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| In [[laser science]], '''laser beam quality''' defines aspects of the beam illumination pattern and the merits of a particular [[laser beam]]'s propagation and transformation properties (space-bandwidth criterion). By observing and recording the beam pattern, for example, one can infer the [[spatial mode]] properties of the beam and whether or not the beam is being clipped by an obstruction; By focusing the laser beam with a [[Lens (optics)|lens]] and measuring the minimum spot size, the number of times [[diffraction limit]] or focusing quality can be computed.
| | I'm Myles (25) from Schofens, Austria. <br>I'm learning Hindi literature at a local university and I'm just about to graduate.<br>I have a part time job in a post office.<br>[http://họcnghề.com ][http://xn--hcngh-461b5c.com/ Hoc nghe] </a> |
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| [[Anthony E. Siegman]] was the first to propose the formalism for a laser beam quality factor that could be measured and used to compare different beams, independent of [[wavelength]].<ref>{{cite paper |url=http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1006401 |title=Defining, measuring, and optimizing laser beam quality |first=Anthony E. |last=Siegman, |journal=Proc. SPIE 1868, Laser Resonators and Coherent Optics: Modeling, Technology, and Applications, |volume=2 |date=February 5, 1993 |doi=10.1117/12.150601}}</ref> The factor is called [[M squared|M<sup>2</sup>]], and it is closely related to the [[beam parameter product]]. While the M<sup>2</sup> factor does not give detail on the spatial characteristics of the beam, it does indicate how close it is to being a fundamental-mode [[Gaussian beam]]. It also determines the smallest spot size for the beam, as well as the [[beam divergence]]. M<sup>2</sup> can also give an indication of beam distortions due to, for example, power-induced [[thermal lensing]] in the [[laser gain medium]], since it will increase.
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| There are some limitations to the M<sup>2</sup> parameter as a simple quality metric. It can be difficult to measure accurately, and factors such as background noise can create large errors in M<sup>2</sup>.<ref name=Siegman_1997>{{cite web |first=A. E. |last=Siegman, |url=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.177.3400&rep=rep1&type=pdf |format=pdf |title=How to (Maybe) Measure Laser Beam Quality |date=October 1997 |accessdate=Nov 25, 2013}} Tutorial presentation at the Optical Society of America Annual Meeting, Long Beach, California</ref> Beams with power well out in the "tails" of the distribution have M<sup>2</sup> much larger than one would expect. In theory, an idealized tophat laser beam has infinite M<sup>2</sup>, although this is not true of any physically realizable tophat beam. For a pure [[Bessel beam]], one cannot even compute M<sup>2</sup>.<ref>{{cite journal |url=http://webusers.fis.uniroma3.it/~ottica/sant/pubs/Max035.pdf |title=M<sup>2</sup> factor of Bessel–Gauss beams |first1=R. |last1=Borghi |first2=M. |last2=Santarsiero |journal=Optics Letters |volume=22 |issue=5 |date=March 1, 1997}}</ref>
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| The definition of "quality" also depends on the application. While a high-quality single-mode Gaussian beam (M<sup>2</sup> close to unity) is optimum for many applications, for other applications a uniform multimode [[tophat beam]] intensity distribution is required. An example is [[laser surgery]].<ref>{{cite book |title=Current Concepts in Aesthetic and Reconstructive Oculoplastic Surgery, |editor=Constance L. Fry, Alan R. Faulkner.}}</ref>
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| Power-in-the-bucket and Strehl ratio are two other attempts to define beam quality. Both these methods use a [[Laser beam profiler]] to measure how much power is delivered to a given area. There is also no simple conversion between M<sup>2</sup>, power-in-the-bucket, and Strehl ratio.
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| ==M<sup>2</sup> definitions==
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| {{main|M squared}}
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| [[Image:M2definition.gif|thumb|403px|right|M<sup>2</sup> definition]]
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| The [[equation]] for the [[Beam divergence|divergence]], of a pure [[Gaussian beam|Gaussian]] TEM<sub>00</sub> unfocused beam propagating through space is given by
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| :<math>\Theta_{00}={4\lambda \over \pi D_{00}}</math>, (1)
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| where ''D''<sub>00</sub> is the diameter of the [[beam waist]], and ''λ'' is the wavelength. Higher mode beams often start with a larger beam waist, ''D''<sub>0</sub>, and/or have a faster divergence ''Θ''<sub>0</sub>. In this case Equation (1) becomes
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| :<math>\Theta_0=M^2 {4\lambda \over \pi D_0}</math>, (2)
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| where ''Θ''<sub>0</sub> and ''D''<sub>0</sub> are the divergence and waist of a higher mode beam and ''M''<sup>2</sup> is greater than 1 and is named the "Beam Propagation [[Ratio]]" per the ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot [[Beam diameter|diameter]] is defined by
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| :<math>d_{00}={4\lambda f \over \pi D_{00}}</math>, (3)
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| where ''d''<sub>00</sub> is the ideal focused spot diameter, ''f'' is the [[focal length]] of the focusing lens, and ''D''<sub>00</sub> is the input beam waist and is placed one focal length from the lens as shown in the figure. However, when a [[Transverse mode|multimode]] beam is focused, Equation (3) becomes
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| :<math>d_0=M^2 {4\lambda f \over \pi D_0}</math>. (4)
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| ==M<sup>2</sup> measurement==
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| M<sup>2</sup> cannot be determined from a single beam profile measurement. The ISO/DIS 11146 define that M<sup>2</sup> should be calculated from a series of measurements as shown in the figure below.<ref>ISO 11146:2005(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios".</ref> M<sup>2</sup> is measured on real beams by focusing the beam with a fixed position lens of known focal length, and then measuring the characteristics of the beam waist and divergence. These measurements can be taken with a [[laser beam profiler]].
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| [[File:Focusinglens.gif|thumb|400px|center|Measurement positions for obtaining M<sup>2</sup>]]
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| The multiple measurements ensure that the minimum beam diameter is found and enable a "curve fit" that improves the accuracy of the calculation by minimizing measurement error.
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| == References ==
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| {{Reflist}}
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| [[Category:Laser science]]
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I'm Myles (25) from Schofens, Austria.
I'm learning Hindi literature at a local university and I'm just about to graduate.
I have a part time job in a post office.
[1]Hoc nghe </a>