<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2006000300008</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Randomly rough rectangular-groove surfaces with predetermined backscatter intensities]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bruce]]></surname>
<given-names><![CDATA[N.C.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional Autónoma de México Centro de Ciencias Aplicadas y Desarrollo Tecnológico ]]></institution>
<addr-line><![CDATA[D.F. ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2006</year>
</pub-date>
<volume>52</volume>
<numero>3</numero>
<fpage>246</fpage>
<lpage>254</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2006000300008&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2006000300008&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2006000300008&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[The backscattered intensity of the scattered light in rectangular-grooved surfaces is used as a design parameter for randomly rough surfaces. A modified Kirchhoff method and the integral equation method are used to calculate the scattered light distribution for these designed surfaces. The results of the two calculation methods are found to show good agreement, with the Kirchhoff method slightly overestimating the double scattered intensity, perhaps due to the limitations of the geometrical shadow functions used in this method. These results show that the backscattered intensity can be controlled in this type of surface.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Se utiliza la intensidad de la retrodispersión de la luz esparcida en una superficie con zurcos de forma rectangular como parámetro de diseño de la superficie. El método de Kirchhoff modificado y el método de la ecuación integral son empleados para calcular la distribución de la luz reflejada de la superficie. Se encuentra que los resultados de los dos métodos están de acuerdo aunque el método de Kirchhoff sobre estima el esparcimiento doble, probablemente debido a las aproximaciones requeridas para las funciones de sombra geométrica utilizada. Los resultados presentados muestran que se puede controlar la intensidad en retrodispersión para este tipo de superficies.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Rough surfaces]]></kwd>
<kwd lng="en"><![CDATA[scattering]]></kwd>
<kwd lng="en"><![CDATA[Kirchhoff approximation]]></kwd>
<kwd lng="es"><![CDATA[Superficies rugosas]]></kwd>
<kwd lng="es"><![CDATA[esparcimiento]]></kwd>
<kwd lng="es"><![CDATA[aproximación de Kirchhoff]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Investigaci&oacute;n</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>Randomly rough rectangular&#150;groove surfaces with predetermined backscatter intensities</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>N.C. Bruce</b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i>Centro de Ciencias Aplicadas y Desarrollo Tecnol&oacute;gico, Universidad Nacional Aut&oacute;noma de M&eacute;xico, Circuito Exterior, Cd. Universitaria, Apartado Postal 70&#150;186, M&eacute;xico, D.F. 04510, M&eacute;xico, e&#150;mail: <a href="mailto:bruce@aleph.cinstrum.unam.mx">bruce@aleph.cinstrum.unam.mx</a></i></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">Recibido el 2 de febrero de 2006    <br>   Aceptado el 18 de abril de 2006</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">The backscattered intensity of the scattered light in rectangular&#150;grooved surfaces is used as a design parameter for randomly rough surfaces. A modified Kirchhoff method and the integral equation method are used to calculate the scattered light distribution for these designed surfaces. The results of the two calculation methods are found to show good agreement, with the Kirchhoff method slightly overestimating the double scattered intensity, perhaps due to the limitations of the geometrical shadow functions used in this method. These results show that the backscattered intensity can be controlled in this type of surface.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords: </b>Rough surfaces; scattering; Kirchhoff approximation.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">Se utiliza la intensidad de la retrodispersi&oacute;n de la luz esparcida en una superficie con zurcos de forma rectangular como par&aacute;metro de dise&ntilde;o de la superficie. El m&eacute;todo de Kirchhoff modificado y el m&eacute;todo de la ecuaci&oacute;n integral son empleados para calcular la distribuci&oacute;n de la luz reflejada de la superficie. Se encuentra que los resultados de los dos m&eacute;todos est&aacute;n de acuerdo aunque el m&eacute;todo de Kirchhoff sobre estima el esparcimiento doble, probablemente debido a las aproximaciones requeridas para las funciones de sombra geom&eacute;trica utilizada. Los resultados presentados muestran que se puede controlar la intensidad en retrodispersi&oacute;n para este tipo de superficies.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores: </b>Superficies rugosas, esparcimiento; aproximaci&oacute;n de Kirchhoff.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS: 42.25.Fx; 42.25.Mj</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v52n3/v52n3a8.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Acknowledgements</b></font></p>     <p align="justify"><font face="verdana" size="2">This work was partially supported through project IN101502 from DGAPA,UNAM.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. E. Jakeman and B.J. Hoenders, <i>Optica Acta </i><b>29</b> (1982) 1587.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318607&pid=S0035-001X200600030000800001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. R.A. Depine and D.C. Skigin, <i>J. Opt. Soc. Am. A </i><b>11</b> (1994) 2844.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318608&pid=S0035-001X200600030000800002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">3. A. Mendoza&#150;Su&aacute;rez and E. R. M&eacute;ndez <i>Applied Optics </i><b>36</b> (1997) 3521.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318609&pid=S0035-001X200600030000800003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">4. N.C. Bruce, <i>Applied Optics </i><b>42 </b>(2003) 2398.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318610&pid=S0035-001X200600030000800004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">5. N.C. Bruce, <i>Applied Optics </i><b>44 </b>(2005) 784.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318611&pid=S0035-001X200600030000800005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">6. R. C. Hollins and D.L. Jordan, <i>Optica Acta </i><b>30</b> (1983) 1725.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318612&pid=S0035-001X200600030000800006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">7. P.F. Gray, Optica Acta <b>25 </b>(1978) 765.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318613&pid=S0035-001X200600030000800007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">8. E.R. M&eacute;ndez and K.A. O'Donnell, <i>J. Opt. Soc. Am. A </i><b>4</b> (1987) 1194.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8318614&pid=S0035-001X200600030000800008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jakeman]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Hoenders]]></surname>
<given-names><![CDATA[B.J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optica Acta]]></source>
<year>1982</year>
<volume>29</volume>
<page-range>1587</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Depine]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Skigin]]></surname>
<given-names><![CDATA[D.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Opt. Soc. Am.]]></source>
<year>1994</year>
<volume>A 11</volume>
<page-range>2844</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mendoza-Suárez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Méndez]]></surname>
<given-names><![CDATA[E. R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied Optics]]></source>
<year>1997</year>
<volume>36</volume>
<page-range>3521</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bruce]]></surname>
<given-names><![CDATA[N.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied Optics]]></source>
<year>2003</year>
<volume>42</volume>
<page-range>2398</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bruce]]></surname>
<given-names><![CDATA[N.C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied Optics]]></source>
<year>2005</year>
<volume>44</volume>
<page-range>784</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hollins]]></surname>
<given-names><![CDATA[R. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Jordan]]></surname>
<given-names><![CDATA[D.L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optica Acta]]></source>
<year>1983</year>
<volume>30</volume>
<page-range>1725</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gray]]></surname>
<given-names><![CDATA[P.F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optica Acta]]></source>
<year>1978</year>
<volume>25</volume>
<page-range>765</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Méndez]]></surname>
<given-names><![CDATA[E.R.]]></given-names>
</name>
<name>
<surname><![CDATA[O'Donnell]]></surname>
<given-names><![CDATA[K.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Opt. Soc. Am.]]></source>
<year>1987</year>
<volume>A 4</volume>
<page-range>1194</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
