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Length measurement

Length measurement, distance measurement, or range measurement (ranging) all refer to the many ways in which length, distance, or range can be measured. The most commonly used approaches are the rulers, followed by transit-time methods and the interferometer methods based upon the speed of light. Surveying is one ancient use of measuring long distances.

For tiny objects such as crystals and diffraction gratings, diffraction is used with X-ray light, or even electron beams. Measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling. These techniques are employed, for example, to measure the tiny features on wafers during the manufacture of chips.

The ruler the simplest kind of length measurement tool: lengths are defined by printed marks or engravings on a stick. The metre was initially defined using a ruler before more accurate methods became available.

Gauge blocks are a common method for precise measurement or calibration of measurement tools.

For small or microscopic objects, microphotography where the length is calibrated using a graticule can be used. A graticule is a piece that has lines for precise lengths etched into it. Graticules may be fitted into the eyepiece or they may be used on the measurement plane.

The basic idea behind a transit-time measurement of length is to send a signal from one end of the length to be measured to the other, and back again. The time for the round trip is the transit time Δt, and the length ℓ is then 2ℓ = Δt*"v", with v the speed of propagation of the signal, assuming that is the same in both directions. If light is used for the signal, its speed depends upon the medium in which it propagates; in SI units the speed is a defined value c0 in the reference medium of classical vacuum. Thus, when light is used in a transit-time approach, length measurements are not subject to knowledge of the source frequency (apart from possible frequency dependence of the correction to relate the medium to classical vacuum), but are subject to the error in measuring transit times, in particular, errors introduced by the response times of the pulse emission and detection instrumentation. An additional uncertainty is the refractive index correction relating the medium used to the reference vacuum, taken in SI units to be the classical vacuum. A refractive index of the medium larger than one slows the light.

Transit-time measurement underlies most radio navigation systems for boats and aircraft, for example, radar and the nearly obsolete Long Range Aid to Navigation LORAN-C. For example, in one radar system, pulses of electromagnetic radiation are sent out by the vehicle (interrogating pulses) and trigger a response from a responder beacon. The time interval between the sending and the receiving of a pulse is monitored and used to determine a distance. In the global positioning system a code of ones and zeros is emitted at a known time from multiple satellites, and their times of arrival are noted at a receiver along with the time they were sent (encoded in the messages). Assuming the receiver clock can be related to the synchronized clocks on the satellites, the transit time can be found and used to provide the distance to each satellite. Receiver clock error is corrected by combining the data from four satellites.

Such techniques vary in accuracy according to the distances over which they are intended for use. For example, LORAN-C is accurate to about 6 km, GPS about 10 m, enhanced GPS, in which a correction signal is transmitted from terrestrial stations (that is, differential GPS (DGPS)) or via satellites (that is, Wide Area Augmentation System (WAAS)) can bring accuracy to a few metres or < 1 metre, or, in specific applications, tens of centimetres. Time-of-flight systems for robotics (for example, Laser Detection and Ranging LADAR and Light Detection and Ranging LIDAR) aim at lengths of 10–100 m and have an accuracy of about 5–10 mm.

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