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| '''Specific (radiative) intensity''' is a quantity used in physics that describes [[electromagnetic radiation]]. It is a term used in much of the older scientific literature. The present-day SI term is [[spectral radiance]], which can be expressed in base SI units as {{nowrap|W m<sup>−2</sup> sr<sup>−1</sup> Hz<sup>−1</sup>}}.
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If the cone could be [http://www.thebestpocketknifereviews.com/ontario-knives-review/ Ontario Knife Reviews] very slender, you might be able to accomplish this step by merely with out the use of power instruments. Push the paneling nail or headless pin contained in the cone's stem. Make certain to depart approximately half-an-inch of the nail or pin sticking outside of the cone.<br><br>After all, I would not be an excellent legal professional with out giving a couple of caveats before I begin. First, do not forget that carrying any weapon, even one that’s authorized, can cause you lots of grief with law enforcement. Cops routinely write tickets and make arrests for issues they incorrectly assume is unlawful. Being discovered “not responsible” won't make up for the time and aggravation of getting arrested and lacking work - not to [http://Act.Jinbo.net/forum2006/index.php/Ontario_Knife_Company_Kukri_Review mention] the cost of hiring an legal professional. 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A nylon sheath can also be included.<br><br>As doctors are wont to do, Dr. Royce Johnson, a professor of medication at UCLA, couldn’t sit back and watch the girl die. Instead of panicking, the very first thing Dr. Johnson referred to as out for was none apart from a pocket knife. When another physician, who happily at all times carries a pocket knife, handed it to Dr. Johnson, he started performing an impromptu tracheotomy. He made an incision in her neck, stuck a pen in and blew air into her lungs. In response to the Davidson County Sheriff’s Workplace, 18-year-outdated Andrew Dale Loflin was arrested Saturday after deputies responded to a report of a stabbing at the suspect’s house on Regina Drive. |
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| It gives a full [[radiometry|radiometric]] description of the [[Field (physics)|field]] of [[classical electromagnetism|classical electromagnetic radiation]] of any kind, including [[thermal radiation]] and [[light]]. It is conceptually distinct from the descriptions in explicit terms of [[James Clerk Maxwell|Maxwellian]] [[electromagnetic fields]] or of [[photon]] distribution. It refers to material [[physics]] as distinct from [[psychophysics]].
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| For the concept of specific intensity, the line of propagation of radiation lies in a semi-transparent medium which varies continuously in its optical properties. The concept refers to an area, projected from the element of source area into a plane at right angles to the line of propagation, and to an element of solid angle subtended by the detector at the element of source area.<ref name="Planck 1914">Planck, M. (1914) ''The Theory of Heat Radiation'', second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, pages 13-15.</ref><ref name="Chandrasekhar 1950">Chandrasekhar, S. (1950). ''Radiative Transfer'', Oxford University Press, Oxford, pages 1-2.</ref><ref name="Mihalas Mihalas 1984">[http://www.filestube.com/9c5b2744807c2c3d03e9/details.html Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York, ISBN 0-19-503437-6.], pages 311-312.</ref><ref>Goody, R.M., Yung, Y.L. (1989). ''Atmospheric Radiation: Theoretical Basis'', 2nd edition, Oxford University Press, Oxford, New York, 1989, ISBN 0-19-505134-3, page 16.</ref><ref>Liou, K.N. (2002). ''An Introduction of Atmospheric Radiation'', second edition, Academic Press, Amsterdam, ISBN 978-0-12-451451-5, page 4.</ref><ref name="Hapke 64">Hapke, B. (1993). ''Theory of Reflectance and Emittance Spectroscopy'', Cambridge University Press, Cambridge UK, ISBN 0-521-30789-9, page 64.</ref><ref>Rybicki, G.B., Lightman, A.P. (1979/2004). ''Radiative Processes in Astrophysics'', reprint, John Wiley & Sons, New York, ISBN 0-471-04815-1, page 3.</ref>
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| The term ''brightness'' is also sometimes been used for this concept.<ref name="Planck 1914"/><ref>Born, M., Wolf, E. (1999). ''Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light'', 7th edition, Cambridge University Press, ISBN 0-521-64222-1, page 194.</ref> The SI system states that the word brightness should not be so used, but should instead refer only to psychophysics.
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| [[File:specific intensity geometry b.jpg|thumb|466px|right|The geometry for the definition of specific (radiative) intensity. Note the potential in the geometry for laws of reciprocity.]]
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| ==Definition==
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| The specific (radiative) intensity is a quantity that describes the rate of radiative transfer of energy at {{math|''P''<sub>1</sub>}}, a point of space with coordinates {{math|'''x'''}}, at time {{math|''t''}}. It is a scalar-valued function of four variables, customarily<ref name="Planck 1914"/><ref name="Chandrasekhar 1950"/><ref name="Mihalas Mihalas 1984"/><ref name="Kondratyev 1969">Kondratyev, K.Y. (1969). ''Radiation in the Atmosphere'', Academic Press, New York, page 10.</ref><ref name="Mihalas 1978">Mihalas, D. (1978). ''Stellar Atmospheres'', 2nd edition, Freeman, San Francisco, ISBN 0-7167-0359-9, pages 2-5.</ref><ref>Born, M., Wolf, E. (1999). ''Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light'', 7th edition, Cambridge University Press, ISBN 0-521-64222-1, pages 194-199.</ref> written as
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| :{{math|''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, ''ν'')}}
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| where:
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| :{{math|''ν''}} denotes frequency.
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| :{{math|'''r'''<sub>1</sub>}} denotes a unit vector, with the direction and sense of the geometrical vector {{math|'''r'''}} in the line of propagation from
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| :the effective source point {{math|''P''<sub>1</sub>}}, to
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| :a detection point {{math|''P''<sub>2</sub>}}.
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| {{math|''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, ''ν'')}} is defined to be such that a virtual source area, {{math|d''A''<sub>1</sub>}} , containing the point {{math|''P''<sub>1</sub>}} , is an apparent emitter of a small but finite amount of energy {{math|d''E''}} transported by radiation of frequencies {{math|(''ν'', ''ν'' + d''ν'')}} in a small time duration {{math|d''t''}} , where
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| :{{math|d''E'' {{=}} ''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, ''ν'') cos ''θ''<sub>1</sub> d''A''<sub>1</sub> d''Ω''<sub>1</sub> d''ν'' d''t''}} , | |
| and where {{math|''θ''<sub>1</sub>}} is the angle between the line of propagation {{math|'''r'''}} and the normal {{math|''P''<sub>1</sub>''N''<sub>1</sub>}} to {{math|d''A''<sub>1</sub>}} ; the effective destination of {{math|d''E''}} is a finite small area {{math|d''A''<sub>2</sub>}} , containing the point {{math|''P''<sub>2</sub>}} , that defines a finite small solid angle {{math|d''Ω''<sub>1</sub>}} about {{math|''P''<sub>1</sub>}} in the direction of {{math|'''r'''}} . The cosine accounts for the projection of the source area {{math|d''A''<sub>1</sub>}} into a plane at right angles to the line of propagation indicated by {{math|'''r'''}} .
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| The use of the differential notation for areas {{math|d''A''<sub>''i''</sub>}} indicates they are very small compared to {{math|''r''<sup>2</sup>}}, the square of the magnitude of vector {{math|'''r'''}}, and thus the solid angles {{math|d<var>''Ω''</var><sub>''i''</sub>}} are also small.
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| There is no radiation that is attributed to {{math|''P''<sub>1</sub>}} itself as its source, because {{math|''P''<sub>1</sub>}} is a [[Point (geometry)|geometrical point]] with no magnitude. A finite area is needed to emit a finite amount of light.
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| ==Invariance==
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| For propagation of light in a vacuum, the definition of specific (radiative) intensity implicitly allows for the [[inverse square law]] of radiative propagation.<ref name="Mihalas 1978"/><ref name="RL 1979">Rybicki, G.B., Lightman, A.P. (1979). ''Radiative Processes in Astrophysics'', John Wiley & Sons, New York, ISBN 0-471-04815-1, pages 7-8.</ref> The concept of specific (radiative) intensity of a source at the point {{math|''P''<sub>1</sub>}} presumes that the destination detector at the point {{math|''P''<sub>2</sub>}} has optical devices (telescopic lenses and so forth) that can resolve the details of the source area {{math|d''A''<sub>1</sub>}}. Then the specific radiative intensity of the source is independent of the distance from source to detector; it is a property of the source alone. This is because it is defined per unit solid angle, the definition of which refers to the area {{math|d''A''<sub>2</sub>}} of the detecting surface.
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| This may be understood by looking at the diagram. The factor {{math|cos ''θ''<sub>1</sub>}} has the effect of converting the effective emitting area {{math|d''A''<sub>1</sub>}} into a virtual projected area {{math|cos ''θ''<sub>1</sub> d''A''<sub>1</sub> {{=}} ''r''<sup>2</sup> d''Ω''<sub>2</sub>}} at right angles to the vector {{math|'''r'''}} from source to detector. The solid angle {{math|d''Ω''<sub>1</sub>}} also has the effect of converting the detecting area {{math|d''A''<sub>2</sub>}} into a virtual projected area {{math|cos ''θ''<sub>2</sub> d''A''<sub>2</sub> {{=}} ''r''<sup>2</sup> d''Ω''<sub>1</sub>}} at right angles to the vector {{math|'''r'''}} , so that {{math|d''Ω''<sub>1</sub> {{=}} cos ''θ''<sub>2</sub> d''A''<sub>2</sub> / ''r''<sup>2</sup>}} . Substituting this for {{math|d''Ω''<sub>1</sub>}} in the above expression for the collected energy {{math|d''E''}}, one finds {{math|d''E'' {{=}} ''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, ''ν'') cos ''θ''<sub>1</sub> d''A''<sub>1</sub> cos ''θ''<sub>2</sub> d''A''<sub>2</sub> d''ν'' d''t'' / ''r''<sup>2</sup>}} : when the emitting and detecting areas and angles {{math|d''A''<sub>1</sub>}} and {{math|d''A''<sub>2</sub>}}, {{math|''θ''<sub>1</sub>}} and {{math|''θ''<sub>2</sub>}}, are held constant, the collected energy {{math|d''E''}} is inversely proportional to the square of the distance {{math|''r''}} between them, with invariant {{math|''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, ''ν'')}} .
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| This may be expressed also by the statement that {{math|''I'' ('''x''', ''t'' ; '''r'''<sub>1</sub>, <var>ν</var>)}} is invariant with respect to the length {{math|''r''}} of {{math|'''r'''}} ; that is to say, provided the optical devices have adequate resolution, and that the transmitting medium is perfectly transparent, as for example a vacuum, then the specific intensity of the source is unaffected by the length {{math|''r''}} of the ray {{math|'''r'''}} .<ref name="Mihalas 1978"/><ref name="RL 1979"/><ref>Bohren, C.F., Clothiaux, E.E. (2006). ''Fundamentals of Atmospheric Radiation'', Wiley-VCH, Weinheim, ISBN 3-527-40503-8, pages 191-192.</ref>
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| For the propagation of light in a transparent medium with a non-unit non-uniform refractive index, the invariant quantity along a ray is the specific intensity divided by the square of the absolute refractive index.<ref name="Planck 1914 p 35">Planck, M. (1914). ''The Theory of Heat Radiation'', second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, page 35.</ref>
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| ==Reciprocity== | |
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| For the propagation of light in a semi-transparent medium, specific intensity is not invariant along a ray, because of absorption and emission. Nevertheless, the Stokes-Helmholtz [[Helmholtz reciprocity|reversion-reciprocity principle]] applies, because absorption and emission are the same for both senses of a given direction at a point in a stationary medium.
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| ==Étendue and Reciprocity==
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| The term [[étendue]] is used to focus attention specifically on the geometrical aspects. The reciprocal character of [[étendue]] is indicated in the article about it. Étendue is defined as a second differential. In the notation of the present article, the second differential of the étendue, {{math|d<sup>2</sup>''G''}} , of the [[pencil beam|pencil of light]] which "connects" the two surface elements {{math|d''A''<sub>1</sub>}} and {{math|d''A''<sub>2</sub>}} is defined as
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| :{{math|d<sup>2</sup>''G'' {{=}} d''A''<sub>1</sub> cos <var>''θ''</var><sub>1</sub> d<var>Ω</var><sub>1</sub> {{=}}}} <math>\frac{\mbox{d}A_1 \ \, \mbox{d}A_2 \ \cos{\theta_1} \ \cos{\theta_2}}{r^2}</math> {{math|{{=}} d''A''<sub>2</sub> cos <var>''θ''</var><sub>2</sub> d<var>Ω</var><sub>2</sub>}}.
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| This can help understand the geometrical aspects of the Stokes-Helmholtz reversion-reciprocity principle.
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| ==Collimated beam==
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| For the present purposes, the light from a star can be treated as a practically [[Collimated light|collimated beam]], but apart from this, a collimated beam is rarely if ever found in nature, though artificially produced beams can be very nearly collimated. For some purposes the rays of the sun can be considered as practically collimated, because the sun subtends an angle of only 32′ of arc.<ref>Goody, R.M., Yung, Y.L. (1989). ''Atmospheric Radiation: Theoretical Basis'', 2nd edition, Oxford University Press, Oxford, New York, 1989, ISBN 0-19-505134-3, page 18.</ref> The specific (radiative) intensity is suitable for the description of an uncollimated radiative field. The integrals of specific (radiative) intensity with respect to solid angle, used for the definition of [[spectral flux density]], are singular for exactly collimated beams, or may be viewed as [[Dirac delta function]]s. Therefore the specific (radiative) intensity is unsuitable for the description of a collimated beam, while [[spectral flux density]] is suitable for that purpose.<ref>Hapke, B. (1993). ''Theory of Reflectance and Emittance Spectroscopy'', Cambridge University Press, Cambridge UK, ISBN 0-521-30789-9, see pages 12 and 64.</ref>
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| ==Rays==
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| Specific (radiative) intensity is built on the idea of a [[pencil beam|''pencil'']] of [[Ray (optics)|rays of light]].<ref>Planck, M. (1914). ''The Theory of Heat Radiation'', second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, Chapter 1.</ref><ref>Levi, L. (1968). ''Applied Optics: A Guide to Optical System Design'', 2 volumes, Wiley, New York, volume 1, pages 119-121.</ref><ref>Born, M., Wolf, E. (1999). ''Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light'', 7th edition, Cambridge University Press, ISBN 0-521-64222-1, pages 116-125.</ref>
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| In an optically isotropic medium, the rays are normals to the [[wavefront]]s, but in an optically anisotropic crystalline medium, they are in general at angles to those normals. That is to say, in an optically anisotropic crystal, the energy does not in general propagate at right angles to the wavefronts.<ref name="BW 1999 792-795">Born, M., Wolf, E. (1999). ''Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light'', 7th edition, Cambridge University Press, ISBN 0-521-64222-1, pages 792-795.</ref><ref name="HJ">Hecht, E., Zajac, A. (1974). ''Optics'', Addison-Wesley, Reading MA, page 235.</ref>
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| ==Alternative approaches==
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| The specific (radiative) intensity is a radiometric concept. Related to it is the intensity in terms of the photon distribution function,<ref name="Mihalas Mihalas 1984"/><ref name="Mihalas 1978 10">Mihalas, D. (1978). ''Stellar Atmospheres'', 2nd edition, Freeman, San Francisco, ISBN 0-7167-0359-9, page 10.</ref> which uses the metaphor<ref>Lamb, W.E., Jr (1995). Anti-photon, ''Applied Physics'', '''B60''': 77-84.[http://www.springerlink.com/content/h16g2307204h5654/]</ref> of a ''particle'' of light that traces the path of a ray.
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| The idea common to the photon and the radiometric concepts is that the energy travels along rays.
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| Another way to describe the radiative field is in terms of the Maxwell electromagnetic field, which includes the concept of the [[wavefront]]. The rays of the radiometric and photon concepts are along the time-averaged [[Poynting vector]] of the Maxwell field.<ref>Mihalas, D. (1978). ''Stellar Atmospheres'', 2nd edition, Freeman, San Francisco, ISBN 0-7167-0359-9, page 11.</ref> In an anisotropic medium, the rays are not in general perpendicular to the wavefront.<ref name="BW 1999 792-795"/><ref name="HJ"/>
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| ==See also==
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| * [[Radiance]]
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| * [[Radiometry]]
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| * [[Radiative transfer]]
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| * [[Etendue|Étendue]]
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| ==References==
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| {{Reflist}}
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| [[Category:Radiometry]]
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