Optically thick limit

There will be a certain proportion of suitcases whose contents are so optically thick that it is impossible to achieve sufficient penetration to acquire a useful number of photons in the diffraction profile. This renders evaluation impossible. Such an impenetrable suitcase raises a dark (sometimes called shield ) alarm. Clearly, the most effective way of reducing the dark alarm rate is to raise the mean photon energy. It is in this respect that the HETRA method of diffraction profile analysis (Section 2.3.1.) may prove helpful as it utilizes photons at the high-energy limit, where the suitcase is most transparent. 

XPS and IR absorption measurements indicated that the films were of a surprisingly high purity with carbon, nitrogen, and oxygen content below the detection limit for both methods. Using calibrated quantitative FT-IR absorption measurements [5] on > 3.2 pm thick films deposited on a metallic substrate and measured in reflection (i.e., the effective optical thickness was i 6.4 pm) we determined the detection limit of 3-10 oxygen atoms per cm. The oxygen content remained below this limit even after several months of their exposure to air at room temperature. 

Section E.5.2, it may be seen from equation (E-50) that Ip is a local property of the gas mixture, not dependent on the experimental environment. Therefore, until the gas begins to become optically thick, which might not occur until sizes on the order of meters are reached, dimensions of the experimental apparatus do not influence any of the terms in equation (9), and predicted limits from radiant loss are apparatus-independent. 

In view of the complexity associated with equation (48), approximate methods are needed for applications. References [6] and [33]-[38] may be consulted for these approximations. While scattering may be important in combustion situations involving large numbers of small condensed-phase particles, often the effects of scattering may be approximated as additional contributions to emission and absorption, thereby eliminating the integral term. Two classical limits in radiation-transport theory are those of optically thick and optically thin media the former limit seldom is applicable in combustion, while the latter often is. In the optically thin limit, gas-phase... 

Roughly half of young T Tauri stars with ages <10Myr are observed to have optically thick disks of gas and dust with masses of 0.001-IM (Beckwith et al., 1990 Strom, 1994). These disks have spectra containing absorption features caused by the presence of water ice and silicates. Ultraviolet and visible emission lines indicate that the central stars are accreting mass from their disks at rates of 10 -10 Mo yr (Hartmann et al., 1998). Optically thick circumstellar disks are not observed around stars older than —10 Myr (Strom, 1995), which provides an approximate upper limit for the lifetime of the Sun s protoplanetary nebula. 

As can be seen from Fig. 5.79, the choice of the correction factor C is arbitrary within certain limits. It also depends on the range of optical thickness in which a particularly good agreement between -A g(kGLrj) and tG(kGsm) is to be reached. This is why the values of sm for some cases in the literature may differ slightly from one another. 

Astrophysical objects that do not contribute to UHECR spectrum are not constrained by the WB limit. In optically thick sources (for which the optical depth is r/r. = Rgource (vp 11 ) 1) nucleons interact while neutrinos... 

The emissivity of the gas media is a function of many parameters including gas pressure, temperature, partial pressures of radiatively participating species, and optical path length or characteristic dimension. Thus, if the concentration of the absorb-ing/emitting species is increased, the emissivity of the media increases as well. If the optical thickness of a medium tends to infinity, then the emissivity of such a medium tends to 1, which corresponds to the blackbody limit. At this limit, radiation becomes a totally diffusive process. 

The optical thickness of a sample must be adapted to the peak absorption of the impurities to avoid saturation of the lines, and this can lead to very thin samples when the impurity concentration is large and cannot be reduced, and when the OS is also large. Inversely, the measurement of small impurity concentrations can require thick samples and this limits the spectroscopic measurements of impurities. In some cases, as an alternative to the increase of the thickness of the sample, it can be cut with a geometry allowing multiple internal reflections, which increases the optical path, as shown schematically in Fig. 4.5. 

Partly because of limited analysis of Antarctic stratospheric temperatures, early studies that followed the discovery of the ozone hole were not specific about the type of particles of which the observed PSCs were composed. It was generally assumed that the particles were mainly water ice (Steele et al., 1983). Stratospheric ice clouds are frequently optically thick and brilliant in color. Such clouds form when temperatures drop below the temperature at which ice forms (frost point), and are now referred to as Type 2 PSCs. However, sensitive satellite measurements (McCormick et al, 1982) suggested that optically thinner PSCs were also present at warmer temperatures. 

The equation of radiative transfer will not be solved here since solutions to some approximations of the equation are well known. In photon radiation, it has served as the framework for photon radiative transfer. It is well known that in the optically thin or ballistic photon limit, one gets the heat flux as q = g T[ - T ) from this equation for radiation between two black surfaces [13]. For the case of phonons, this is known as the Casimir limit. In the optically thick or diffusive limit, the equation reduces to q = -kpVT where kp is the photon thermal conductivity. The same results can be derived for phonon radiative transfer [14,15]. 

SPR has been used to analyze immunochemicals and to detect gases. The main limitation of SPR, however, is that the sensitivity depends on the optical thickness of the adsorbed layer, and, therefore, small molecules cannot be measured in very low concentrations. 

As a result, O Brien and Bowman developed a comprehensive photopolymerization model. It incorporates heat and mass transfer effects, diffusion-controlled propagation and termination, and temporal and spatial variation of species concentration, temperature, and hght intensity. This model is applied to systems with varying diermal and optical properties. The absorbance of the polymerizing system is varied by altering either the initiator concentration, sample thickness, or molar absorption coefficient of the initiator. Based on simulations they concluded that the choice of initiator and sample thickness limits the initiator concentration usable to achieve complete monomer... 

This method is compared to a totally independent procedure, the VLT method, where diffuse reflection spectra are collected at several controlled powder thicknesses. Assuming that the backing is either completely transparent or completely opaque, the diffuse reflectance of the powder layers increases with increasing sample thickness until the reflectance of an optically thick sample (Roo) is reached. For each measured wavelength, an exponential function is fitted to the experimental data (plots of log(l /R) vs. sample thickness, where R is the measured reflectance). Using the 98% limit, the effective sample size can be obtained from the exponential fit (see [75] for a detailed discussion of the VLT method). 

We have obtained spatial and average dependences of the optical thickness, shape and width of the resonance radiation absorption on the initial optical density tq and the ratio of the limiting gas expansion velocity Vr to the thermal velocity of atoms Vo (a = Vr/Vo) in a self-similarly expanding gaseous sphere. The asymptotic and numerical estimates appear to be in good agreement for both small and large a. 

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