Absorption coefficient functions

The mathematical reconstruction of a property field, F(x,y), from its projection in the 0 direction is the basis of "Computerized Tomography" (1,2). An identical technique can be used to reconstruct a field of linear absorption coefficient functions in a combusting flow field from multiangular path integrated absorption measurements. The linear absorption coefficient is the familiar N.Q. product, where is the concentration of species i and Q. is the absorption cross section of species i at the frequency v. The Bouguer-Lambert-Beer law states that... 

The linear absorption coefficient functions can thus be reconstructed using only projection data. 

Significance of the Peak Absorption Coefficient Functions for Quantitative Millimetre Wavelength Spectrometry... 

The sensitivity of the luminescence IP s in the systems employed here decreases with increasing x-ray energy more strongly than in the case of x-ray film. Therefore, this phenomenon must be compensated by using thicker lead front and back screens. The specific contrast c,p [1,3] is an appropriate parameter for a comparison between IP s and film, since it may be measured independently of the spatial resolution. Since the absorption coefficient p remains roughly constant for constant tube voltage and the same material, it suffices to measure and compare the scatter ratio k. Fig. 2 shows k as a function of the front and back screen thickness for the IP s for 400 keV and different wall thicknesses. The corresponding measured scatter ratios for x-ray films with 0,1 mm front and back screens of lead are likewise shown. The equivalent value for the front and back screen thicknesses is found from the intersection of the curves for the IP s and the film value. 

The detailed examination of the behavior of light passing through or reflected by an interface can, in principle, allow the determination of the monolayer thickness, its index of refiraction and absorption coefficient as a function of wavelength. The subjects of ellipsometry, spectroscopy, and x-ray reflection deal with this goal we sketch these techniques here. 

Fig. 3. Spectra showing absorption coefficient as a function of the photon energy in a direct band gap semiconductor where (—) represents absorption,...

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

In this expression, z is the distance from the surface into the sample, a(z) is the absorption coefficient, and S, the depth of penetration, is given by Eq. 2. A depth profile can be obtained for a given functional group by determining a(z), which is the inverse Laplace transform of A(S), for an absorption band characteristic of that functional group. 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

Fig. 1-10. Log-log plot showing mass absorption coefficient as a function of wavelength for three common metals. Note that the discontinuities locate the absorption edges, (K) and (L). (Liebhafsky, Ann. N.Y. Acad. Sci., 53, 997.)...

Between absorption edges, the photoelectric (true) mass absorption coefficient r can be expressed as the following approximate empirical function of Z and X ... 

In his treatment, Sherman makes use of emission coefficients t that perform the function of the empirical k in Equation 6-4. Both quantities are proportional to. the product of absorption coefficient, of fluorescence yield and of (1 — 1/r), where r is the absorption-jump ratio involved (4.4). 

Fig. 2.3. Schematic variation of absorption coefficient as a function of the frequency of absorbed radiation experimental curve (1) and theoretical curves in Debye approximation (2) and impact approximation (3) (Rocard formula).

Fig. 2.8. The absorption coefficient of CHBr3 in CCL as a function of dimensionless frequency [113] (— —) theory 2. (—) experiment.

The penetration of ions from the subphase into the shell of spread particles is a general phenomenon and can be used to modify and functionalize the particle surface. For example, metal ions, such as Ba and Fe, or cationic polyelectrolytes, such as the polycation of polyallylamine, can be adsorbed at anionic particles, while anionic water-soluble dyes, such as phthalocyanine tetrasulfonic acid and 1.4-diketo-3.6-diphenylpyrrolo[3.4-c]pyrrole-4, 4 -disulfonic acid (DPPS) [157], can be adsorbed at cationic particles. However, since only a monolayer of the dye is adsorbed, a deep coloration of the particles is not obtained unless a dye with very high absorption coefficient is used [156],... 

A linear relation exists between the sound-absorption coefficients in the melts and their volumes V, cm ) as a function of temperature ... 

Perturbation of a spin-state equilibrium by ultrasound results in the absorption of sound, the absorption coefficient a (neper cm ) being determined as a function of frequency /(Hz) according to ... 

For all chemical elements, mass absorption coefficients p/p arc tabulated [13, 85] as a function of the X-ray wavelength. Chemical composition, mass density p, and thickness t of the sample are known. 

Deduce the selective absorption coefficients /q(Av, x,) as functions of depth and distance from the line centre. 

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

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