Transmittance

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This article is about transmission through a volume. For transmission through a surface, see Fresnel equations.
Diagram of Beer-Lambert Law of transmittance of a beam of light as it travels through a cuvette of width l.
Earth's atmospheric transmittance over 1 nautical mile sea level path (infrared region[1]). Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.
Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the ruby laser.

In optics and spectroscopy, transmittance is the fraction of incident light (electromagnetic radiation) at a specified wavelength that passes through a sample.[2][3] The terms visible transmittance (VT) and visible absorptance (VA), which are the respective fractions for the spectrum of light visible radiation, are also used. The natural radiation of the cuvette corresponding to the temperature of the cuvette remains ignored - see radiative transfer equation.

A related term is absorbance,[4] or absorption factor,[5] which is the fraction of radiation absorbed by a sample at a specified wavelength.

Definition[edit]

Transmittance is given by:[2]

T = \frac{I}{I_0},

where

  • I is the intensity of the radiation coming out of the sample;
  • I0 is the intensity of the incident radiation.

In these equations, scattering and reflection are considered to be close to zero or otherwise accounted for. The transmittance of a sample is sometimes given as a percentage.

Note that the term "transmission" refers to the physical process of radiation passing through a sample, whereas transmittance refers to the mathematical quantity.

Relation to absorbance[edit]

Transmittance is related to absorbance A as:[4]

T = 10^{-A},
A = -\log_{10} T.

Relation to optical depth[edit]

Transmittance is related to optical depth τ as:

{T} = e^{-\tau},
\tau = - \ln T.

Non-normal geometry[edit]

In plane geometry:

T = e^{-\tau / \mu},

where, when the plane parallel assumption is invoked, μ = cos θ with θ the angle of propagation of the ray from the normal of the surface.

Beer–Lambert law[edit]

Main article: Beer–Lambert law

In case of uniform attenuation, optical depth is simply:

\tau = \Sigma l = N \sigma l,

where

So the transmittance is:

T = e^{-\Sigma l} = e^{N \sigma l}.

In the general nonuniform case, optical depth is an integral quantity:

\tau = \int_0^l \Sigma(l')\, \mathrm{d}l' = \sigma \int_0^l N(l')\, \mathrm{d}l',

so:

T = e^{-\int_0^l \Sigma(l')\, \mathrm{d}l'}.

This is the case of atmospheric science applications and also of radiation shielding theory.

See also[edit]

References[edit]

  1. ^ "Electronic warfare and radar systems engineering handbook". 
  2. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Transmittance".
  3. ^ Verhoeven, J. W. (1996). "Glossary of terms used in photochemistry (IUPAC Recommendations 1996)". Pure and Applied Chemistry 68 (12): 2223–2286. doi:10.1351/pac199668122223. ISSN 0033-4545. 
  4. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Absorbance".
  5. ^ "CRC Dictionary of pure and applied physics, CRC Press, Editor: Dipak Basu (2001)".