Effective path length

Sensitivity can be improved by factors of 10 using intracavity absorption, placing an absorber inside a laser resonator cavity and detecting dips in the laser emission spectmm. The enhancement results from both the increased effective path length, and selective quenching of laser modes that suffer losses by being in resonance with an absorption feature. 

Realistically, the flow path through the seal volume will not consist of uniform cylindrical capillaries aligned normal to the seal. The actual leakage paths will be longer, less direct (convoluted), and of nonuniform cross-section. To account for these effects, the effective path length is increased by a tortuosity factor, t, typically having a value in the range of 2 to 3. 

In general Rytov approximation provides better reconstruction than Born approximation [8]. Here, MBLL is approximated locally at each sampling volume and the effective path length is estimated using the Rytov approximation as... 

This method is commonly nsed on spectral data to correct for multiplicative variations between spectra. In spectroscopy, snch variations often originate from nnintended or uncontrolled differences in sample path length (or effective path length, in the case of reflectance spectroscopy), caused by variations in sample physical properties (particle size, thickness), sample preparation, sample presentation, and perhaps even variations in spectrometer optics. Snch variations can be particularly problematic because they are confounded with mnltiplicative effects from changes in component concentrations, which often constitute the signal in qnantitative applications. It is important to note that multiplicative variations cannot be removed by derivatives, mean-centering or variable-wise scaling. 

The effective path length with the TIR cell is much shorter and composition information can be abstracted from the fingerprint region as well as direct observation of metal carbonyl species and CO2. However, the shorter path length can make detection and quantification of low concentrations of catalyst species more difficult. 

The use of the sun or moon as the light source allows one to measure the total column abundance, i.e., the concentration integrated through a column in the atmosphere. This approach has been used for a number of years (e.g., see Noxon (1975) for NOz measurements) and provided the first measurements of the nitrate radical in the atmosphere (Noxon et al., 1978). As discussed later in this chapter, such measurements made as a function of solar zenith angle also provide information on the vertical distributions of absorbing species. Cloud-free conditions are usually used for such measurements as discussed by Erie et al. (1995), the presence of tropospheric clouds can dramatically increase the effective path length (by an order of... 

The reason for the different dependencies of absorption on the concentration can be seen starting with the Beer-Lambert Law. If L° is the radiance of frequency v incident on an absorber with absorption coefficient a present at concentration N and the effective path length is /, the transmitted radiance Lv is given by... 

One important aspect of radiation and clouds that may ultimately prove to be important in this issue of excess cloud absorption is the very long effective path lengths for light inside clouds due to multiple scatter-... 

Temperature Sensing. As shown in Fig. 16, a layer of silicon (whose refractive index changes with temperature) is placed in the optical path in place of the evacuated cavity, as previously described. The second reflector (glass) is rigid. The effective path length thus changes with temperature. 

Fig. 16. Fiber-optic temperature sensor. A thin layer of silicon placed in the optical path exhibits a large change in refractive index with temperature, changing the effective path length. (Yazbak, Foxboro, Massachusetts)...

Fig. 17. Fiber-optic refractive index sensor. Fluid of interesl is drawn by capillary action into a duct through a glass substrate. The effective path length varies in proportion with the refractive index. (Yazbak, Foxboro, Massachusetts)...

The special properties of OTEs that permit the use of transmission spectro-electrochemical techniques are often at cross purposes with the acquisition of reliable electrochemical data. The desire to have the superior electrical properties of bulk conducting materials, and thereby reliable electrochemical data, together with the power of a coupled optical probe led groups to develop various diffraction and reflection approaches to spectroelectrochemistry. Light diffracted by a laser beam passing parallel to a planar bulk electrode can be used to significantly increase the effective path length and sensitivity in spectroelectrochemistry [66]. 

Any contribution from error (i) results in an overestimate of erT since the effective path length in the gas is greater by a factor sec 0 than the assumed value see equation (2.11). Error (iv) also leads to an underestimate of aT since not all the scattered projectiles are so identified. All reported experimental values of aT may be subject to one or more of the errors (i)-(iv), and it is important to bear this in mind when making comparisons between the results from different groups. 

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