Method spectral projection

New Methods for Use in Scattering Calculations The Spectral Projection Method and the Stabilization Method... 

Note the similarity between the above equation and Eq. (25) originating from the spectral projection method of previous section. The symmetry of Eq. (49) which is due to the choice of Xp implies that the only integrals needed at each chosen energy are of the + or - form of... 

Acquiring spectral projections pertains to measuring linear cross sections in the time domain. This can be considered as a special case of a more general sampling scheme, where data points are sampled at any position of the time domain. The method is known as non-uniform or non-linear sampling (NUS or NLS). A historical perspective of this approach is well presented in Chap. 3. It was introduced almost a quarter of a century ago in a seminal publication by Laue and co-workers... 

Some "fast methods" such as single-scan experiments,93 94 Hadamard95 and projection-reconstruction techniques96 take a few seconds to produce 2D spectra, but suffer from a lack of spectral resolution. As mentioned... 

In our initial use of VIRS methods, we have chosen a diverse set of projects. These include epithermal-style precious metal mineralization (eastern and central Newfoundland), mesothermal gold mineralization (Central Newfoundland), syngenetic VMS mineralization and related alteration (Central Newfoundland), porphyry-style Mo-Cu mineralization (southern Newfoundland) and uranium mineralization in the Central Mineral Belt of Labrador. Space does not permit detailed discussion of results, but in all cases we were able to recognize distinctive alteration species and document their distribution. In some cases, results provided surprises, eg., the recognition of topaz in quartz-alunite alteration and possible Li-rich micas in VMS alteration influenced by magmatic fluids. In some cases, the resolution of species in mixed assemblages proved to be difficult, but the overall spectral patterns could still be used to discriminate alteration facies and demonstrate their superposition. 

Alternatively, the right-hand side can be written in terms of a projection tensor and a convolution (Pope 2000). The form given here is used in the pseudo-spectral method. 

If one of the stars in the binary is not a neutron star, then the tests become less precise. Suppose that one observes the optical light from the companion to a neutron star. In addition to the spectral information that allows measurement of P and i i, one also has photometric information (e.g., the total optical flux from the companion). The companion is distorted into a pear shape by the gravity of the neutron star, with the point towards the neutron star. Therefore, from the side there is more projected area and hence greater flux than from either end. If the orbit is edge-on (i = 90°) then the flux varies maximally if the orbit is face-on (i = 0°) then there is no variation. Therefore, by modeling the system one can estimate the inclination from the flux variations. This is called the method of ellipsoidal light curves (Avni Bahcall 1975). 

During the Western Project, a total of 3000 grab samples were assayed by using the rapid spectral method to determine 32 elements and chemical adsorption to determine gold. Spectral assay data were processed in order to determine the distribution of 24 elements. Background (Cf) values were calculated using Lognormal Statistics software. 

Other multivariate methods have been applied to ICP spectra for quantitative measurements. As examples, they include multicomponent spectral fitting (which is incorporated in several commercial instrument software) [81] matrix projection, which avoids measurement of background species [94,95] generalised standard additions [96] and Bayesian analysis [97]. 

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