertainties for a DESI-like survey and be safely neglected for other less ambitious surveys.

The diffraction by a terminated, semi-infinite parallel- plate waveguide with four-layer material loading is rigorously analyzed for the H-polarized plane wave incidence by means of the Wiener- Hopf technique. Introducing the Fourier transform for the unknown scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations. The Wiener-Hopf equations are solved via the factorization and decomposition procedure together with the use of the edge condition leading to exact and approximate solutions. The scattered field inside and outside the waveguide is evaluated by taking the inverse Fourier transform and applying the saddle point method. Numerical examples on the radar cross section (RCS) are presented for various physical parameters, and the backscattering characteristics of the waveguide are discussed.

The plane wave diffraction by a finite parallel-plate waveguide with four-layer material loading is rigorously analyzed using the Wiener-Hopf technique for both E and H polarizations. Representative numerical examples of the radar cross section are shown for various physical parameters and the far field scattering characteristics are discussed in detail.