Absorption path

One effect of saturation, and the dependence of e on /, is to decrease the maximum absorption intensity of a spectral line. The central part of the line is flattened and the intensity of the wings is increased. The result is that the line is broadened, and the effect is known as power, or saturation, broadening. Typically, microwave power of the order of 1 mW cm may produce such broadening. Minimizing the power of the source and reducing the absorption path length t can limit the effects of power broadening. 

It is interesting to note that a similar specttum of the 0-0 band of the a-X system, leading to the same value of the absorption intensity, has been obtained using a Fourier transform spectrometer (see Section 3.3.3.2) but with an absorption path, using a multiple reflection cell, of 129 m and half the pressure of gas. 

Cavity-enhanced absorption techniques are also applied in flames in the near infrared [22-25]. The multiple absorption paths provided with these techniques are the reason for their superb sensitivity in the ppb range. Absolute concentrations can be obtained, provided the absorption coefficient for the respective transition is known. CRDS can be used in conjunction with other laser-based combustion diagnostics for... 

In the author s laboratory, an Autoanalyzer turntable is used which rotates, at a speed, so that the 40 specimens can be assayed in a 10 - 15 minute period. Figure 24 shows the principle of atomic absorption. Note that an elongated absorption path is provided for higher sensitivity. 

C02-IR detection systems for example contain a light source emitting infrared light ideally at wavelengths around 4.2 pm (often a simple light bulb), an absorption path (the so called cuvette), a spectral filter and a detector (thermopile). The filter is normally integrated into the detector housing. 

Infrared diode laser spectroscopy has been used for the measurement of hydrocarbon and CO concentrations in exhaust (13, 14, 15). The adsorption path length, and thus the absorption cell volume, required for hydrocarbon measurement is rather large, limiting the time-resolution of the measurement. The absorption path length required for CO measurement, however, is relatively short and approximately equal to the diameter of a standard exhaust pipe. This allows CO to be measured with high time-resolution by an infrared laser beam passed through an... 

Absorption by the analyte causes a change in dip depth that, when small (weak analyte absorption), is proportional to the change in analyte absorption coefficient, in analogy with Beer s law. A theoretical effective absorption path length L ff can then be obtained from the dip-depth dependence on the absorption coefficient of the analyte... 

In the absence of solvent absorption, this effective absorption path length can be expressed as... 

An experimental effective absorption path length L ff can be found by measuring the dip depth in the absence of analyte (M0) and in the presence of analyte (M0 + AM0)... 

As with (5.4), this holds for small changes in dip depth or aaL ff 1. Comparison of experimental and theoretical effective absorption path lengths for detection of atmospheric trace gases shows good agreement4, as discussed in Sect. 5.3. 

Let the effective loss coefficient now include, in addition to intrinsic loss, a contribution due to absorption (and scattering) by the analyte contained in the evanescent fraction/of the WGM y = yx +/xa. The effect of the analyte on the resonant (single-frequency) drop signal D0a, when analyte absorption is a small fraction of the total loss, can be written in terms of an approximate effective absorption path length Leff as defined below ... 

Here, Leff is the effective absorption path length as defined in the low-analyte-absorption limit. However, the last expression forD0a is valid even for large analyte absorption, that is, there are no restrictions on the size of aaLeffas long as/aaL 1. 

The rest of the detector signal is noise filtered and amplified by a lock-in amplifier. The output of the lock-in amplifier is monitored by an oscilloscope, and recorded as the laser scans across the gas s absorption line. The result is a spectral profile of the gas absorption, impressed on the depth of the locked resonance dip. This is then analyzed using (5.6) to find an experimental effective absorption path length. 

In Table 5.1, the theoretical effective absorption path length is calculated from (5.5) using, for example, in the case of methane, x = 0.28 (calculated from the dip depth M0 the dip gets shallower with analyte absorption, so the WGM is undercoupled), / = 1.6% (estimated from a computation of the field distributions at the same wavelength in a microsphere of the same diameter), and oq = 0.0061 cm 1... 

The intensity of an electric dipole transition in absorption or emission depends, on one hand, on factors particular to the experiment measuring the intensity, e.g., the number density of molecules in the initial state of the transition and, for absorption experiments, the absorption path length and the intensity of the incident light. On the other hand, the intensity involves a factor independent of the experimental parameters. This factor, the line strength 5(f <— i), determines the probability that a molecule in the initial state i of the transition f <— i will end up in the final state f within unit time. 

Figure 2. Relation of sample thickness to absorption path length in an ideahstic, plan-parallel...

If the effect of absorption can not be neglected in the sample, the ratio of measured intensities contains the ratio of two exponentials from Beer s law. It corresponds to a difference inside the exponential. In practice, it is the mass absorption coefficients (ju/p) and the absorption path lengths expressed in mass thickness (pL) that are used. 

It can be seen that calculation of the absorption correction also needs the values of the sample density and the linear value of the absorption path length beside the mass absorption coefficients. It is also important to note that it is the difference of the absorption coefficients, what coimts in determining if the thin film criterion is fulfilled for a given sample (geometry). It frequently happens that the sample is thin for one pair of its components and thick if another pair of elements is considered from its components. 

Atomic absorption follows an exponential relationship between the intensity / of transmitted light and the absorption path length 1, which is similar to Lambert s law in molecular spectroscopy ... 

One problem of the measurement of weak absorption in the far IR is that short absorption paths must be used. At wavelengths comparable to the beam apertures diffraction effects lead to beam divergence [252]. (The combination of high gas pressures and short absorption paths may not be useful if many-body induction effects must be avoided, and an accurate measurement of a under conditions of weak absorption, I/Iq 1, is difficult [368].)... 

Lambert s law), where L is the absorption path length. The absorption coefficient a(v) is a function not only of frequency, but also of temperature, density, and, of course, the nature, composition, and state of matter (gaseous, liquid, solid) of the sample as is amply illustrated below. Absolute intensities of absorption spectra may often be determined which are of interest for the comparison of measurements with the fundamental theory and in many applications (atmospheric sciences). 

Table 3.1 lists measured spectral moments of rare gas mixtures at various temperatures. (We note that absorption in helium-neon mixtures has been measured recently [253]. This mixture absorbs very weakly so that pressures of 1500 bar had to be used. Under these conditions, one would expect significant many-body interactions the measurement almost certainly does not represent binary spectra.) For easy reference below, we note that the precision of the data quoted in the Table is not at all uniform. Accurate values of the moments require good absorption measurements over the whole translational frequency band, from zero to the highest frequencies where radiation is absorbed. Such data are, however, difficult to obtain. Good measurements of the absorption coefficient a(v) require ratios of transmitted to incident intensities, /(v)//o, that are significantly smaller than unity and, at the same time, of the order of unity, i.e., not too small. Since in the far infrared the lengths of absorption paths are limited to a few meters and gas densities are limited to obtain purely... 

Fig. 3.10. The rototranslational absorption spectrum of H2-H2 pairs, recorded in equilibrium hydrogen (i.e., para-Fh and ortho-FL concentrations are in thermal equilibrium proportions) at three temperatures 77.4 K ( ), 195 K (x), and 293 K ( ). Various pressures from 10 to 100 atmospheres and a 3 m absorption path length were used after [37],...

The measurement of spectral moments requires the recording of complete spectra, including regions of high and low absorption where accurate measurements are difficult. In ordinary spectroscopy, these difficulties are often alleviated through the use of variable absorption path lengths and pressure variation. In the far infrared where the wavelengths are compa-... 

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