Area density

The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the kilogram per square metre (kg·m−2). A related area number density can be defined by replacing mass in by number of particles or other countable quantity. In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (g/m2); for paper in particular, it may be expressed as pounds per ream of standard sizes ("basis ream"). Area density can be calculated as: or where ρA is the average area density, m is the total mass of the object, A is the total area of the object, ρ is the average density, and l is the average thickness of the object. A special type of area density is called column (mass) density (also columnar mass density), denoted ρA or σ. It is the mass of substance per unit area integrated along a path; It is obtained integrating volumetric density over a column: In general the integration path can be slant or oblique incidence (as in, for example, line of sight propagation in atmospheric physics). A common special case is a vertical path, from the bottom to the top of the medium: where denotes the vertical coordinate (e.g., height or depth). Columnar density is closely related to the vertically averaged volumetric density as where ; , , and have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively. Column number density refers instead to a number density type of quantity: the number or count of a substance—rather than the mass—per unit area integrated along a path: It is a quantity commonly retrieved by remote sensing instruments, for instance the Total Ozone Mapping Spectrometer (TOMS) which retrieves ozone columns around the globe. Columns are also returned by the differential optical absorption spectroscopy (DOAS) method and are a common retrieval product from nadir-looking microwave radiometers.