<?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>S0035-001X2007000100010</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Flatness measurement using a grazing incidence interferometer]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Alcalá Ochoa]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mendiola]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Landgrave]]></surname>
<given-names><![CDATA[J.E.A.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Centro de Investigaciones en Óptica  ]]></institution>
<addr-line><![CDATA[Leon Guanajuato]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>02</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>02</month>
<year>2007</year>
</pub-date>
<volume>53</volume>
<numero>1</numero>
<fpage>66</fpage>
<lpage>71</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2007000100010&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2007000100010&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2007000100010&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[The purpose of this work is to report results of flatness measurements using a grazing incidence interferometer. We show that this interferometer provides enough accuracy to measure nominally flat polishing tools and rough surfaces. In order to calculate the deformation of the surface under test, an interferogram is analyzed with digital imaging techniques based on Fourier methods. We found experimentally that the entire surface topography can be recovered with errors lower than ~ 0.6 &#956;m, or ~ &#955;eqv/6, where &#955;eqv = 3.6441 &#956;m is the equivalent wavelength of the interferometer.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[El propósito de este trabajo es el de reportar resultados de medición de planicidad usando un interferómetro de incidencia oblicua. Se muestra que este interferómetro proporciona la exactitud necesaria para medir la planicidad de herramientas de pulido y superficies rugosas. Con el propósito de evaluar las irregularidades de la superficie bajo prueba, el interferograma obtenido se analiza con técnicas de procesamiento digital de imágenes basadas en métodos de Fourier. Encontramos experimentalmente que la superficie completa se puede medir con errores menores a ~ 0.6 &#956;m, o ~ &#955;eqv/6, donde &#955;eqv = 3.6441 &#956;m es la longitud de onda equivalente del interferómetro.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Optical testing]]></kwd>
<kwd lng="en"><![CDATA[interferometry]]></kwd>
<kwd lng="en"><![CDATA[fringe analysis]]></kwd>
<kwd lng="en"><![CDATA[laser applications]]></kwd>
<kwd lng="es"><![CDATA[Pruebas ópticas]]></kwd>
<kwd lng="es"><![CDATA[intereferometría]]></kwd>
<kwd lng="es"><![CDATA[análisis de franjas]]></kwd>
<kwd lng="es"><![CDATA[aplicaciones de láseres]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Instrumentaci&oacute;n</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>Flatness measurement using a grazing incidence interferometer</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>N. Alcal&aacute; Ochoa*, G. Mendiola, and J.E.A. Landgrave</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 Investigaciones en &Oacute;ptica, Apartado Postal 1&#150;948, Leon, Guanajuato, M&eacute;xico, *e&#150;mail: <a href="mailto:alon@foton.cio.mx" target="_blank">alon@foton.cio.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 12 de agosto de 2005    <br>   Aceptado el 30 de noviembre 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 purpose of this work is to report results of flatness measurements using a grazing incidence interferometer. We show that this interferometer provides enough accuracy to measure nominally flat polishing tools and rough surfaces. In order to calculate the deformation of the surface under test, an interferogram is analyzed with digital imaging techniques based on Fourier methods. We found experimentally that the entire surface topography can be recovered with errors lower than ~ 0.6<i> &mu;</i>m, or ~ <i>&lambda;<sub>eqv</sub></i>/6, where <i><i>&lambda;<sub>eqv</sub></i> </i>= 3.6441 <i>&mu;</i>m is the equivalent wavelength of the interferometer.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords:  </b>Optical testing; interferometry; fringe analysis; laser applications.</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">El prop&oacute;sito de este trabajo es el de reportar resultados de medici&oacute;n de planicidad usando un interfer&oacute;metro de incidencia oblicua. Se muestra que este interfer&oacute;metro proporciona la exactitud necesaria para medir la planicidad de herramientas de pulido y superficies rugosas. Con el prop&oacute;sito de evaluar las irregularidades de la superficie bajo prueba, el interferograma obtenido se analiza con t&eacute;cnicas de procesamiento digital de im&aacute;genes basadas en m&eacute;todos de Fourier. Encontramos experimentalmente que la superficie completa se puede medir con errores menores a ~ 0.6<i> &mu;</i>m, o ~ <i>&lambda;<sub>eqv</sub>/6, </i>donde <i><i>&lambda;</i><sub>eqv</sub> </i>= 3.6441 <i>&mu;</i>m es la longitud de onda equivalente del interfer&oacute;metro.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores: </b>Pruebas &oacute;pticas; intereferometr&iacute;a; an&aacute;lisis de franjas; aplicaciones de l&aacute;seres. </font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS: 06.20.&#150;f; 42.62.&#150;b; 42.62.Cf</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/v53n1/v53n1a10.pdf">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">The authors would like to express their gratitude to the members of the optical and the mechanical workshops at CIO, in particular to Carlos Perez Santos, and also to Zacar&iacute;as Malacara Hern&aacute;ndez, of the Optical Engineering Group, for their assistance in various tasks that were essential for the successful completion of this work.</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. M. Guti&eacute;rrez Mungu&iacute;a and E. Landgrave Manjarrez, <i>Dise&ntilde;o y fabricaci&oacute;n de un interfer&oacute;metro de incidencia oblicua, </i>MSc Thesis, CIO (1992).</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=8330751&pid=S0035-001X200700010001000001&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. N. Alcal&aacute; Ochoa, G. Mendiola, E. Landgrave Manjarrez, and J.C. S&aacute;nchez Roldan, <i>Cuantificaci&oacute;n de planicidad de objetos usando un interfer&oacute;metro de incidencia oblicua, </i>Tech. Rep., CIO (2001).</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=8330752&pid=S0035-001X200700010001000002&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. The cemented doublets of the GII were corrected for spherical aberration and coma for &#955; = 0.6328 <i>&#956;</i>m.</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=8330753&pid=S0035-001X200700010001000003&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. K.H. 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Commun. </i><b>117</b> (1995) 213. </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=8330756&pid=S0035-001X200700010001000006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify"><font face="verdana" size="2">7. By the variance of a function <i>f(x, y) </i>we shall mean</font></p>     <p align="justify"><font face="verdana" size="2"><img src="/img/revistas/rmf/v53n1/a10f1.jpg"></font></p>     <p align="justify"><font face="verdana" size="2">where the bar denotes average over the domain of the function <i>f(x,y), </i>denoted here by D, and</font></p>     <p align="justify"><font face="verdana" size="2"><img src="/img/revistas/rmf/v53n1/a10f2.jpg"></font></p>     <p align="justify"><font face="verdana" size="2">is the area of D. In our case, <i>A </i>is clearly the area under inspection.</font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">8. K. Creath, "Temporal Phase Measurement Methods", in <i>Interferogram Analysis, </i>D.W. Robinson and G.T. Reid, Eds. (IOP Publishing, Bristol, UK, 1993) Chap. 4.</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=8330762&pid=S0035-001X200700010001000007&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">9. N. Alcal&aacute; Ochoa, J.L. Marroquin, and A. D&aacute;vila, <i>Opt. Commun. </i><b>163</b> (1999) 15.</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=8330763&pid=S0035-001X200700010001000008&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">10. This expression for <i>&#968;(x, y) </i>can be derived as we do in the case of interference in thin films. See, for instance, M. Born and E. Wolf, <i>Principles of Optics, 6<sup>th</sup> </i>(corrected) ed. (Pergamon, Oxford, 1984) Chap. 7, p. 286.</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=8330764&pid=S0035-001X200700010001000009&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">11. Wyko is a trademark. The Wyko interferometer is a Fizeau, phase&#150;stepping, digital interferometer, used to test plane and spherical specular surfaces in an optical workshop.</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=8330765&pid=S0035-001X200700010001000010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
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