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| {{redirect|Beam width|cases related to radio antennas|beamwidth}}
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| The '''beam diameter''' or '''beam width''' of an [[Light beam|electromagnetic beam]] is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many different ways. Five definitions of the beam width are in common use: D4σ, 10/90 or 20/80 knife-edge, 1/e<sup>2</sup>, FWHM, and D86. The beam width can be measured in units of length at a particular plane perpendicular to the beam axis, but it can also refer to the [[Angular diameter|angular width]], which is the angle subtended by the beam at the source.
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| Beam diameter is usually used to characterize electromagnetic beams in the optical regime, and occasionally in the [[microwave]] regime, that is, cases in which the [[aperture (antenna)|aperture]] from which the beam emerges is very large with respect to the [[wavelength]].
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| Beam diameter usually refers to a beam of circular cross section, but not necessarily so. A beam may, for example, have an elliptical cross section, in which case the orientation of the beam diameter must be specified, for example with respect to the major or minor axis of the elliptical cross section. The term "beam width" may be preferred in applications where the beam does not have circular symmetry.
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| ==Width definitions==
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| ===Full width at half maximum===
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| {{details|Full width at half maximum}}
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| The simplest way to define the width of a beam is to choose two diametrically opposite points at which the [[irradiance]] is a specified fraction of the beam's peak irradiance, and take the distance between them as a measure of the beam's width. An obvious choice for this fraction is ½ (−3 [[Decibel|dB]]), in which case the diameter obtained is the full width of the beam at half its maximum intensity (FWHM). This is also called the ''half-power beam width'' (HPBW).
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| === 1/e<sup>2</sup> width ===
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| The 1/e<sup>2</sup> width is equal to the distance between the two points on the marginal distribution that are 1/e<sup>2</sup> = 0.135 times the maximum value. In many cases, it makes more sense to take the distance between points where the intensity falls to 1/e<sup>2</sup> = 0.135 times the maximum value. If there are more than two points that are 1/e<sup>2</sup> times the maximum value, then the two points closest to the maximum are chosen. The 1/e<sup>2</sup> width is important in the mathematics of [[Gaussian beam]]s.
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| The American National Standard Z136.1-2007 for Safe Use of Lasers (p. 6) defines the beam diameter as the distance between diametrically opposed points in that cross-section of a beam where the power per unit area is 1/e (0.368) times that of the peak power per unit area. This is the beam diameter definition that is used for computing the maximum permissible exposure to a laser beam. In addition, the Federal Aviation Administration also uses the 1/e definition for laser safety calculations in FAA Order 7400.2F, "Procedures for Handling Airspace Matters," February 16, 2006, p. 29-1-2.
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| Measurements of the 1/e<sup>2</sup> width only depend on three points on the marginal distribution, unlike D4σ and knife-edge widths that depend on the integral of the marginal distribution. 1/e<sup>2</sup> width measurements are noisier than D4σ width measurements. For [[transverse mode|multimodal]] marginal distributions (a beam profile with multiple peaks), the 1/e<sup>2</sup> width usually does not yield a meaningful value and can grossly underestimate the inherent width of the beam. For multimodal distributions, the D4σ width is a better choice. For an ideal single-mode Gaussian beam, the D4σ, D86 and 1/e<sup>2</sup> width measurements would give the same value.
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| For a Gaussian beam, the relationship between the 1/e<sup>2</sup> width and the full width at half maximum is <math>2w = \frac{\sqrt 2\ \mathrm{FWHM}}{\sqrt{\ln 2}} = 1.699 \times \mathrm{FWHM}</math>, where <math>2w</math> is the full width of the beam at 1/e<sup>2</sup>.<ref name=zemax>{{cite web |url=http://www.radiantzemax.com/kb-en/Knowledgebase/How-To-Convert-FWHM-Measurements-to-1e-Squared-Halfwidths |title=
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| How to convert FWHM measurements to 1/e-squared halfwidths |first=Dan |last=Hill |date=April 4, 2007 |work=Radiant Zemax Knowledge Base |accessdate=Nov 15, 2012}}</ref>
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| === D4σ or second moment width ===
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| The D4σ width of a beam in the horizontal or vertical direction is 4 times σ, where σ is the [[standard deviation]] of the horizontal or vertical marginal distribution, respectively. Mathematically, the D4σ beam width in the x-dimension for the beam profile <math> I(x,y) </math> is expressed as
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| :<math> D4\sigma = 4 \sigma = 4 \sqrt{\frac{\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}I(x,y) (x-\bar{x})^2 \,dx\, dy} {\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}I(x,y)\, dx \,dy}} </math>,
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| where
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| :<math> \bar{x} = \frac{\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}I(x,y) x\, dx\, dy} {\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}I(x,y) \,dx \,dy} </math> | |
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| is the [[centroid]] of the beam profile in the x-direction.
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| When a beam is measured with a [[laser beam profiler]], the wings of the beam profile influence the D4σ value more than the center of the profile since the wings are weighted by the square of its distance, ''x''<sup>2</sup>, from the center of the beam. If the beam does not fill more than a third of the beam profiler’s sensor area, then there will be a significant number of pixels at the edges of the sensor that register a small baseline value (the background value). If the baseline value is large or if it is not subtracted out of the image, then the computed D4σ value will be larger than the actual value because the baseline value near the edges of the sensor are weighted in the D4σ integral by ''x''<sup>2</sup>. Therefore, baseline subtraction is necessary for accurate D4σ measurements. The baseline is easily measured by recording the average value for each pixel when the sensor is not illuminated. The D4σ width, unlike the FWHM and 1/e<sup>2</sup> widths, is meaningful for multimodal marginal distributions — that is, beam profiles with multiple peaks — but requires careful subtraction of the baseline for accurate results. The D4σ is the ISO international standard definition for beam width.
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| === Knife-edge width ===
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| Before the advent of the [[charge-coupled device|CCD]] beam profiler, the beam width was estimated using the knife-edge technique: slice a laser beam with a razor and measure the power of the clipped beam as a function of the razor position. The measured curve is the integral of the marginal distribution, and starts at the total beam power and decreases monotonically to zero power. The width of the beam is defined as the distance between the points of the measured curve that are 10% and 90% (or 20% and 80%) of the maximum value. If the baseline value is small or subtracted out, the knife-edge beam width always corresponds to 60%, in the case of 20/80, or 80%, in the case of 10/90, of the total beam power no matter what the beam profile. On the other hand, the D4σ, 1/e<sup>2</sup>, and FWHM widths encompass fractions of power that are beam-shape dependent. Therefore, the 10/90 or 20/80 knife-edge width is a useful metric when the user wishes to be sure that the width encompasses a fixed fraction of total beam power. Most CCD beam profiler's software can compute the knife-edge width numerically.
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| === D86 width ===
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| The D86 width is defined as the diameter of the circle that is centered at the centroid of the beam profile and contains 86% of the beam power. The solution for D86 is found by computing the area of increasingly larger circles around the centroid until the area contains 0.86 of the total power. Unlike the previous beam width definitions, the D86 width is not derived from marginal distributions. The percentage of 86, rather than 50, 80, or 90, is chosen because a circular Gaussian beam profile integrated down to 1/e<sup>2</sup> of its peak value contains 86% of its total power. The D86 width is often used in applications that are concerned with knowing exactly how much power is in a given area. For example, applications of high-energy [[laser weapon]]s and [[lidar]]s require precise knowledge of how much transmitted power actually illuminates the target. | |
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| ==== ISO11146 beam width for elliptic beams<ref name="ISO11146-3">ISO 11146-3:2004(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios — Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods."</ref> ====
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| The definition given before holds for stigmatic (circular symmetric) beams only. For astigmatic beams however, a more rigorous definition of the beam width has to be used,
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| :<math> d_{\sigma x} = 2 \sqrt{2} \left( \langle x^2 \rangle + \langle y^2 \rangle + \gamma \left( \left( \langle x^2 \rangle - \langle y^2 \rangle \right)^2 + 4 \langle xy \rangle^2 \right)^{1/2} \right)^{1/2} </math>
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| :<math> d_{\sigma y} = 2 \sqrt{2} \left( \langle x^2 \rangle + \langle y^2 \rangle - \gamma \left( \left( \langle x^2 \rangle - \langle y^2 \rangle \right)^2 + 4 \langle xy \rangle^2 \right)^{1/2} \right)^{1/2}. </math>
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| This definition also incorporates information about x-y-correlation <math> \langle xy \rangle </math>, but for circular symmetric beams, both definitions are the same.
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| Some new symbols appeared within the formulas, which are the first- and second-order moments
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| :<math> \langle x \rangle = \frac{1}{P} \int{I(x,y) x dx dy}, </math>
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| :<math> \langle y \rangle = \frac{1}{P} \int{I(x,y) y dx dy}</math> and
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| :<math> \langle x^2 \rangle = \frac{1}{P} \int{I(x,y) (x - \langle x \rangle )^2 dx dy}, </math>
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| :<math> \langle xy \rangle = \frac{1}{P} \int{I(x,y) (x - \langle x \rangle ) (y - \langle y \rangle ) dx dy}, </math>
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| :<math> \langle y^2 \rangle = \frac{1}{P} \int{I(x,y) (y - \langle y \rangle )^2 dx dy}, </math>
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| the beam power | |
| :<math> P = \int{I(x,y) dx dy} </math>
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| :<math> \gamma = \sgn \left( \langle x^2 \rangle - \langle y^2 \rangle \right) = \frac{\langle x^2 \rangle - \langle y^2 \rangle}{|\langle x^2 \rangle - \langle y^2 \rangle|}. </math>
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| Using this general definition, also the beam's azimutal-angle <math> \phi </math> can be expressed. It is the angle between the beam's directions of minimum and maximum elongation, known as principal axis, and the laboratory system, being the <math>x</math>- and <math>y</math>-axis of the detector and given by
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| :<math> \phi = \frac{1}{2} \arctan \frac{2 \langle xy \rangle}{\langle x^2 \rangle - \langle y^2 \rangle }.</math>
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| ==Measurement==
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| International standard ISO 11146-1:2005 specifies methods for measuring beam widths (diameters), [[beam divergence|divergence angles]] and beam propagation ratios of laser beams (if the beam is stigmatic) and for general astigmatic beams ISO 11146-2 is applicable.<ref name="11146-1">ISO 11146-1:2005(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams."</ref><ref name="11146-2">ISO 11146-2:2005(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios — Part 2: General astigmatic beams."</ref> The D4σ beam width is the ISO standard definition and the measurement of the [[Beam parameter product|M² beam quality parameter]] requires the measurement of the D4σ widths.<ref name="11146-1"/><ref name="11146-2"/><ref>ISO 11146-3:2005(E), "Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles and beam propagation ratios — Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods."</ref>
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| The other definitions provide complementary information to the D4σ. The D4σ and knife-edge widths are sensitive to the baseline value, whereas the 1/e<sup>2</sup> and FWHM widths are not. The fraction of total beam power encompassed by the beam width depends on which definition is used.
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| ==See also==
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| *[[Beam divergence]]
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| *[[Laser beam profiler]]
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| ==References==
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| <references/>
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| [[Category:Antennas (radio)]]
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| [[Category:Optics]]
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The former Nike air cushion was formed in a resilient synthetic rubber layer which formed by pouring the air gas into a resilient synthetic rubber cheap nike free run under a high pressure.
Air-Sole was nike air max belong to cheap nike free run the "modest' kind, because its modest performance in cushioning ability, stability performance and reaction speed performance. Until today, this air cushion is in a wide application range among the series sports.
Visible Air-Sole: This kind of air cushion was made the Air-Sole into a visible type, such as the heel portion of the AIR JORDAN 3 was used this visible Air-Sole. Being regarded as the transitional form between Air-Sole and Max Air, Visible 180 Air-Sole can perform a good damping force and a perfect visible impact.
Air Max was launched in 1994, with an initial form of the U-shaped, and then developed into multi-sealed chamber Air Max and the trachea-shaped Tube Max Air. It possessed a multi-interval which was in multiple pressures, with a 5PSI pressure in the low pressure zone and 25PSI pressure in the high pressure zone. Air Max cushioning ability was very strong, can provide appropriateness protection to your feet and your knees, but may cause the loss of machine power. Running shoes and basketball shoes were always adopted this kind of technology.
The only 4-8mm thickness air cushion-Zoom Air was an air cushion by using a three-dimensional fabric to keep its flat shape, and not it would turn to a ball shape, with the air pressure of 20PSI. The damping effect with an excellent sense of site sensitive rebound effect and excellent acceleration, Zoom Air was widely used in extensive outside basketball shoes (such as FLIGHT series, the AJ series), and speed of running shoes (such as Air zoom Miler). The external Zoom Air cushion was not perfect in its damping ability, its capacity was also increased.
Turnes Air cushion was a hemisphere-shape cushioning system which can provide a maximum force protection, stable and comfort foot feeling, the most eye-catching place was that its variable hemisphere-shape shoe body can changing the air pressure according to its demand. TN Air contained the PBAX thermoplastic material which can provide a fast reflection, rubbing, and lightweight, flexible and suitable feet feeling for the appropriate thickness characteristics, its hemispheric body pressure was 20PSI and the cushion pressure was 5PSI.
The Total Air cushion can be seen as the enlarged version of the Max Air, with its forefoot grow to 1.5 cm. The most successful Total Air Cushion was the Total Air Foamposite Max-Steel.
The mid-sole mechanical cushioning system was composed by the special highly elastic foam materials (advanced PU materials) damping elastic column, and double TPU trays. SHOX used in the basketball and running shoes were with different roles. The SHOX cushion (people who are under 70kg are not obvious) provided excellent cushioning effect and stability, which was widely use in all kinds of sports shoes. The simplified version of SHOX-the IMPAX changed the columnar bottom into a horizontal punch technology to perform an excellent damping and stability performance.
Nike developed IPS system which an provide relatively independent and organic complexes cylindrical shock absorber for the research and development of Air Jordan XX shoes, under the help of 20 pieces Phylon material with different density, thickness, size and location.