Spectral intensity distribution

In addition to qualitative identification of the elements present, XRF can be used to determine quantitative elemental compositions and layer thicknesses of thin films. In quantitative analysis the observed intensities must be corrected for various factors, including the spectral intensity distribution of the incident X rays, fluorescent yields, matrix enhancements and absorptions, etc. Two general methods used for making these corrections are the empirical parameters method and the fimdamen-tal parameters methods. 

The nonconverted part of the laser output is focused into a gas-filled cell. A microplasma is produced in the focus (see Section III.9), and this emits a wavelength continuum between 2000-8000 A having sufficient intensity to be used as lightsource for the analysing pulse. Its pulse duration, as well as the spectral intensity distribution, depends on the gas used in the cell. With 1 atmosphere oxygen, for instance, the pulsewidth is 30 nsec. 

This is accomplished by splitting the continuum into two parallel beams displaced from one another by several millimeters. Both are focused into the sample cell through a dichroic mirror used to collinearly recombine the ultraviolet excitation pulse with the main continuum beam. In the sample, then, that continuum beam passes through the excited volume while the replica continuum beam traverses an unexcited region. A comparison of the two resulting spectral intensity distributions allows a determination of the desired induced absorbance spectrum. 

Coherent light sources are characterized by a spectral intensity distribution E(oj) and a frequency-dependent phase 0(w). According to first-order perturbation theory, linear absorption probabilities are given by the overlap between the spectrum of the light source E(w) and the optical transition, and are independent of the phase function In non-linear processes (2nd... 

A comparison of the UV Raman spectrum measured for coke deposited during the MTH reaction with that deposited during butane dehydrogenation catalyzed by chromia on alumina (66) shows clear differences in the spectral intensity distribution (Fig. 11). In particular, the intensity of the features in the regions 1340-1440cm and 1560 1630 cm are nearly equal for the MTH reaction. 

Balloon-Borne Ultraviolet Spectrographs. By using the spectrograph, from the spectral intensity distribution I (A, h) in the ultraviolet region of the solar spectrum, the ozone amount, x(h)j at a height h above the instrument was determined. As the... 

The theoretical studies of the spectral intensity distributions are complemented, and the insight gained is essentially augmented, by time-dependent investigations of the nonadiabatic nuclear dynamics. Here it should be recalled that the information... 

Apart from the atomic and ion lines of the species present in a plasma source an emission spectrum has a continuum on which the emission lines are superimposed. This extends over the whole spectrum. It is due to the interactions between free electrons ( Bremsstrahlung ) and to the interaction of free and bound electrons ( recombination continuum ). The former is particularly important in the UV spectral region, whereas the latter is important at longer wavelengths. The spectral intensity distribution for the continuum radiation is given by ... 

If therefore we know the mean energy of an oscillator, we know also the spectral intensity distribution of the cavity radiation. 

Here, d//dA denotes the spectral intensity distribution of the incident X-ray beam V is the volume of sample illuminated V0 is the sample unit cell volume 0 is the Bragg angle for the reflection h P is the polarisation factor A is an absorption correction for the sample in its capillaiy and D is a detector sensitivity and obliquity factor. Quantities such as P, A and D vary with any or all of A, 0 and x, the position of the diffracted beam on the detector the spectral intensity distribution is, in general, not precisely known in advance and the detector may suffer from spatial distortion and non-uniformity. Thus equation (7.17) may be written as... 

Figure 7.3 Reflection approximation Potential energy curves, repulsive wavefunctions, and intensity distribution for CI2 (from Herzberg, 1950, p.392). The wavefunctions are shown as thin full lines and Xv"=ol2 s shown as a dashed curve. The lower state x 2 is reflected on the upper state potential curve to give the spectral intensity distribution. The reflection approximation amounts to replacing the upper state wavefunction by a (5-function (shown as a narrow dashed curve labeled <5) at the turning point.

The polychromatic photons supplied to the system and reaching the mesh supporting the Ti02 can be estimated using the spectral intensity distribution with intensity in watts m nm . The intensity spectrum can be measured using the Sola Scope 2000 spectro-radiometer for the 300-390 nm range for every 0.5 nm (Ibrahim and de Lasa, 2002). In addition, similar measurements with the Sola Scope 2000 probe at different locations of the mesh of the Photo-CREC-Air unit can be used to confirm the uniform intensity disti ibution of photons reaching the mesh (Ibrahim, 2001). 

Let the intensity distribution at the focus be represented by the function G(o ), the reflectivity of the monochromator crystal by R(J, a, X), and the spectral intensity distribution of the primary beam by i(X - Xg) " 16 reflection intensity from the monochromator is proportional to the product of these functions [6]. The total intensity of the monochromator beam when the monochromator is placed at the Bragg angle (t> = t>g) is then defined by the following expression ... 

A thorough theoretical treatment of optical pumping can be found in the review of Happer [515] and [516]. Specific aspects of optical pumping by lasers with particular attention to problems arising from the spectral intensity distribution of the pump laser and from saturation effects were treated in [517, 518]. Applications of optical pumping methods to the investigation of small molecules were discussed in [508]. 

Fig. 6.57 Spectral intensity distribution of the higher harmonics produced by focussing a femtosecond terawatt laser at X = 720 nm into a neon jet [749]...

The desired spectroscopic information is obtained by numerical Fourier transformation of the experimental points of Fig.6. The result is shown in Fig. 7a where the computed spectral intensity distribution is plotted. A number of spectral lines is readily seen. Fig. 7a represents experimental information without use of the available spectroscopic data of CH. For improved frequency resolution we also applied the maximum entropy method (MEM). The spectrum obtained for this nonlinear transformation is depicted in Fig. 7b. 

Assume that a wave with the spectral intensity distribution 7o(y) traverses an interferometer with two mirrors, each having the reflectivity R and transmission factor T (Fig. 5.21). For the passive interferometer we obtain a frequency spectrum of the transmitted intensity according to (4.50). With an amplifying medium inside the resonator, the incident wave experiences the amplification factor (5.58) per round-trip and we obtain, analogous to (4.61) by summation over all interfering amplitudes, the total transmitted intensity... 

The spectral intensity distribution of the laser output is the superposition... 

In the time-independent approach, the object of primary importance is the spectral intensity distribution for an electronic transition into the vibroni-cally interacting manifold. According to Fermi s golden rule it can be written as... 

By definition, (t) represents the probabihty amphtude that, after a finite evolution time t, the system is stiU in the same state as at time t = 0. Referring back to Eq. (32), we see that (t) and the spectral intensity distribution P E) are related by Fourier transformation and thus contain the same information on the system dynamics. The square (t)P is also known as survival probability and provides a measure of noiuadiative decay processes occurring on picosecond or nanosecond time scales. ... 

The other approach, internal reflection, takes advantage of the fact that if an electromagnetic wave is totally reflected at the interface between an optically thicker and an optically thinner medium (refraction index of the optical thicker medium is higher), a part of the electromagnetic wave penetrates into the optical thinner medium (the so-called evanescent wave) where it may interact with any species present and may be absorbed. The spectral intensity distribution of the reflected light thus differs from that of the incident beam and contains information about species present in the interphase of the optical thinner medium. In practical setups ATR (attenuated total reflection) single crystals are used, onto which the electrode under investigation is deposited. The beam baths of internal and external reflection are visualized in Fig. 1. 

Here Wq is the centre angular frequency. The evaluation of this expression involves the same type of mathematics as that used for calculating the spectral intensity distribution from a grating, and we have... 

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