Dimensional metrology

Dimensional metrology is the science of calibrating and using physical measurement equipment to quantify the physical size of or distance from any given object.
History of metrology.
Early Mesopotamian and Egyptian metrologists created a set of measurement standards based on body measures such as fingers, palms, hands, feet, Cubits, and paces and agricultural measures such as feet, yards, paces, fathoms, rods, cords, perch, stadia, miles and degrees of the Earth's circumference. Early Egyptian rulers based on units of fingers, palms and feet based on inscription grids that incorporated standards of measure as canons of proportion were made commensurate with Mesopotamian standards based on fingers, hands and feet so that four palms or three hands equaled one foot and ten hands equaled one meter. These standards which were used to measure and define property such as buildings and fields were adopted by the Greeks, Romans and Persians as legal standards and became the basis of European standards of measure. They were also used to relate length to area with units such as the khet, setat and aroura, area to volume with units such as the artaba and space to time with units such as the Egyptian minute of march, the itrw which recorded an hours travel on a river, and the days sail. Specialized units for carpenters, masons and other craftsmen such as the remen were worked into a system of unit fractions that allowed calculations utilizing analytic geometry. Carpenters and surveyors were some of the first dimensional inspectors.
Tools.
Modern measurement equipment include hand tools, CMMs (coordinate-measuring machines), machine vision systems, laser trackers, and optical comparators. For hand tools, see gauge. A CMM is based on CNC technology to automate measurement of Cartesian coordinates using a touch probe, contact scanning probe, or non-contact sensor. Optical comparators are used when physically touching the part is undesirable. Instruments can now build 3D models of a part and its internal passages using x-ray technology or 3D laser scanners.
Relative measurement.
Measurements are often expressed as a size relative to a theoretically perfect part that has geometry defined in a print or computer model. A print is a blueprint illustrating the defined geometry of a part and its features. Each feature can have a size, a distance from other features, and a tolerance set on each element. The international language used to describe physical parts is called GD&T. Prints can be hand drawn or automatically generated by a computer CAD model. Computer controlled measurement systems can measure a part relative to a CAD model without the need for a print.
Mechanical engineering.
Industrial metrology is common in manufacturing quality control systems. The prints and CAD models described above are usually made by a mechanical engineer.