140.113.15.171: /* Definition of statistical coupling energy */

2014-07-04T05:44:56Z

Definition of statistical coupling energy

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	~~The [[Marcel Minnaert\|Minnaert]] function is~~ a ~~[[photometry (astronomy)\|photometric]] function used~~ to ~~interpret [[astronomical]] observations <ref>http://dx.doi.org/10.1016/S0019-1035(03)00075-7</ref><ref>http://dx.doi.org/10.1016/j.icarus.2006.05.006</ref>~~ and ~~[[remote sensing]] data~~ for ~~the [[Earth]]~~.<~~ref~~>~~http://dx.doi.org/10.1080/01431160500104194~~<~~/ref~~> This function expresses the [[radiance factor]] (RADF) as a function the [[phase angle]] (<math>\alpha</math>) and the [[photometric latitude]] (<math>\varphi</math>) and the [[photometric longitude]] (<math>\lambda</math>).		I lately had the chance to test a plugin called the WooCommerce Reserving and Appointments Plugin from Tyche Softwares. It adds reserving and appointment functionality to your WordPress powered web site, and integrates properly with WooCommerce to charge a payment for these bookings.<br><br>

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	~~\text{RADF} = \frac{I}{F} = \pi~A_M~\mu_0^k~\mu^{k-1}~~
	~~</math>~~
	~~where <math>A_M</math> is~~ the ~~'''Minnaert [[albedo]]'''~~, ~~<math>k</math>~~ is ~~an empirical parameter~~, ~~<math>I</math> is the scattered [[radiance]]~~ in ~~the direction <math>~~(~~\alpha,\varphi,\lambda~~)<~~/math~~>, <~~math~~>~~\pi F</math> is~~ the ~~incident radiance~~, and
	:~~<math>~~
	~~\mu_0~~ = ~~\cos\varphi~\cos(\alpha-\lambda) ~;~~ \mu = \cos\varphi~\cos\lambda ~~~.
	</~~math>~~
	~~The phase angle is~~ the ~~angle between~~ the ~~light source~~ and ~~the observer with the object as the center.~~

	~~The assumptions made~~ are:
	* the ~~surface is illuminated~~ by ~~a distant point source.~~
	* the ~~surface is isotropic~~ and ~~flat~~.

	~~Minnaert's contribution is the introduction of the parameter~~ <~~math~~>k<~~/math~~>, ~~having a value between 0~~ and 1,~~<ref>~~http://~~articles~~.~~adsabs~~.~~harvard.edu~~/~~cgi-bin~~/~~nph-iarticle_query?1941ApJ~~....~~93..403M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf</ref> originally~~ for a ~~better interpretation of observations~~ of the ~~[[Moon]]~~. ~~In remote sensing the use of~~ this ~~function~~ is ~~referred~~ to as '~~'Minnaert topographic correction''~~, a ~~necessity when interpreting images of rough terrain~~.

	~~== References ==~~
	~~<references/>~~

	~~[[Category:Optics]]~~

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The [[Marcel Minnaert|Minnaert]] function is a [[photometry (astronomy)|photometric]] function used to interpret [[astronomical]] observations <ref>http://dx.doi.org/10.1016/S0019-1035(03)00075-7</ref><ref>http://dx.doi.org/10.1016/j.icarus.2006.05.006</ref> and [[remote sensing]] data for the [[Earth]].<ref>http://dx.doi.org/10.1080/01431160500104194</ref> This function expresses the [[radiance factor]] (RADF) as a function the [[phase angle]] (<math>\alpha</math>) and the [[photometric latitude]] (<math>\varphi</math>) and the [[photometric longitude]] (<math>\lambda</math>).

:<math>
\text{RADF} = \frac{I}{F} = \pi~A_M~\mu_0^k~\mu^{k-1}
</math>
where <math>A_M</math> is the '''Minnaert [[albedo]]''', <math>k</math> is an empirical parameter, <math>I</math> is the scattered [[radiance]] in the direction <math>(\alpha,\varphi,\lambda)</math>, <math>\pi F</math> is the incident radiance, and
:<math>
\mu_0 = \cos\varphi~\cos(\alpha-\lambda) ~;~~ \mu = \cos\varphi~\cos\lambda ~.
</math>
The phase angle is the angle between the light source and the observer with the object as the center.

The assumptions made are:
* the surface is illuminated by a distant point source.
* the surface is isotropic and flat.

Minnaert's contribution is the introduction of the parameter <math>k</math>, having a value between 0 and 1,<ref>http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1941ApJ....93..403M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf</ref> originally for a better interpretation of observations of the [[Moon]]. In remote sensing the use of this function is referred to as ''Minnaert topographic correction'', a necessity when interpreting images of rough terrain.

== References ==
<references/>

[[Category:Optics]]

Statistical coupling analysis - Revision history

140.113.15.171: /* Definition of statistical coupling energy */

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