Reduced absorption coefficients

Figure 8.22. Fluorescence reabsorption in a finite scattering layer with K°/S = 0.1 as a function of the scattering thickness Sd. Ordinate fraction of emitted to true fluorescence intensity in backward (upper) and forward direction (lower). Parameter reduced absorption coefficient at the fluorescence wavelength.

The spectrum k(p,T) thus calculated should be corrected, since, as pointed out by KRO, the asymptotic value p( ) from their calculations should be increased by 1050 cm (i.e. by a factor of 1.066) in order to obtain the correct experimental Na D transition frequency. Previously (L2) our correction procedure has been to multiply the frequency scale of the calculated spectrum by this factor of 1.066. It has been pointed out to us (D.D. Konowalow, private communication) that a more appropriate correction procedure is to increase the separation of the KRO potential curves involved by 1050 cm", i.e. to add 1050 cm to the frequency scale of the spectrum as calculated in the previous paragraph. We have adopted this latter procedure and a resulting spectrum of the reduced absorption coefficient k(i, T)/[Na] is given by the fully drawn curves in Figure 3 for T= 2000 K. The spectrum contains four partly overlapping contributions due to the four optically allowed Na2 transitions in the visible and near-infrared part of the spectrum, namely X Sg,... 

Figure 3. The drawn curves represent the reduced absorption coefficient k/[Nap as a function of wavelength, calculated for 2000 K from Table III of Ref. 14, using Eq. 1, and adding 1050 cm to all transition frequencies. The spectrum has been folded with a Gaussian curve 7 nm wide (FWHM) to smooth the satellites. The four contributions from the four optically allowed Na ...

Figure 4. Experimental spectrum of the reduced absorption coefficient k/[NaP, from Ref. 12. The spectrum was constructed from absorption spectra measured for sodium vapor pressures in between 100 and 1000 torr. The error bar indicates the absolute accuracy of this procedure (relative errors are considerably smaller). The Na nonresonance lines and the K and Cs resonance lines (see Fig. 2) were omitted.

The above has completely ignored stimulated emission. It may be shown that this effect can be accurately corrected by using a reduced absorption coefficient... 

For calculating the reduced absorption coefficients directly observed in the spectra, the quasi-static approximation [85] was used. From this approximation, the collision-induced absorption spectra are determined by the following three quantities, (1) excitation energies, (2) Boltzmann distribution of the ground state and (3) induced transition moments as the functions of the internuclear distance. 

Fig. 39.9. Reduced absorption coefficients for the (a) 5d and (b) 7s states of CsXe. The experimental spectrum is due to Moe et al. [82], and the SAC-CI theoretical spectrum is from ours [84].

Thickness. The traditional definition of thermal conductivity as an intrinsic property of a material where conduction is the only mode of heat transmission is not appHcable to low density materials. Although radiation between parallel surfaces is independent of distance, the measurement of X where radiation is significant requires the introduction of an additional variable, thickness. The thickness effect is observed in materials of low density at ambient temperatures and in materials of higher density at elevated temperatures. It depends on the radiation permeance of the materials, which in turn is influenced by the absorption coefficient and the density. For a cellular plastic material having a density on the order of 10 kg/m, the difference between a 25 and 100 mm thick specimen ranges from 12—15%. This reduces to less than 4% for a density of 48 kg/m. References 23—27 discuss the issue of thickness in more detail. 

Only slightly less accurate ( 0.3—0.5%) and more versatile in scale are other titration techniques. Plutonium maybe oxidized in aqueous solution to PuO " 2 using AgO, and then reduced to Pu" " by a known excess of Fe", which is back-titrated with Ce" ". Pu" " may be titrated complexometricaHy with EDTA and a colorimetric indicator such as Arsenazo(I), even in the presence of a large excess of UO " 2- Solution spectrophotometry (Figs. 4 and 5) can be utilized if the plutonium oxidation state is known or controlled. The spectrophotometric method is very sensitive if a colored complex such as Arsenazo(III) is used. Analytically usehil absorption maxima and molar absorption coefficients ( s) are given in Table 10. Laser photoacoustic spectroscopy has been developed for both elemental analysis and speciation (oxidation state) at concentrations of lO " — 10 M (118). Chemical extraction can also be used to enhance this technique. 

From Eq. (3.28), one finds that the oscillator strength is proportional to the square of the soliton-anlisolilon separation R. Using this, Eq. (3.33) reduces to the following form for the average absorption coefficient at low photon eneigy ... 

Bunsen (1855), to whom we owe the first accurate measurements of the solubilities of gases in liquids, expressed his results in terms of an absorption coefficient /3, which he defined as the volume of gas, reduced to 0° C. and 76 cm., dissolved by 1 c.c. of the liquid at any given temperature under the same pressure. If v c.c. of gas are dissolved by Y c.c. of liquid at a temperature 6 and pressure p cm., the volume reduced to normal conditions is... 

The metal formed is deposited on the colloidal particles and causes the absorption of the solution to increase at all wavelengtlK. The depositel cadmium is very reactive. It is reoxidized when air is admitted to the illuminated solution. Addition of methyl viologen to the illuminated solution under the exclusion of air yields the blue colour of the semi-ceduced methyl viologen, MV". As the absorption coefficient of MV" is known, the concentration of reduced cadmium can be readily calculated. reoxidises cadmium atoms ... 

Since then, number of researcher have studied and experimented with TRS including Chance and Oda [61] [63] [76] [80] [81] [73] [82] [113] [114], TRS instruments rely on a picosecond pulsed laser with a detector that is designed to detect the time evolution of the light intensity [44], With the time profile of light intensity through the medium, it is possible to measure both absorption and reduced scattering coefficients [32], A ma-... 

Y. Yamashita, M. Oda, H. Naruse, and M. Tamura. In vivo measurement of reduced scattering and absorption coefficients of living tissue using time-resolved spectroscopy. OSA TOPS, 2 387-390, 1996. 

Silicon is the most popular material for photovoltaic (PV) power. Another material is gallium arsenide (GaAs), which is a compound semiconductor. GaAs has a crystal structure similar to that of silicon, but it consists of alternating gallium and arsenic atoms. It is well suited for PV applications since it has a high light absorption coefficient and only a thin layer of material is required, which reduces the cost. 

Because Si — Ti absorption has a very small molar absorption coefficient, we would expect (because of the inverse relation between 8 and T0) the Ti state to have a much greater luminescent lifetime than the same molecules in the Si state. As a result of this longer lifetime, the Ti state is particularly susceptible to quenching, such that phosphorescence in fluid solution is not readily observed as the Ti state is quenched before emission can occur. This quenching in solution involves the diffusion together of either two Ti molecules or the Ti molecule and a dissolved oxygen molecule or some impurity molecule. In order to observe phosphorescence it is necessary to reduce or prevent the diffusion processes. The techniques most often used are ... 

When a polymer absorbs very strongly in the visible region, near IR incident radiation is used. In a very coloured solution the scattered intensity is reduced by a factor exp(—e)2) where e is the absorption coefficient of the solvent. Hence i0 must be multiplied by exp(+e ) in order to obtain the true scattered intensity undiminished by absorption effects. For small values of efi, the quantity exp(efi) approximates well to (1 + e2) so that Eq. (42) becomes38. ... 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

The speed of response of the photodiode depends on the diffusion of carriers, the capacitance of the depletion layer, and the thickness of the depletion layer. The forward bias itself increases the width of the depletion layer thus reducing the capacitance. Nevertheless, some design compromises are always required between quantum efficiency and speed of response. The quantum efficiency of a photodiode is determined largely by the absorption coefficient of the absorbing semiconductor layer. Ideally all absorption should occur in the depletion region. This can be achieved by increasing the thickness of the depletion layer, but then the response time increases accordingly. 

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