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Optical density

Optical density is the absorbance of an optical element for a given wavelength λ per unit distance:

$OD_\lambda = {A_\lambda \over l} = -{1 \over l} \log_{10} T = {1 \over l}\log_{10} \left ({I_0 \over I} \right )$

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Where:

$l$	= the distance that light travels through the sample (i.e., the sample thickness), measured in cm
$A λ$	= the absorbance at wavelength λ
$T$	= the per-unit transmittance
$I 0$	= the intensity of the incident light beam
$I$	= the intensity of the transmitted light beam

Although absorbance does not have true units, it is quite often reported in "Absorbance Units" or AU. Accordingly, optical density is measured in ODU, which are equivalent to AU cm⁻¹.

The higher the optical density, the lower the transmittance. Optical density times 10 is equal to a transmission loss rate expressed in decibels per cm, e.g., an optical density of 0.3 corresponds to a transmission loss of 3 dB per cm.

Optical density is often defined without regard to the length of the sample; in this case it is a synonym for absorbance. Neutral density filters are typically quantified this way. Some filters, notably welding glass, are rated by shade number, which is 7/3 times the optical density. A shade number of 14 is regarded as safe for direct observation of the sun.