A small attenuation coefficient indicates that the material in question is relatively transparent, while a larger value indicates greater degrees of opacity. The attenuation coefficient is dependent upon the type of material and the energy of the radiation. Generally, for electromagnetic radiation, the higher the energy of the incident photons and the less dense the material in question, the lower the corresponding attenuation coefficient will be.
Absorption Coefficient
The spectral hemispherical attenuation coefficient in frequency and spectral hemispherical attenuation coefficient in wavelength of a volume, denoted ÎÎ and ÎÎ respectively, are defined as:[6]
The spectral directional attenuation coefficient in frequency and spectral directional attenuation coefficient in wavelength of a volume, denoted ÎÎ,Î and ÎÎ,Î respectively, are defined as[6]
When a narrow (collimated) beam passes through a volume, the beam will lose intensity due to two processes: absorption and scattering. Absorption indicated energy that is lost from the beam, while scattering indicates light that is redirected in a (random) direction, and hence is no longer in the beam, but still present, resulting in diffuse light.
In this context, the "absorption coefficient" measures how quickly the beam would lose radiant flux due to the absorption alone, while "attenuation coefficient" measures the total loss of narrow-beam intensity, including scattering as well. "Narrow-beam attenuation coefficient" always unambiguously refers to the latter. The attenuation coefficient is at least as large as the absorption coefficient; they are equal in the idealized case of no scattering.
The (Napierian) attenuation coefficient and the decadic attenuation coefficient of a material sample are related to the number densities and the amount concentrations of its N attenuating species as
The absorption coefficient determines how far into a material light of a particular wavelength can penetrate before it is absorbed. In a material with a low absorption coefficient, light is only poorly absorbed, and if the material is thin enough, it will appear transparent to that wavelength. The absorption coefficient depends on the material and also on the wavelength of light which is being absorbed. Semiconductor materials have a sharp edge in their absorption coefficient, since light which has energy below the band gap does not have sufficient energy to excite an electron into the conduction band from the valence band. Consequently, this light is not absorbed. The absorption coefficient for several semiconductor materials is shown below.
The above graph shows that even for those photons which have an energy above the band gap, the absorption coefficient is not constant, but still depends strongly on wavelength. The probability of absorbing a photon depends on the likelihood of having a photon and an electron interact in such a way as to move from one energy band to another. For photons which have an energy very close to that of the band gap, the absorption is relatively low since only those electrons directly at the valence band edge can interact with the photon to cause absorption. As the photon energy increases, not just the electrons already having energy close to that of the band gap can interact with the photon. Therefore, a larger number of electrons can interact with the photon and result in the photon being absorbed.
Tables and graphs of the photon mass attenuation coefficient Î/Ï and the mass energy-absorption coefficient Îen/Ï are presented for all of the elements Z = 1 to 92, and for 48 compounds and mixtures of radiological interest. The tables cover energies of the photon (x-ray, gamma ray, bremsstrahlung) from 1 keV to 20 MeV. The Î/Ï values are taken from the current photon interaction database at the National Institute of Standards and Technology, and the Îen/Ï values are based on the new calculations by Seltzer described in Radiation Research 136, 147 (1993). These tables of Î/Ï and Îen/Ï replace and extend the tables given by Hubbell in the International Journal of Applied Radiation and Isotopes 33, 1269 (1982).
where hE and ha are, respectively, heat transfer dissipates into the Earth ground and ambient air, TE and Tg are temperature of the Earth's surface and that in the ground far from the Earth's surface, ÏE, εE are diffuse reflectivity and emissivity of the Earth's surface, and σ is Stefan-Boltzmann constant. The reference temperature T(9900) is chosen to be temperature nearly independent of heat transfer from the Earth's surface. The term on the left-hand side of Eq. (20) is heat conduction from the Earth's surface to air. Terms on the right-hand sides are heat transfer into the ground, convection to the troposphere, and absorption and emission of radiation by the Earth's surface, respectively. Boundary condition at the tropopause is
Comparison of absorption coefficient of carbon dioxide in bands with wavelength centered at 15, 4.3, 2.7, and 2 Îm, predicted from available theory [29] and exponential wide band model from this work [23]. Abscissa for 1 atm-cm = 2.69Ã1019molecules/cm2 at STP. An increase in concentration of carbon dioxide increases absorption coefficient.
Absorption coefficient, temperature, density, band intensity, correlation parameter related to band width and effective width of bands centered at (a) 15 Îm for s =10 m, absorption coefficient, temperature, band intensity and effective width of bands centered at (b) 15 Îm for s = 104 m, absorption coefficient, band intensity and effective width of bands centered at (c) 4.3 Îm for s = 104 m and carbon dioxide concentration of 350 ppm, and absorption coefficient, band intensity, optical thickness at band center, overlap parameter and effective width of bands centered at (d) 15 Îm for s = 104 m and carbon dioxide concentration of 100 ppm across the troposphere.
The effects of carbon dioxide concentration on absorption coefficient across the troposphere in different bands centered at (a) 15 Îm, (b) 4.3 Îm, (c) 2.7 Îm, and (d) 2 Îm. An increase in carbon dioxide concentration significantly enhances change in absorption coefficient across troposphere.
The molar absorption coefficient, epsilon, of a protein is usually based on concentrations measured by dry weight, nitrogen, or amino acid analysis. The studies reported here suggest that the Edelhoch method is the best method for measuring epsilon for a protein. (This method is described by Gill and von Hippel [1989, Anal Biochem 182:319-326] and is based on data from Edelhoch [1967, Biochemistry 6:1948-1954]). The absorbance of a protein at 280 nm depends on the content of Trp, Tyr, and cystine (disulfide bonds). The average epsilon values for these chromophores in a sample of 18 well-characterized proteins have been estimated, and the epsilon values in water, propanol, 6 M guanidine hydrochloride (GdnHCl), and 8 M urea have been measured. For Trp, the average epsilon values for the proteins are less than the epsilon values measured in any of the solvents. For Tyr, the average epsilon values for the proteins are intermediate between those measured in 6 M GdnHCl and those measured in propanol. Based on a sample of 116 measured epsilon values for 80 proteins, the epsilon at 280 nm of a folded protein in water, epsilon (280), can best be predicted with this equation: epsilon (280) (M-1 cm-1) = (#Trp)(5,500) + (#Tyr)(1,490) + (#cystine)(125) These epsilon (280) values are quite reliable for proteins containing Trp residues, and less reliable for proteins that do not. However, the Edelhoch method is convenient and accurate, and the best approach is to measure rather than predict epsilon.
Despite the fact that others use equivalents, I will present the oxy anddeoxy-hemoglobin spectra in terms of molar extinction coefficient. To convert from the molar extinction coefficient e to absorbance A, multiply by the molar concentrationand the pathlength. For example, if x is the number of grams per literand a 1 cm cuvette is being used, then the absorbance is given by
The absorption coefficient Î has been observed by sending a beam of electrons through thallium vapor and measuring the decrease in intensity of the beam as a function of the pressure of the vapor. Î, plotted as a function of the velocity of the electrons, decreases rapidly to a minimum of 15 at 1.4 volts, rises less rapidly to a maximum of 51 at 4.5 volts, and then slopes off gradually to 20 at 100 volts.
Over the last few decades, research works have focused on elucidating the optical properties of semiconductor materials. Despite remarkable progress in the measurement and calculation of the absorption coefficient for semiconductor materials, there is a lack of comprehensive review on the comparative study of absorption coefficient properties for different types of bulk semiconductor materials and their methods for calculating the absorption coefficient. Hence, this paper summarizes the fundamentals of the various methods used to determine the absorption coefficient properties of bulk growth semiconductor crystals, and discusses their advantages and disadvantages. Furthermore, this review provides comprehensive results from recent studies and findings on the absorption properties of near- to mid-infrared (wavelengths from 800 to 7300 nm) group III-V semiconductor materials. In addition, the absorption coefficient of the conventional group IV semiconductors (silicon and Ge) were included for performance comparison. Critical analysis was done for the reviewed materials concerning their material properties, such as band gap structure, crystal quality, and the structural design of the device. The related studies on the methods to determine the absorption coefficients of semiconductors and to improve the likelihood of absorption performance were well highlighted. This review also provides an in-depth discussion on the knowledge of absorption coefficient based on a wide range of semiconductor materials and their potential for sensors, photodetectors, solar and photovoltaic application in the near to mid infrared region. Lastly, the future prospects for research on absorption coefficients are discussed and the advancement in the determination of absorption coefficients for new ternary and quaternary materials is proposed using artificial intelligence such as neural networks and genetic algorithm.
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