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Applied Spectroscopy Spectroscopic Nomenclature Absorbance, A Negative logarithm to the base 10 of the transmittance: A = –log10(T). (Not used: absorbancy, extinction, or optical density). (See Note 3). Absorptance, α Ratio of the radiant power absorbed by the sample to the incident radiant power; approximately equal to (1 – T). (See Notes 2 and 3). Absorption The absorption of electromagnetic radiation when light is transmitted through a medium; hence ‘‘absorption spectrum’’ or ‘‘absorption band’’. (Not used: ‘‘absorbance mode’’ or ‘‘absorbance band’’ or ‘‘absorbance spectrum’’ unless the ordinate axis of the spectrum is Absorbance.) (See Note 3). Absorption index, k See imaginary refractive index. Absorptivity, α Internal absorbance divided by the product of sample path length, ℓ , and mass concentration, ρ , of the absorbing material.

α = Ai /ρℓ SI unit: m2 kg–1. Common unit: cm2 g–1; L g–1 cm–1. (Not used: absorbancy index, extinction coefficient, or specific extinction.) Attenuated total reflection, ATR A sampling technique in which the evanescent wave of a beam that has been internally reflected from the internal surface of a material of high refractive index at an angle greater than the critical angle is absorbed by a sample that is held very close to the surface. (See Note 3.) Attenuation The loss of electromagnetic radiation caused by both absorption and scattering. Beer–Lambert law Absorptivity of a substance is constant with respect to changes in path length and concentration of the absorber. Often called Beer’s law when only changes in concentration are of interest. Brewster’s angle, θB The angle of incidence at which the reflection of p-polarized radiation is zero. Circular birefringence

nL – nR, the difference between the refractive index of a medium for left, nL, and right, nR, circularly polarized radiation. Like the refractive indices, circular birefringence changes with wavenumber. SI unit: none, a dimensionless quantity. Circular dichroism In general, the property of different absorption of left and right circularly polarized radiation by an optically active material. Specifically, the circular dichroism is kL – kR, where kL and kR are the absorption indices (imaginary refractive indices) of the sample for left and right circularly polarized radiation, respectively. Note that some authors use the absorptivity or molar absorptivity instead of the absorption index. Like absorption of radiation, circular dichroism changes with wavenumber. Complex refractive index¸ ñ The complex sum of the real refractive index, n, and the imaginary refractive index, k. (ñ = n + ik) Critical angle, θC The angle above which a beam in an optically rare medium (low refractive index, n1) that is incident at an interface with an optically dense medium (higher refractive index, n2) is totally reflected. θC = sin-1(n1/ n2) Diffuse reflectance The ratio of the spectral intensity reflected by a scattering sample to that reflected by an equivalent non-absorbing reference that replaces the sample; sometimes refers to a measurement where specularly reflected radiation has been prevented from reaching the detector. The term ‘‘Remittance’’ may be used in place of ‘‘Diffuse reflectance’’ to emphasize inclusion of the specularly reflected radiation. SI unit: none, a dimensionless quantity. Diffuse reflection The process in which radiation is incident on a scattering sample at a certain angle and is returned (or remitted) over all angles. Diffuse reflection is a complicated process that involves transmission, reflection, and scattering. (See Note 3). Diffuse transmission The process in which radiation is transmitted by a scattering sample and leaves the sample in directions other than that required by Snell’s law of refraction. The process is complicated and involves transmission, reflection, and scattering. (See Note 3). Emittance, ε Ratio of the radiant flux emitted by the sample to that emitted by a black body at the same temperature. (See Notes 2 and 3).

Frequency, f, ν Number of cycles in unit time. SI unit: Hertz (1 Hz = 1 s–1). Imaginary refractive index, k A dimensionless parameter indicating the amount of absorption loss when an electromagnetic wave propagates through a material. k is equal to α/2π !ν , where α is the linear absorption coefficient (cm-1) and !ν is the wavenumber. (Also used: Index of absorption, absorption index; not used: index of attenuation.) Intensity, I The radiant power that crosses unit area. Intensity and irradiance are formally the same quantity, but the term intensity is usually used for collimated beams of radiation. SI unit: W m–2. Interactance spectroscopy A term coined by Karl Norris to describe a variant of conventional near-infrared diffuse reflection spectroscopy applicable to scattering samples whereby the Raman scattered light is collected from a region that is displaced from the point where the NIR beam is incident on the sample. Internal absorbance, Ai Negative logarithm to the base 10 of the internal transmittance: Ai = –log10(Ti). Internal Absorptance, α i Ratio of the radiant power absorbed by the sample to the incident radiant power, fully corrected for reflection losses and any window absorption. (See Notes 6 and 7) Internal reflection element, IRE A transparent material of high refractive index that is used for ATR measurements. Note: These materials are often not crystalline and so should not be called ATR crystals. Internal transmittance, Ti, τ i Ratio of the radiant power transmitted by the sample to the incident radiant power, fully corrected for reflection losses and any window absorption. (See Notes 6 and 7). Irradiance, I The radiant power received on unit area. SI unit: W m–2.

Kubelka–Munk function, Remission function, f (R∞ ) This function is defined as: f (R∞ ) = (1− R∞ )

2 / 2R∞ , where R∞ is the diffuse reflectance from a sample of infinite depth. Theoretically, f (R∞ ) equals the ratio of the linear absorption coefficient to the scattering coefficient. Under the assumptions of the Kubelka–Munk theory, if the scattering coefficient at a given wavenumber is a constant for a given set of samples, then f (R∞ ) is directly proportional to the product of the absorptivities and concentrations of the components of a mixture, analogous to the behavior of absorbance under Beer’s law. Kubelka–Munk reflection or Volume reflection The process of light penetrating into a powdered sample and re-emerging from the surface of incidence; sometimes incorrectly called diffuse reflection. The combined process of volume reflection and specular reflection is known as diffuse reflection or remission. Linear absorption coefficient, α The Napierian absorbance divided by the path length, α = Ae / ℓ . Linear remission coefficient, b The negative Napierian logarithm of the fraction of light remitted by a non- absorbing scattering sample, divided by the path length ℓ . b = − lne(IR / I0 ) / ℓ SI unit: m–1. Low-emissivity (‘‘low-e’’) glass slides Slides that are made of glass coated with a thin Ag/SnO2 layer. They are chemically inert and nearly transparent to visible light. However, they reflect mid- infrared radiation almost completely and thus are ideal and inexpensive substrates for transflection infrared microspectroscopy, as they allow both visual and infrared images to be collected from the same sample. Mass concentration, c Mass of sample divided by volume of solution or mixture. SI unit: kg/m3. Common unit: g/L; mg/L. Mass fraction, wB The mass of component B divided by the total mass of the sample. Frequently given as ppm or ppb. (See Notes 8 and 9).

Molar absorptivity (preferably) or Molar decadic absorption coefficient, ε Internal absorbance divided by the product of sample path length, ℓ , and molar concentration, c, of the absorbing material. ε = Ai / cℓ SI unit: m2 mol–1 Common unit: L mol–1 cm–1; cm2 mo–1. (Not used: molar absorbancy index or molar extinction coefficient.) Molar concentration, or molarity, M Moles of sample divided by volume of solution or mixture. SI unit: mol/m3. Common unit: mol/L. Mole fraction, χB The number of moles of component B divided by the total number of moles in the mixture. (See Note 8). Napierian absorbance, Ae The absorbance calculated in base e, i.e., ln (1/T) Net absorption cross section, σnet The absorptivity per molecule, i.e., the molar absorptivity, ε , divided by Avogadro’s number, usually corrected to base e through σnet = 2.303 ε /NA. SI unit: m2. Optical absorption depth, µβ The depth in a sample at which the radiant intensity is reduced to 1/e of its value at the surface of the sample. It equals the reciprocal of the linear absorption coefficient. SI unit: m. Common unit: µm. Percent transmission Transmittance X 100. (Not used: Percent transmittance) Penetration depth, dp In attenuated total reflection, the distance from the boundary with the internal reflection element at which the mean square electric field intensity of the evanescent wave, i.e., the intensity of a collimated radiation beam, is reduced to 1/e of its value at the boundary.

In photoacoustic (PA) spectroscopy, an analogous definition may be cited for strongly absorbing samples. For weakly absorbing PA samples, the depth of penetration is given by the thermal diffusion depth. In practice, the depth below the surface that gives rise to most of the measured PA spectr