HOME

TheInfoList



OR:

Length measurement, distance measurement, or range measurement (ranging) refers to the many ways in which length,
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
, or
range Range may refer to: Geography * Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra) ** Mountain range, a group of mountains bordered by lowlands * Range, a term used to i ...
can be
measured Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
. The most commonly used approaches are the rulers, followed by transit-time methods and the interferometer methods based upon the speed of light. For objects such as crystals and diffraction gratings,
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
is used with
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10 nanometers, corresponding to frequencies in the range 30  ...
s and 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.


Standard rulers

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.


Transit-time measurement

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 International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
the speed is a defined value ''c''0 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 Radio navigation or radionavigation is the application of radio frequencies to determine a position of an object on the Earth, either the vessel or an obstruction. Like radiolocation, it is a type of radiodetermination. The basic principles a ...
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 The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sys ...
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 GPS about enhanced GPS, in which a correction signal is transmitted from terrestrial stations (that is,
differential GPS Differential Global Positioning Systems (DGPSs) supplement and enhance the positional data available from global navigation satellite systems (GNSSs). A DGPS for GPS can increase accuracy by about a thousandfold, from approximately to . DGPSs ...
(DGPS)) or via satellites (that is, Wide Area Augmentation System (WAAS)) can bring accuracy to a few meters or or, in specific applications, tens of centimeters. Time-of-flight systems for robotics (for example, Laser Detection and Ranging LADAR and Light Detection and Ranging
LIDAR Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...
) aim at lengths of and have an accuracy of about


Interferometer measurements

In many practical circumstances, and for precision work, measurement of dimension using transit-time measurements is used only as an initial indicator of length and is refined using an interferometer. Generally, transit time measurements are preferred for longer lengths, and interferometers for shorter lengths. The figure shows schematically how length is determined using a Michelson interferometer: the two panels show a laser source emitting a light beam split by a ''
beam splitter A beam splitter or ''beamsplitter'' is an optical device that splits a beam of light into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as interferometers, also finding wide ...
'' (BS) to travel two paths. The light is recombined by bouncing the two components off a pair of ''
corner cube A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat surfaces, which reflects waves directly towards the source, but translated. The three intersecting surfaces often have square shapes. Radar ...
s'' (CC) that return the two components to the beam splitter again to be reassembled. The corner cube serves to displace the incident from the reflected beam, which avoids some complications caused by superposing the two beams. The distance between the left-hand corner cube and the beam splitter is compared to that separation on the fixed leg as the left-hand spacing is adjusted to compare the length of the object to be measured. In the top panel the path is such that the two beams reinforce each other after reassembly, leading to a strong light pattern (sun). The bottom panel shows a path that is made a half wavelength longer by moving the left-hand mirror a quarter wavelength further away, increasing the path difference by a half wavelength. The result is the two beams are in opposition to each other at reassembly, and the recombined light intensity drops to zero (clouds). Thus, as the spacing between the mirrors is adjusted, the observed light intensity cycles between reinforcement and cancellation as the number of wavelengths of path difference changes, and the observed intensity alternately peaks (bright sun) and dims (dark clouds). This behavior is called interference and the machine is called an
interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opti ...
. By ''counting fringes'' it is found how many wavelengths long the measured path is compared to the fixed leg. In this way, measurements are made in units of wavelengths ''λ'' corresponding to a particular atomic transition. The length in wavelengths can be converted to a length in units of metres if the selected transition has a known frequency ''f''. The length as a certain number of wavelengths ''λ'' is related to the metre using ''λ'' = . With ''c0'' a defined value of 299,792,458 m/s, the error in a measured length in wavelengths is increased by this conversion to metres by the error in measuring the frequency of the light source. By using sources of several wavelengths to generate sum and difference beat frequencies, absolute distance measurements become possible. This methodology for length determination requires a careful specification of the wavelength of the light used, and is one reason for employing a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
source where the wavelength can be held stable. Regardless of stability, however, the precise frequency of any source has linewidth limitations. Other significant errors are introduced by the interferometer itself; in particular: errors in light beam alignment, collimation and fractional fringe determination. Corrections also are made to account for departures of the medium (for example, air) from the reference medium of classical vacuum. Resolution using wavelengths is in the range of ΔL/L ≈ depending upon the length measured, the wavelength and the type of interferometer used. The measurement also requires careful specification of the medium in which the light propagates. A ''refractive index correction'' is made to relate the medium used to the reference vacuum, taken in SI units to be the classical vacuum. These refractive index corrections can be found more accurately by adding frequencies, for example, frequencies at which propagation is sensitive to the presence of water vapor. This way non-ideal contributions to the refractive index can be measured and corrected for at another frequency using established theoretical models. It may be noted again, by way of contrast, that the transit-time measurement of length is independent of any knowledge of the source frequency, except for a possible dependence of the correction relating the measurement medium to the reference medium of classical vacuum, which may indeed depend on the frequency of the source. Where a pulse train or some other wave-shaping is used, a range of frequencies may be involved.


Diffraction measurements

For small objects, different methods are used that also depend upon determining size in units of wavelengths. For instance, in the case of a crystal, atomic spacings can be determined using X-ray diffraction. The present best value for the lattice parameter of silicon, denoted ''a'', is: ::a = 543.102 0504(89) × 10−12 m, corresponding to a resolution of ΔL/L ≈ Similar techniques can provide the dimensions of small structures repeated in large periodic arrays like a diffraction grating. Such measurements allow the calibration of
electron microscope An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a h ...
s, extending measurement capabilities. For non-relativistic electrons in an electron microscope, the de Broglie wavelength is: :\lambda_e = \frac \ , with ''V'' the electrical voltage drop traversed by the electron, ''me'' the electron mass, ''e'' the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
, and ''h'' the Planck constant. This wavelength can be measured in terms of inter-atomic spacing using a crystal diffraction pattern, and related to the metre through an optical measurement of the lattice spacing on the same crystal. This process of extending calibration is called '' metrological traceability''. See The use of metrological traceability to connect different regimes of measurement is similar to the idea behind the
cosmic distance ladder The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
for different ranges of astronomical length. Both calibrate different methods for length measurement using overlapping ranges of applicability.


Far and moving targets

Ranging is technique that measures distance or
slant range In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction between two points. If the two points are at the same level Level or levels may refer to: Engineering *Level (instr ...
from the observer to a target, especially a far and moving target. Active methods use unilateral transmission and passive reflection. Active rangefinding methods include
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
(
lidar Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...
), radar, sonar, and ultrasonic rangefinding. Other devices which measure distance using
trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
are stadiametric,
coincidence A coincidence is a remarkable concurrence of events or circumstances that have no apparent causal connection with one another. The perception of remarkable coincidences may lead to supernatural, occult, or paranormal claims, or it may lead t ...
and
stereoscopic rangefinder A stereoscopic rangefinder or stereoscopic telemeter is an optical device that measures distance from the observer to a target, using the observer's capability of binocular vision. It looks similar to a coincidence rangefinder, which uses differen ...
s. Older methodologies that use a set of known information (usually distance or target sizes) to make the measurement, have been in regular use since the 18th century. Special ranging makes use of actively synchronized transmission and travel time measurements. The time difference between several received signals is used to determine exact distances (upon multiplication by the speed of light). This principle is used in satellite navigation. In conjunction with a standardized model of the Earth's surface, a location on that surface may be determined with high accuracy. Ranging methods without accurate time synchronization of the receiver are called pseudorange, used, for example, in
GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
positioning. With other systems ranging is obtained from passive radiation measurements only: the
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
or radiation signature of the object generates the signal that is used to determine range. This
asynchronous Asynchrony is the state of not being in synchronization. Asynchrony or asynchronous may refer to: Electronics and computing * Asynchrony (computer programming), the occurrence of events independent of the main program flow, and ways to deal with ...
method requires multiple measurements to obtain a range by taking multiple bearings instead of appropriate
scaling Scaling may refer to: Science and technology Mathematics and physics * Scaling (geometry), a linear transformation that enlarges or diminishes objects * Scale invariance, a feature of objects or laws that do not change if scales of length, energ ...
of active pings, otherwise the system is just capable of providing a simple bearing from any single measurement. Combining several measurements in a time sequence leads to tracking and tracing. A commonly used term for residing terrestrial objects is surveying.


Other techniques

Measuring dimensions of localized structures (as opposed to large arrays of atoms like a crystal), as in modern integrated circuits, is done using the scanning electron microscope. This instrument bounces electrons off the object to be measured in a high vacuum enclosure, and the reflected electrons are collected as a photodetector image that is interpreted by a computer. These are not transit-time measurements, but are based upon comparison of Fourier transforms of images with theoretical results from computer modeling. Such elaborate methods are required because the image depends on the three-dimensional geometry of the measured feature, for example, the contour of an edge, and not just upon one- or two-dimensional properties. The underlying limitations are the beam width and the wavelength of the electron beam (determining
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
), determined, as already discussed, by the electron beam energy. and The calibration of these scanning electron microscope measurements is tricky, as results depend upon the material measured and its geometry. A typical wavelength is and a typical resolution is about Other small dimension techniques are the
atomic force microscope Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the op ...
, the focused ion beam and the helium ion microscope. Calibration is attempted using standard samples measured by transmission electron microscope (TEM). Nuclear Overhauser effect spectroscopy (NOESY) is a specialized type of
nuclear magnetic resonance spectroscopy Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic fie ...
where distances between atoms can be measured. It is based on the effect where nuclear spin cross-relaxation after excitation by a radio pulse depends on the distance between the nuclei. Unlike spin-spin coupling, NOE propagates through space and does not require that the atoms are connected by bonds, so it is a true distance measurement instead of a chemical measurement. Unlike diffraction measurements, NOESY does not require a crystalline sample, but is done in solution state and can be applied to substances that are difficult to crystallize.


Astronomical distance measurement


Other systems of units

In some systems of units, unlike the current SI system, lengths are fundamental units (for example, ''wavelengths'' in the older SI units and ''bohrs'' in
atomic units The Hartree atomic units are a system of natural units of measurement which is especially convenient for atomic physics and computational chemistry calculations. They are named after the physicist Douglas Hartree. By definition, the following four ...
) and are not defined by times of transit. Even in such units, however, the ''comparison'' of two lengths can be made by comparing the two transit times of light along the lengths. Such time-of-flight methodology may or may not be more accurate than the determination of a length as a multiple of the fundamental length unit.


List of devices


Contact devices

* Architect's scale *
Caliper A caliper ( British spelling also calliper, or in plurale tantum sense a pair of calipers) is a device used to measure the dimensions of an object. Many types of calipers permit reading out a measurement on a ruled scale, a dial, or a digital d ...
* Diagonal scale * Engineer's scale *
Feeler gauge A feeler gauge is a tool used to measure gap widths. Feeler gauges are mostly used in engineering to measure the clearance between two parts. Description They consist of a number of small lengths of steel of different thicknesses with measure ...
,
used in metal working to measure size of gaps * Gauge blocks *
Gunter's chain Gunter's chain (also known as Gunter’s measurement) is a distance measuring device used for surveying. It was designed and introduced in 1620 by English clergyman and mathematician Edmund Gunter (1581–1626). It enabled plots of land to be ac ...
* Measuring rod *
Meter stick A meterstick, metrestick, or yardstick is either a straightedge or foldable ruler used to measure length, and is especially common in the construction industry. They are often made of wood or plastic, and often have metal or plastic joints so ...
* Metric scale *
Micrometer Micrometer can mean: * Micrometer (device), used for accurate measurements by means of a calibrated screw * American spelling of micrometre The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...
*
Opisometer An opisometer, also called a curvimeter, meilograph, or map measurer, is an instrument for measuring the lengths of arbitrary curved lines. Description A simple opisometer consists of a toothed wheel of known circumference on a handle. The whee ...
or curvimeter *
Pacing (surveying) Pacing is a reasonably easy and quick method of measuring distance in the field. It is used to measure a distance and is often used with a sighting or a hand compass. Most commonly, pacing is split up into segments, such as chains, which are set me ...
* Ruler *
Stadimeter A stadimeter is an optical device for estimating the range to an object of known height by measuring the angle between the top and bottom of the object as observed at the device. It is similar to a sextant, in that the device is using mirrors to ...
*
Surveyor's wheel A surveyor's wheel, also called a clickwheel, hodometer, waywiser, trundle wheel, measuring wheel or perambulator is a device for measuring distance. Origin The origins of the surveyor's wheel are connected to the origins of the odometer. W ...
* Tape measure * Thread pitch gauge * Ultrasonic thickness gauge * Yard stick


Non-contact devices

*
Ranging Length measurement, distance measurement, or range measurement (ranging) refers 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 in ...


Based on time-of-flight

*
Electronic distance meter Length measurement, distance measurement, or range measurement (ranging) refers 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 int ...
* Ultrasonic ranging module ( sonar, echo sounding) * Radar distance measurement * Laser rangefinder,
lidar Lidar (, also LIDAR, or LiDAR; sometimes LADAR) is a method for determining ranges (variable distance) by targeting an object or a surface with a laser and measuring the time for the reflected light to return to the receiver. It can also be ...


See also

* Distance-based road exit numbers *
Linear referencing Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing in engineering and construction, in which the locations of physical features along a linear element are described in te ...
* Meridian arc * Milestone *
Rangefinder A rangefinder (also rangefinding telemeter, depending on the context) is a device used to measure distances to remote objects. Originally optical devices used in surveying, they soon found applications in other fields, such as photography an ...
*
GPS The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
,
indirect by runtime measurement of electromagnetic waves in the GHz-range *
Hypsometer A hypsometer is an instrument for measuring height or elevation. Two different principles may be used: trigonometry and atmospheric pressure. Etymology The English word ''hypsometer'' originates from the Ancient Greek words ὕψος (húpsos, ...
*
Interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opti ...
* Macrometer *
Odometer An odometer or odograph is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. The device may be electronic, mechanical, or a combination of the two (electromechanical). The noun derives from ancient Gr ...
*
Position sensor A position sensor is a sensor that detects an object's position. A position sensor may indicate the absolute position of the object (its location) or its relative position (displacement) in terms of linear travel, rotational angle or three-dimension ...
* Positioning system * Standard ruler, in astronomy * Tachymeter * Taximeter, measure usually includes a time component as well * Tellurometer *
Travelling microscope A travelling microscope is an instrument for measuring length with a resolution typically in the order of 0.01mm. The precision is such that better-quality instruments have measuring scales made from Invar to avoid misreadings due to thermal effe ...
* Angular measuring instrument *
Altimeter An altimeter or an altitude meter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth under water. The m ...
, height *
Distance measuring equipment (aviation) In aviation, distance measuring equipment (DME) is a radio navigation technology that measures the slant range (distance) between an aircraft and a ground station by timing the propagation delay of radio signals in the frequency band between 9 ...
* Ellipsometry#Imaging ellipsometry * Frequency-modulated continuous-wave radar (FMCW) *
Length scale In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot ...
* Low-energy electron microscopy *
Orders of magnitude (length) The following are examples of orders of magnitude for different lengths. __TOC__ Overview Detailed list To help compare different orders of magnitude, the following list describes various lengths between 1.6 \times 10^ metres and 10^ ...
* Pulse-Doppler radar * Range ambiguity resolution *
Cosmic distance ladder The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
*
Bradley A. Fiske Rear Admiral Bradley Allen Fiske (June 13, 1854 – April 6, 1942) was an officer in the United States Navy who was noted as a technical innovator. During his long career, Fiske invented more than a hundred and thirty electrical and mechanica ...
*
Dazzle camouflage Dazzle camouflage, also known as razzle dazzle (in the U.S.) or dazzle painting, is a family of ship camouflage that was used extensively in World War I, and to a lesser extent in World War II and afterwards. Credited to the British marine a ...
* Depression range finder * Fire-control system * Range-finder painting * Rangefinding telemeter *
Slant range In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction between two points. If the two points are at the same level Level or levels may refer to: Engineering *Level (instr ...
* Tacheometry * Telemeter chronograph * Tellurometer


References


Further reading

* {{citizendium, title=Metre (unit) SI units Metrology Scientific techniques Length, distance, or range measuring devices