Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Magnetometer
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Survey magnetometers== Survey magnetometers can be divided into two basic types: *''[[Scalar (mathematics)|Scalar]] magnetometers'' measure the total strength of the magnetic field to which they are subjected, but not its direction *''[[Euclidean vector|Vector]] magnetometers'' have the capability to measure the component of the magnetic field in a particular direction, relative to the [[spatial orientation]] of the device. A vector is a mathematical entity with both magnitude and direction. The Earth's magnetic field at a given point is a vector. A [[magnetic compass]] is designed to give a horizontal [[bearing (navigation)|bearing]] direction, whereas a ''vector magnetometer'' measures both the magnitude and direction of the total magnetic field. Three [[orthogonal]] sensors are required to measure the components of the magnetic field in all three dimensions. They are also rated as "absolute" if the strength of the field can be calibrated from their own known internal constants or "relative" if they need to be calibrated by reference to a known field. A ''magnetograph'' is a magnetometer that continuously records data over time. This data is typically represented in magnetograms.<ref>{{cite web |title=Magnetograms |url=https://www.bgs.ac.uk/information-hub/scanned-records/magnetograms/ |website=BGS Information Hub |publisher=British Geological Survey |access-date=5 December 2022}}</ref> Magnetometers can also be classified as "AC" if they measure fields that vary relatively rapidly in time (>100 Hz), and "DC" if they measure fields that vary only slowly (quasi-static) or are static. AC magnetometers find use in electromagnetic systems (such as [[magnetotellurics]]), and DC magnetometers are used for detecting [[Mineralization (geology)|mineralisation]] and corresponding [[geological]] structures.{{cn|date=January 2025}} ===Scalar magnetometers=== ====Proton precession magnetometer==== {{Main|Proton magnetometer}} ''Proton precession magnetometer''s, also known as ''[[proton magnetometer]]s'', PPMs or simply mags, measure the resonance frequency of [[proton]]s (hydrogen nuclei) in the magnetic field to be measured, due to [[nuclear magnetic resonance]] (NMR). Because the precession frequency depends only on atomic constants and the strength of the ambient magnetic field, the accuracy of this type of magnetometer can reach 1 [[part per million|ppm]].<ref>Dr. Ivan Hrvoic, Ph.D., P.Eng. "[https://web.archive.org/web/20131212042401/http://info.orrvweb.com/wp-content/uploads/whitepaper/gemprotonaccuracy.pdf Requirements for obtaining high accuracy with proton magnetometers]". GEM Systems Inc., 11 January 2010.</ref> A direct current flowing in a [[solenoid]] creates a strong magnetic field around a [[hydrogen]]-rich fluid ([[kerosene]] and [[decane]] are popular, and even water can be used), causing some of the protons to align themselves with that field. The current is then interrupted, and as protons realign themselves with the [[wikt:ambient|ambient]] magnetic field, they [[precession|precess]] at a frequency that is directly proportional to the magnetic field. This produces a weak rotating magnetic field that is picked up by a (sometimes separate) inductor, [[amplifier|amplified]] electronically, and fed to a digital frequency counter whose output is typically scaled and displayed directly as field strength or output as digital data. For hand/backpack carried units, PPM sample rates are typically limited to less than one sample per second. Measurements are typically taken with the sensor held at fixed locations at approximately 10 metre increments. Portable instruments are also limited by sensor volume (weight) and power consumption. PPMs work in field gradients up to 3,000 nT/m, which is adequate for most mineral exploration work. For higher gradient tolerance, such as mapping [[banded iron formation]]s and detecting large ferrous objects, [[#Overhauser effect magnetometer|Overhauser magnetometers]] can handle 10,000 nT/m, and [[#Caesium vapour magnetometer|caesium magnetometers]] can handle 30,000 nT/m. They are relatively inexpensive (< US$8,000) and were once widely used in mineral exploration. Three manufacturers dominate the market: GEM Systems, Geometrics and Scintrex. Popular models include G-856/857, Smartmag, GSM-18, and GSM-19T. For mineral exploration, they have been superseded by Overhauser, caesium, and potassium instruments, all of which are fast-cycling, and do not require the operator to pause between readings. ====Overhauser effect magnetometer==== The ''Overhauser effect magnetometer'' or ''Overhauser magnetometer'' uses the same fundamental effect as the ''proton precession magnetometer'' to take measurements. By adding [[free radical]]s to the measurement fluid, the [[nuclear Overhauser effect]] can be exploited to significantly improve upon the proton precession magnetometer. Rather than aligning the [[proton]]s using a solenoid, a low power radio-frequency field is used to align (polarise) the electron spin of the free radicals, which then couples to the protons via the Overhauser effect. This has two main advantages: driving the RF field takes a fraction of the energy (allowing lighter-weight batteries for portable units), and faster sampling as the electron-proton coupling can happen even as measurements are being taken. An Overhauser magnetometer produces readings with a 0.01 nT to 0.02 nT standard deviation while sampling once per second. ====Caesium vapour magnetometer==== The ''optically pumped [[caesium]] vapour magnetometer'' is a highly sensitive (300 fT/Hz<sup>0.5</sup>) and accurate device used in a wide range of applications. It is one of a number of alkali vapours (including [[rubidium]] and [[potassium]]) that are used in this way.<ref name="snare" /> The device broadly consists of a [[photon]] emitter, such as a laser, an absorption chamber containing caesium vapour mixed with a "[[buffer gas]]" through which the emitted [[photon]]s pass, and a photon detector, arranged in that order. The buffer gas is usually [[helium]] or [[nitrogen]] and they are used to reduce collisions between the caesium vapour atoms. The basic principle that allows the device to operate is the fact that a caesium atom can exist in any of nine [[energy level]]s, which can be informally thought of as the placement of [[electron]] [[atomic orbital]]s around the [[atomic nucleus]]. When a caesium atom within the chamber encounters a photon from the laser, it is excited to a higher energy state, emits a photon and falls to an indeterminate lower energy state. The caesium atom is "sensitive" to the photons from the laser in three of its nine energy states, and therefore, assuming a closed system, all the atoms eventually fall into a state in which all the photons from the laser pass through unhindered and are measured by the photon detector. The caesium vapour has become transparent. This process happens continuously to maintain as many of the electrons as possible in that state. At this point, the sample (or population) is said to have been optically pumped and ready for measurement to take place. When an external field is applied it disrupts this state and causes atoms to move to different states which makes the vapour less transparent. The photo detector can measure this change and therefore measure the magnitude of the magnetic field. In the most common type of caesium magnetometer, a very small AC magnetic field is applied to the cell. Since the difference in the energy levels of the electrons is determined by the external magnetic field, there is a frequency at which this small AC field makes the electrons change states. In this new state, the electrons once again can absorb a photon of light. This causes a signal on a photo detector that measures the light passing through the cell. The associated electronics use this fact to create a signal exactly at the frequency that corresponds to the external field. Another type of caesium magnetometer modulates the light applied to the cell. This is referred to as a Bell-Bloom magnetometer, after the two scientists who first investigated the effect. If the light is turned on and off at the frequency corresponding to the Earth's field,{{clarify|date=July 2013}} there is a change in the signal seen at the photo detector. Again, the associated electronics use this to create a signal exactly at the frequency that corresponds to the external field. Both methods lead to high performance magnetometers. ====Potassium vapour magnetometer==== Potassium is the only optically pumped magnetometer that operates on a single, narrow electron spin resonance (ESR) line in contrast to other alkali vapour magnetometers that use irregular, composite and wide spectral lines and helium with the inherently wide spectral line.<ref>Hrvoic I (2008) Development of a new high sensitivity Potassium magnetometer for geophysical mapping, First Break 26:81–85</ref> ====Metastable helium-4 scalar magnetometer==== Magnetometers based on [[helium-4]] excited to its metastable triplet state thanks to a plasma discharge have been developed in the 1960s and 70s by [[Texas Instruments]], then by its spinoff Polatomic,<ref>{{Cite web |title=Polatomic - Welcome |url=http://www.polatomic.com/ |access-date=2022-05-11 |website=www.polatomic.com}}</ref> and from late 1980s by [[CEA-Leti: Laboratoire d'électronique des technologies de l'information|CEA-Leti]]. The latter pioneered a configuration which cancels the dead-zones,<ref>{{Cite journal |last1=Leger |first1=Jean-Michel |last2=Bertrand |first2=François |last3=Jager |first3=Thomas |last4=Le Prado |first4=Matthieu |last5=Fratter |first5=Isabelle |last6=Lalaurie |first6=Jean-Claude |date=2009-09-01 |title=Swarm Absolute Scalar and Vector Magnetometer Based on Helium 4 Optical Pumping |journal=Procedia Chemistry |series=Proceedings of the Eurosensors XXIII conference |language=en |volume=1 |issue=1 |pages=634–637 |doi=10.1016/j.proche.2009.07.158 |issn=1876-6196|doi-access=free }}</ref> which are a recurrent problem of atomic magnetometers. This configuration was demonstrated to show an accuracy of 50 pT in orbit operation. The [[European Space Agency|ESA]] chose this technology for the [[Swarm (spacecraft)|Swarm mission]], which was launched in 2013. An experimental vector mode, which could compete with fluxgate magnetometers was tested in this mission with overall success.<ref>{{Cite journal |last1=Léger |first1=Jean-Michel |last2=Jager |first2=Thomas |last3=Bertrand |first3=François |last4=Hulot |first4=Gauthier |last5=Brocco |first5=Laura |last6=Vigneron |first6=Pierre |last7=Lalanne |first7=Xavier |last8=Chulliat |first8=Arnaud |last9=Fratter |first9=Isabelle |date=2015-04-25 |title=In-flight performance of the Absolute Scalar Magnetometer vector mode on board the Swarm satellites |journal=Earth, Planets and Space |language=en |volume=67 |issue=1 |pages=57 |doi=10.1186/s40623-015-0231-1 |bibcode=2015EP&S...67...57L |s2cid=55990684 |issn=1880-5981|doi-access=free }}</ref> ====Applications==== The caesium and potassium magnetometers are typically used where a higher performance magnetometer than the proton magnetometer is needed. In archaeology and geophysics, where the sensor sweeps through an area and many accurate magnetic field measurements are often needed, caesium and potassium magnetometers have advantages over the proton magnetometer. The caesium and potassium magnetometer's faster measurement rate allows the sensor to be moved through the area more quickly for a given number of data points. Caesium and potassium magnetometers are insensitive to rotation of the sensor while the measurement is being made. The lower noise of caesium and potassium magnetometers allow those measurements to more accurately show the variations in the field with position. ===Vector magnetometers=== Vector magnetometers measure one or more components of the magnetic field electronically. Using three orthogonal magnetometers, both azimuth and dip (inclination) can be measured. By taking the square root of the sum of the squares of the components the total magnetic field strength (also called total magnetic intensity, TMI) can be calculated by the [[Pythagorean theorem]]. Vector magnetometers are subject to temperature drift and the dimensional instability of the ferrite cores. They also require leveling to obtain component information, unlike total field (scalar) instruments. For these reasons they are no longer used for mineral exploration. ====Rotating coil magnetometer==== The magnetic field induces a sine wave in a rotating [[electromagnetic coil|coil]]. The amplitude of the signal is proportional to the strength of the field, provided it is uniform, and to the [[sine]] of the angle between the rotation axis of the coil and the field lines. This type of magnetometer is obsolete. ====Hall effect magnetometer==== {{Main|Hall effect sensor}} The most common magnetic sensing devices are [[solid state electronics|solid-state]] [[Hall effect]] sensors. These sensors produce a voltage proportional to the applied magnetic field and also sense polarity. They are used in applications where the magnetic field strength is relatively large, such as in [[anti-lock braking system]]s in cars, which sense wheel rotation speed via slots in the wheel disks. ====Magnetoresistive devices==== {{Main|Magnetoresistance}} These are made of thin strips of [[Permalloy]], a high [[magnetic permeability]], nickel-iron alloy, whose electrical resistance varies with a change in magnetic field. They have a well-defined axis of sensitivity, can be produced in 3-D versions and can be mass-produced as an integrated circuit. They have a response time of less than 1 microsecond and can be sampled in moving vehicles up to 1,000 times/second. They can be used in compasses that read within 1°, for which the underlying sensor must reliably resolve 0.1°.<ref>{{citation|title=Applications of Magnetoresistive Sensors in Navigation Systems|author=Michael J. Caruso|publisher=Honeywell Inc.|url=http://www.ssec.honeywell.com/position-sensors/datasheets/sae.pdf|archive-url=https://web.archive.org/web/20100705002122/http://www.ssec.honeywell.com/position-sensors/datasheets/sae.pdf|url-status=dead|archive-date=5 July 2010|access-date=21 October 2012}}</ref> ====Fluxgate magnetometer==== {{See also|Gradiometer}} [[File:Magnetometr transduktorowy by Zureks.jpg|thumb|A uniaxial fluxgate magnetometer]] [[File:Floating core fluxgate inclinometer compass autonnic.jpg|thumb|A [[fluxgate compass]]/inclinometer]] [[File:Fluxgate Magnetometers.ogv|thumb|Basic principles of a fluxgate magnetometer]] A fluxgate magnetometer consists of a small magnetically susceptible core wrapped by two coils of wire. An alternating electric current is passed through one coil, driving the core through an alternating cycle of [[saturation (magnetic)|magnetic saturation]]; i.e., magnetised, unmagnetised, inversely magnetised, unmagnetised, magnetised, and so forth. This constantly changing field induces a voltage in the second coil which is measured by a detector. In a magnetically neutral background, the input and output signals match. However, when the core is exposed to a background field, it is more easily saturated in alignment with that field and less easily saturated in opposition to it. Hence the alternating magnetic field and the induced output voltage, are out of step with the input current. The extent to which this is the case depends on the strength of the background magnetic field. Often, the signal in the output coil is integrated, yielding an output analog voltage proportional to the magnetic field. The fluxgate magnetometer was invented by H. Aschenbrenner and G. Goubau in 1936.<ref name="snare">{{cite book |last1=Snare |first1=Robert C. |chapter=A History of Vector Magnetometry in Space |chapter-url=https://faculty.epss.ucla.edu/~ctrussell/ESS265/History.html |pages=[https://books.google.com/books?id=hHC5FTZMSRkC&pg=PA101 101–114] |editor1-first=Robert F. |editor1-last=Pfaff |editor2-first=Joseph E. |editor2-last=Borovsky |editor3-first=David T. |editor3-last=Young|title=Measurement Techniques in Space Plasmas: Fields |date=1998 |publisher=[[American Geophysical Union]] |publication-place=Washington, D.C. |isbn=0-87590-086-0 |issn=0065-8448 |series=Geophysical Monograph |volume=103 |bibcode=1998GMS...103..101S }}</ref><ref>{{cite book |last1=Musmann |first1=Günter Dr. |title=Fluxgate Magnetometers for Space Research |date=2010 |publisher=Books on Demand |location=Norderstedt |isbn=9783839137024}}</ref>{{rp|4}} A team at Gulf Research Laboratories led by [[Victor Vacquier]] developed airborne fluxgate magnetometers to detect submarines during [[World War II]] and after the war confirmed the theory of [[plate tectonics]] by using them to measure shifts in the magnetic patterns on the sea floor.<ref name="lat">{{cite journal |author=Thomas H. Maugh II |date=24 January 2009 |title=Victor Vacquier Sr. dies at 101; geophysicist was a master of magnetics |url=http://www.latimes.com/news/science/la-me-vacquier24-2009jan24,0,3328591.story |journal=[[The Los Angeles Times]]}}</ref> A wide variety of sensors are currently available and used to measure magnetic fields. [[Fluxgate compass]]es and [[gradiometer]]s measure the direction and magnitude of magnetic fields. Fluxgates are affordable, rugged and compact with miniaturization recently advancing to the point of complete sensor solutions in the form of IC chips, including examples from both academia <ref>{{cite journal |doi=10.3390/s140813815 |doi-access=free|title=High-Sensitivity Low-Noise Miniature Fluxgate Magnetometers Using a Flip Chip Conceptual Design|year=2014|last1=Lu|first1=Chih-Cheng|last2=Huang|first2=Jeff|last3=Chiu|first3=Po-Kai|last4=Chiu|first4=Shih-Liang|last5=Jeng|first5=Jen-Tzong|journal=Sensors|volume=14|issue=8|pages=13815–13829|pmid=25196107|pmc=4179035|bibcode=2014Senso..1413815L}}</ref> and industry.<ref>http://www.ti.com/lit/gpn/drv425 {{Bare URL PDF|date=March 2022}}</ref> This, plus their typically low power consumption makes them ideal for a variety of sensing applications. Gradiometers are commonly used for archaeological prospecting, and [[unexploded ordnance]] (UXO) detection such as the German military's popular ''Foerster''.<ref>{{cite web |url=http://pdf.directindustry.com/pdf/foerster-instruments/landmine-and-uxo-detection-brochure/16605-113277.html |title=Landmine and UXO detection brochure – Foerster Instruments |access-date=25 October 2012}}</ref> Utility location specialists also use gradiometers for locating underground utilities such as pipeline valves, septic tanks, and manhole covers.<ref>{{Cite web |last=Foster |first=Ryan |date=2024-10-01 |title=The Ultimate Guide to Magnetic Locators |url=https://precisionoutdoortech.com/blogs/information-articles/the-ultimate-guide-to-magnetic-locators |access-date=2024-11-10 |website=Precision Outdoor Tech |language=en}}</ref> The typical fluxgate magnetometer consists of a "sense" (secondary) coil surrounding an inner "drive" (primary) coil that is closely wound around a highly permeable core material, such as [[mu-metal]] or [[permalloy]]. An alternating current is applied to the drive winding, which drives the core in a continuous repeating cycle of saturation and unsaturation. To an external field, the core is alternately weakly permeable and highly permeable. The core is often a toroidally wrapped ring or a pair of linear elements whose drive windings are each wound in opposing directions. Such closed flux paths minimise coupling between the drive and sense windings. In the presence of an external magnetic field, with the core in a highly permeable state, such a field is locally attracted or gated (hence the name fluxgate) through the sense winding. When the core is weakly permeable, the external field is less attracted. This continuous gating of the external field in and out of the sense winding induces a signal in the sense winding, whose principal frequency is twice that of the drive frequency, and whose strength and phase orientation vary directly with the external-field magnitude and polarity. There are additional factors that affect the size of the resultant signal. These factors include the number of turns in the sense winding, magnetic permeability of the core, sensor geometry, and the gated flux rate of change with respect to time. Phase synchronous detection is used to extract these harmonic signals from the sense winding and convert them into a DC voltage proportional to the external magnetic field. Active current feedback may also be employed, such that the sense winding is driven to counteract the external field. In such cases, the feedback current varies linearly with the external magnetic field and is used as the basis for measurement. This helps to counter inherent non-linearity between the applied external field strength and the flux gated through the sense winding. ====SQUID magnetometer==== {{Main|SQUID}} [[SQUID]]s, or superconducting quantum interference devices, measure extremely small changes in magnetic fields. They are very sensitive vector magnetometers, with noise levels as low as 3 fT Hz<sup>−½</sup> in commercial instruments and 0.4 fT Hz<sup>−½</sup> in experimental devices. Many liquid-helium-cooled commercial SQUIDs achieve a flat noise spectrum from near DC (less than 1 Hz) to tens of kilohertz, making such devices ideal for time-domain biomagnetic signal measurements. SERF atomic magnetometers demonstrated in laboratories so far reach competitive noise floor but in relatively small frequency ranges. SQUID magnetometers require cooling with liquid [[helium]] ({{Val|4.2|ul=K}}) or [[liquid nitrogen]] ({{Val|77|u=K}}) to operate, hence the packaging requirements to use them are rather stringent both from a thermal-mechanical as well as magnetic standpoint. SQUID magnetometers are most commonly used to measure the magnetic fields produced by laboratory samples, also for brain or heart activity ([[magnetoencephalography]] and [[magnetocardiography]], respectively). Geophysical surveys use SQUIDs from time to time, but the logistics of cooling the SQUID are much more complicated than other magnetometers that operate at room temperature. ====Zero-field optically-pumped magnetometers==== Magnetometers based on atomic gasses can perform vector measurements of the magnetic field in the low field regime, where the decay of the atomic coherence becomes faster than the [[Larmor frequency]]. The physics of such magnetometers is based on the [[Hanle effect]]. Such zero-field optically pumped magnetometers have been tested in various configurations and with different atomic species, notably [[Alkali metal|alkali]] (potassium, rubidium and cesium), [[helium]] and [[Mercury (element)|mercury]]. For the case of alkali, the coherence times were greatly limited due to spin-exchange relaxation. A major breakthrough happened at the beginning of the 2000 decade, Romalis group in Princeton demonstrated that in such a low field regime, alkali coherence times can be greatly enhanced if a high enough density can be reached by high temperature heating, this is the so-called [[SERF|SERF effect]]. The main interest of optically-pumped magnetometers is to replace SQUID magnetometers in applications where cryogenic cooling is a drawback. This is notably the case of medical imaging where such cooling imposes a thick thermal insulation, strongly affecting the amplitude of the recorded biomagnetic signals. Several startup companies are currently developing optically pumped magnetometers for biomedical applications: those of TwinLeaf,<ref>{{Cite web |title=MicroSERF Twinleaf magnetometers |url=https://twinleaf.com/vector/microSERF/}}</ref> quSpin<ref>{{Cite web |title=quSpin QZFM magnetometers |url=https://quspin.com/products-qzfm/}}</ref> and FieldLine<ref>{{Cite web |title=FieldLine website |url=https://fieldlineinc.com/}}</ref> being based on alkali vapors, and those of Mag4Health on metastable helium-4.<ref>{{Cite web |title=Mag4Health website |url=https://www.mag4health.com/technology/mag4health-quantum-sensors/}}</ref> =====Spin-exchange relaxation-free (SERF) atomic magnetometers===== {{Main|SERF}} At sufficiently high atomic density, extremely high sensitivity can be achieved. Spin-exchange-relaxation-free ([[SERF]]) atomic magnetometers containing [[potassium]], [[caesium]], or [[rubidium]] vapor operate similarly to the caesium magnetometers described above, yet can reach sensitivities lower than 1 fT Hz<sup>−{{1/2}}</sup>. The SERF magnetometers only operate in small magnetic fields. The Earth's field is about 50 [[tesla (unit)|μT]]; SERF magnetometers operate in fields less than 0.5 μT. Large volume detectors have achieved a sensitivity of 200 aT Hz<sup>−{{1/2}}</sup>.<ref>{{cite journal|last1=Kominis |first1=I.K. |last2=Kornack |first2=T.W. |last3=Allred |first3=J.C. |last4=Romalis |first4=M.V.|doi=10.1038/nature01484 |date=4 February 2003|title=A subfemtotesla multichannel atomic magnetometer|bibcode= 2003Natur.422..596K |volume=422 |issue=6932 |pmid=12686995| journal=Nature| pages=596–9|s2cid=4204465 }}</ref> This technology has greater sensitivity per unit volume than SQUID detectors.<ref>{{cite journal |last1=Budker |first1=D. |last2=Romalis |first2=M.V. |date=2006 |title=Optical Magnetometry |arxiv=physics/0611246 |doi=10.1038/nphys566 |volume=3 |issue=4 |journal=Nature Physics |pages=227–234| bibcode=2007NatPh...3..227B |s2cid=96446612 }}</ref> The technology can also produce very small magnetometers that may in the future replace coils for detecting radio-frequency magnetic fields.{{Citation needed|date=January 2012}} This technology may produce a magnetic sensor that has all of its input and output signals in the form of light on fiber-optic cables.<ref>{{Cite book |last1= Kitching |first1= J. |last2= Knappe |first2= S. |last3= Shah |first3= V. |last4= Schwindt |first4= P. |last5= Griffith |first5= C. |last6= Jimenez |first6= R. |last7= Preusser |first7= J. |last8= Liew |first8= L. -A. |last9= Moreland |first9= J. |chapter= Microfabricated atomic magnetometers and applications |doi= 10.1109/FREQ.2008.4623107 |title= 2008 IEEE International Frequency Control Symposium |pages= 789 |year= 2008 |isbn= 978-1-4244-1794-0 |s2cid= 46471890 |chapter-url= https://zenodo.org/record/1232197 }}</ref> This lets the magnetic measurement be made near high electrical voltages.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)