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Transmission, also referred to as transmittance, usually denoted by T [non-dimensional], of light by a layer of the medium with the thickness z is defined as a non-dimensional ratio:
| T = Φ(z0 + z) / Φ(z0) | (1) |
where Φ(z) is the light power at z. The choice of the base thickness, z0 and the incremental thickness, z, of the medium, as well as the way the power Φ is measured at z are important. Indeed, consider a unidirectional light source, oriented along the z-axis in a dispersion of particles, in which the particles contribute significantly to the attenuation of light. At z0 and z (assumed < z0) that are each much smaller than the scattering length (Equation 2 in Scattering coefficients), the unscattered light significantly contributes to Φ(z), while the contribution of the scattered light is small. Note that this latter contribution depends on the way of measuring power Φ. Under this assumption, transmission, T, characterizes the propagation of the collumated light beam in the single-scattering regime (see Single and multiple scattering). However, if z0 is much greater than the scattering length, multiple scattering dominates. Here, transmission, T, not only characterizes the propagation of diffuse light in the dispersion, but also significantly depends on the geometry of the detector of power Φ (see, for example, Attenuation coefficient: Measurement). Hence, to avoid ambiguity, transmission T, is meant to represent propagation of light in the single-scattering regime, which implies that z0 and z are each much smaller than the scattering length of the dispersion.
Strictly speaking, the term transmission might be viewed as referring primarily to the process of passing of light through a medium. Hence, the transmittance, i.e. a property of the medium, might be regarded as a more correct term here. However, both terms are used to describe the optical property of the medium.
Optical density, usually denoted by OD [non-dimensional], of a layer of a medium with the transmission T is defined as follows:
| OD = - logT | (2) |
where log is the logarithm with the base of 10. For example, an optical density, OD, of 1 corresponds to transmission, T, of 0.1. Optical density is equivalent to the linear absorbance (for example, Braslavsky SE 2007, pp. 296-297) for media that do not significantly scatter light. This latter condition is rarely stated (for example, Braslavsky SE 2007). The use of the term "optical density" has been discouraged (Braslavsky SE 2007, p. 378).
According to the Lambert law, OD is the product of the attenuation coefficient, c, and the layer thickness, z.
| OD | = - (1 / ln10) lnT | |
| = (1 / ln10) cz | (3) |
The product cz is referred to as the optical thickness or optical depth of a layer of the medium with thickness (depth) z. The optical thickness, usually denoted by τ, is the layer thickness expressed using the attenuation length, zc = 1/c, as the unit length:
| τ | = cz | |
| = z / ( 1 / c) | ||
| = z / zc | (4) |
Since the attenuation length is the average distance between two successive interactions of a photon with the turbid medium, i.e. the free pathlength for attenuation, tau; equals the average number of such interactions (Berrocal E et al 2007).
If light is attenuated in a mono-sized dispersion only by the particles of the dispersion, then (in the small thickness limit) the optical thickness, t, can be expressed (for example, Swanson NL and Billard 2000) in terms of the single-scattering characteristics of particles of the medium, as follows:
| τ | = cz | |
| = (Ccn) z | ||
| = (QcGn) z | (5) |
where Cc [length2] is the attenuation cross section of the particle, n [length-3] is the number concentration of particles in the dispersion, Qc [nondim] is the attenuation efficiency of the particle, and G [length2] is the geometric cross section of the particle. This result follows from Equation 2 in Attenuation cross section and the first line of the above equation. For a dispersion of nonspherical particles, both Qc and G, are meant to be averages over all particle orientations.
| CITATION: Jonasz M. 2006. Transmission, optical density, and thickness (www.tpdsci.com/Tpc/TOdOt.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 18-Jan-2006 Modified17-Nov-2009: Peer-reviewed: PENDING |
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