Ground-water availability on the Kitsap Peninsula, Washington

Transform Methods of Computerized Tomography in Studying Electronic Structure and Fermi Surfaces of Solids

“…This is summarized in Table, where the following abbreviations are used: CM -Cormack method (with orthogonal Chebyshev polynomials) [1,12]; DFT -direct Fourier transform [58,74]; FBP -filtered back projection [3] using Eq. (13); F-B -Fourier Bessel [52,53]; HP -Hermite polynomials [39]; JPJacobi polynomials [33]; ME -maximum entropy [81,84]; MFBP -modified FBP [50]; MM -Mijnarends' method [2]; PM -Pecora method [75].…”

“…In this technique, applied in papers [76][77][78][79], one calculates the 1D FT of measured 2D spectra which represent the 3D FT of the 3D density. By expanding FT into the lattice harmonics, one reconstructs the 3D density according to the Fourier-Bessel method proposed for plane pro- 1D CP ⇒ 2D densities CM [29][30][31][32] DFT [70][71][72][73] 1D NS ⇒ 3D densities HP [41,42] jections [52,53]. This method is equivalent to the following procedure.…”

“…(2), (3). Such a procedure, called the FourierBessel (F-B) method, was applied to reconstruct 2D densities from 2D ACAR data [51] and 3D densities from 1D Compton profiles [52][53][54][55][56] (for 3D space |q| in Eq. (11) should be replaced by q 2 ).…”

Reconstruction of Densities from Compton Profiles with Applying Jacobi Polynomials

“…Of course, in order to check if this method is the most efficient indeed, we intend to apply other techniques [1][2][3] to the same model projections in the future work.…”

“…Up to now four various algorithms have been known: Mijnarends [1] and Fourier transform [2] methods, orthogonal polynomial expansion [3] and application of maximum entropy [4]. So far, only two first algorithms [1,2] have been applied to the experimental data. In this paper we present the results of usage of a new technique that is proposed in the paper [5] and shortly described below.…”