<?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>2007-8196</journal-id>
<journal-title><![CDATA[Epistemus (Sonora)]]></journal-title>
<abbrev-journal-title><![CDATA[Epistemus (Sonora)]]></abbrev-journal-title>
<issn>2007-8196</issn>
<publisher>
<publisher-name><![CDATA[Universidad de Sonora, División de Ingeniería]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-81962024000200203</article-id>
<article-id pub-id-type="doi">10.36790/epistemus.v18i37.367</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Holografía y matemática]]></article-title>
<article-title xml:lang="en"><![CDATA[Holography and Mathematics]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González González]]></surname>
<given-names><![CDATA[Rodrigo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González Valenzuela]]></surname>
<given-names><![CDATA[Amy Gabriela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Sonora Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Hermosillo Sonora]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Sonora Departamento de Investigación en Física ]]></institution>
<addr-line><![CDATA[Hermosillo Sonora]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<volume>18</volume>
<numero>37</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-81962024000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-81962024000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-81962024000200203&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo general de este escrito es analizar matemáticamente el proceso físico de reproducción de un holograma de transmisión, con el fin de contrastar resultados directamente observables respecto a aproximaciones obtenidas de forma teórica. Por una parte, al observar un holograma se localiza sobre este una región en la que se reproduce fielmente un objeto tridimensional impreso con una técnica fotográfica especial llamada holografía. Por otra parte, al aplicar un modelo matemático simple para describir este hecho, por medio de la conocida ecuación de onda clásica -con solución dada en forma de Kirchhoff, la cual se analiza con un método asintótico de análisis complejo- se obtiene un resultado aproximado que permite realizar una conclusión congruente sobre este proceso particular.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The general objective of this paper is to analyze mathematically the physical process of reproduction of a transmission hologram, in order to contrast directly observable results with approximations obtained theoretically. On one hand, when observing a hologram, a region is located on it where a three-dimensional object is faithfully reproduced using a special photographic technique called holography. On the other hand, by applying a simple mathematical model to describe this fact, through the well-known classical wave equation -with a solution given in Kirchhoff form, which is analyzed using an asymptotic method of complex analysis- an approximate result is obtained that allows for a congruent conclusion about this particular process.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Holograma]]></kwd>
<kwd lng="es"><![CDATA[luz láser]]></kwd>
<kwd lng="es"><![CDATA[ecuación de onda]]></kwd>
<kwd lng="es"><![CDATA[solución de Kirchhoff]]></kwd>
<kwd lng="es"><![CDATA[fase estacionaria]]></kwd>
<kwd lng="en"><![CDATA[Hologram]]></kwd>
<kwd lng="en"><![CDATA[laser light]]></kwd>
<kwd lng="en"><![CDATA[wave equation]]></kwd>
<kwd lng="en"><![CDATA[Kirchhoff solution]]></kwd>
<kwd lng="en"><![CDATA[stationary phase]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Garabedian]]></surname>
<given-names><![CDATA[P.R]]></given-names>
</name>
</person-group>
<source><![CDATA[Partial Differential Equations]]></source>
<year>1986</year>
<publisher-name><![CDATA[Chelsea Publishing Co]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Saxby]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<source><![CDATA[Practical Holography]]></source>
<year>2004</year>
<publisher-loc><![CDATA[Boca Raton, Florida ]]></publisher-loc>
<publisher-name><![CDATA[IoP Publishing]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[H.M]]></given-names>
</name>
</person-group>
<source><![CDATA[Principles of Holography]]></source>
<year>1979</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Flores-Espinoza]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
<name>
<surname><![CDATA[González-González]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Temas y Problemas Selectos de Análisis Matemático. Teoremas de Existencia y Aplicaciones]]></source>
<year>2022</year>
<publisher-loc><![CDATA[Hermosillo, Sonora ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Sonora]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Marsden]]></surname>
<given-names><![CDATA[J.E]]></given-names>
</name>
</person-group>
<source><![CDATA[Elementary Classical Analysis]]></source>
<year>1974</year>
<publisher-loc><![CDATA[San Francisco ]]></publisher-loc>
<publisher-name><![CDATA[W.H Freeman and Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[M.G]]></given-names>
</name>
<name>
<surname><![CDATA[González-González]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Notas de Cálculo Vectorial]]></source>
<year>2019</year>
<publisher-loc><![CDATA[Hermosillo, Sonora ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Sonora]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Arfken]]></surname>
<given-names><![CDATA[G.B]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Methods for Physicists]]></source>
<year>1985</year>
<edition>3.a</edition>
<publisher-loc><![CDATA[Orlando ]]></publisher-loc>
<publisher-name><![CDATA[cademic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Courant]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
<name>
<surname><![CDATA[Hilbert]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<source><![CDATA[Methods of Mathematical Physics: Vol. II. Partial Differential Equations]]></source>
<year>1965</year>
<publisher-name><![CDATA[Interscience Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dettman]]></surname>
<given-names><![CDATA[J.W]]></given-names>
</name>
</person-group>
<source><![CDATA[Applied Complex Variables]]></source>
<year>1984</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Dover Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Erdelyi]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<source><![CDATA[Asymptotic Expansions]]></source>
<year>1956</year>
<publisher-name><![CDATA[Dover Publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Friedman]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<source><![CDATA[Lectures on Applications-Oriented Mathematics]]></source>
<year>1991</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Keener]]></surname>
<given-names><![CDATA[J.P]]></given-names>
</name>
</person-group>
<source><![CDATA[Principles of Applied Mathematics. Transformation and Approximation]]></source>
<year>1988</year>
<publisher-name><![CDATA[Addison-Wesley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mihaylova]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<source><![CDATA[Holography-Basic Principles and Contemporary Applications]]></source>
<year>2013</year>
<publisher-name><![CDATA[InTech DTP]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stakgold]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
</person-group>
<source><![CDATA[Green's Functions and Boundary Value Problems.]]></source>
<year>1979</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
