Absorbance
Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample (excluding the effects on cell walls)". Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample". The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms. What these uses of the  term tend to have in common is that they refer to a logarithm of the ratio of a quantity of light incident on a sample or material to that which is detected after the light has interacted with the sample.   The term absorption refers to the physical process of absorbing light, while absorbance does not always measure only absorption; it may measure attenuation (of transmitted radiant power) caused by absorption, as well as reflection, scattering, and other physical processes. History and uses of the term absorbance. Bouguer-Lambert law. The roots of the term absorbance are in the law of  Bouguer (Bouguer-Lambert law).  As light moves through a media, it will become dimmer as it is being "extinguished".  Bouguer recognized that this extinction (now often called attenuation) was not linear with distance traveled through the medium, but related by what we now refer to as an exponential function.  If formula_1 is the intensity of the light at the beginning of the travel and formula_2 is the intensity of the light detected after travel of a distance formula_3, the fraction transmitted, formula_4, is given by:  formula_5, where formula_6 is called an attenuation constant (a term used in various fields where  a signal is transmitted though a medium) or coefficient.  The amount of light transmitted is falling off exponentially with distance.  Taking the Napierian (natural) logarithm in the above equation, we get:  formula_7 . For scattering media, the constant is often divided into two parts, formula_8 , separating it into a scattering coefficient, formula_9, and an absorption coefficient, formula_10, obtaining:formula_11 . If a size of a detector is very small compared to the distance traveled by the light, any light that is scattered by a particle, either in the forward or backward direction, will not strike the detector. In such case, a plot  of formula_12 as a function of wavelength will yield a superposition of the effects of absorption and scatter. Because the absorption portion is more distinct and tends to ride on a background of the scatter portion, it is often used to identify and quantify the absorbing species. Consequently this is often referred to as absorption spectroscopy, and the plotted quantity is called "absorbance", symbolized as formula_13 . Some disciplines by convention use decadic absorbance rather than Napierian absorbance, resulting in: formula_14 (with the subscript 10 usually not shown). Beer's law with non-scattering samples. Within a homogeneous media such as  a solution, there is no scattering. For this case, researched extensively by August Beer, the concentration of the absorbing species follows the same linear response as the path-length. Additionally, the contributions of individual absorbing species are additive. This is a very favorable situation, and made absorbance an absorption metric far preferable to absorption fraction (absorptance). This is the case for which the term "absorbance" was first used. A common expression of the Beer's law relates the attenuation of light in a material as: formula_15 , where formula_13 is the absorbance; formula_17 is the molar attenuation coefficient or absorptivity of  the attenuating species; formula_18 is the optical path length; and formula_19 is the concentration of the attenuating species. Absorbance for scattering samples. For samples which scatter light, absorbance is defined as "the negative logarithm of one minus absorptance (absorption fraction: formula_20) as measured on a uniform sample". For decadic absorbance, this may be symbolized as: formula_21 . If a sample both transmits and remits light, and is not luminescent, the fraction of light absorbed (formula_20), remitted (formula_23), and transmitted (formula_4) add to 1, or: formula_25 . Note that formula_26 , and the formula may be written as: formula_27 . For a sample which does  not scatter, formula_28 , and formula_29 , yielding the formula for absorbance of a material discussed below. Even though this absorbance function is very useful with scattering samples, the function does not have the same desirable characteristics as it does for non-scattering samples. There is, however, a property called which may be estimated for these samples. The of a single unit thickness of material making up a scattering sample is the same as the absorbance of the same thickness of the materiel in the absence of scatter. Optics. In optics, absorbance or decadic absorbance is the "common logarithm" of the ratio  of incident to "transmitted" radiant power through a material, and spectral absorbance or spectral decadic absorbance is the common logarithm of the ratio of incident to "transmitted" spectral radiant power through a material. Absorbance is dimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for absorbance is discouraged. Mathematical definitions. Absorbance of a material. The absorbance of a material, denoted "A", is given by where Absorbance is a dimensionless quantity. Nevertheless, the absorbance unit or  AU is commonly used in ultraviolet–visible spectroscopy and its high-performance liquid chromatography applications, often in derived units such as the milli-absorbance unit (mAU) or milli-absorbance unit-minutes (mAU×min), a unit of absorbance integrated over time. Absorbance is related to optical depth by where "τ" is the optical depth. Spectral absorbance. Spectral absorbance in frequency and spectral absorbance in wavelength of a material, denoted "A" and "A" respectively, are given by where Spectral absorbance is related to spectral optical depth by where Although absorbance is properly unitless, it is sometimes reported in "absorbance units", or AU. Many  people, including scientific researchers, wrongly state the results from absorbance measurement experiments in terms of these made-up units. Relationship with attenuation. Attenuance. Absorbance is a number that measures the "attenuation" of the transmitted radiant power in a material. Attenuation can be caused by the physical process of "absorption", but also reflection, scattering, and other physical processes. Absorbance of a material is approximately equal to its "attenuance" when both the absorbance is much less than 1 and the emittance of that material (not to be confused with radiant exitance or emissivity) is much less than the absorbance. Indeed, where that  is equivalent to where and according to Beer–Lambert law, , so and finally Attenuation coefficient. Absorbance of a material is also related to its "decadic attenuation coefficient" by where If "a"("z") is uniform along the path, the attenuation is said to be a "linear attenuation", and the relation becomes Sometimes the relation is given using the "molar attenuation coefficient" of the material, that is its attenuation coefficient divided by its molar concentration: where If "c"("z") is uniform along the path, the relation becomes The use of the term "molar absorptivity" for molar attenuation coefficient is discouraged. Measurements. Logarithmic vs. directly  proportional measurements. The amount of light transmitted through a material diminishes exponentially as it travels through the material, according to the Beer–Lambert law (A=(ε)(l)). Since the absorbance of a sample is measured as a logarithm, it is directly proportional to the thickness of the sample and to the concentration of the absorbing material in the sample. Some other measures related to absorption, such as transmittance, are measured as a simple ratio so they vary exponentially with the thickness and concentration of the material. Instrument measurement range. Any real measuring instrument has a limited range over which it can accurately  measure absorbance. An instrument must be calibrated and checked against known standards if the readings are to be trusted. Many instruments will become non-linear (fail to follow the Beer–Lambert law) starting at approximately 2 AU (~1% transmission). It is also difficult to accurately measure very small absorbance values (below 10) with commercially available instruments for chemical analysis. In such cases, laser-based absorption techniques can be used, since they have demonstrated detection limits that supersede those obtained by conventional non-laser-based instruments by many orders of magnitude (detections have been demonstrated all the way down to 5  × 10). The theoretical best accuracy for most commercially available non-laser-based instruments is attained in the range near 1 AU. The path length or concentration should then, when possible, be adjusted to achieve readings near this range. Method of measurement. Typically, absorbance of a dissolved substance is measured using absorption spectroscopy. This involves shining a light through a solution and recording how much light and what wavelengths were transmitted onto a detector. Using this information, the wavelengths that were absorbed can be determined. First, measurements on a "blank" are taken using just the solvent for reference purposes. This  is so that the absorbance of the solvent is known, and then any change in absorbance when measuring the whole solution is made by just the solute of interest. Then measurements of the solution are taken. The transmitted spectral radiant flux that makes it through the solution sample is measured and compared to the incident spectral radiant flux. As stated above, the spectral absorbance at a given wavelength is The absorbance spectrum is plotted on a graph of absorbance vs. wavelength. A UV-Vis spectrophotometer will do all this automatically. To use this machine, solutions are placed in a small  cuvette and inserted into the holder. The machine is controlled through a computer and, once it has been "blanked", automatically displays the absorbance plotted against wavelength. Getting the absorbance spectrum of a solution is useful for determining the concentration of that solution using the Beer–Lambert law and is used in HPLC. Shade number. Some filters, notably welding glass, are rated by shade number (SN), which is 7/3 times the absorbance plus one: or For example, if the filter has 0.1% transmittance (0.001 transmittance, which is 3 absorbance units), its shade number would be 8.