Two-dimensional Legendre polynomials as a basis for interpolation of data to optimize the solution of the irradiance transport equation analyzed as a boundary problem on surfaces testing
In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs' surf...
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| Veröffentlicht in: | Applied optics (2004) 2019-06, Vol.58 (18), p.5057-5066 |
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| container_title | Applied optics (2004) |
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| creator | Arriaga-Hernández, J A Cuevas-Otahola, B Oliveros-Oliveros, J Morín-Castillo, M |
| description | In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs' surface to the data in order to obtain the wavefront surface (
(
,
) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (
(
,
)). |
| doi_str_mv | 10.1364/AO.58.005057 |
| format | Article |
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(
,
) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (
(
,
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(
,
) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (
(
,
)).</description><subject>Differential equations</subject><subject>Interpolation</subject><subject>Irradiance</subject><subject>Polynomials</subject><subject>Sharpness</subject><subject>Transport equations</subject><subject>Wave fronts</subject><issn>1559-128X</issn><issn>2155-3165</issn><issn>1539-4522</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNpdkc1rHCEYxqU0JNs0t56L0EsPna0fq6PHJfQjsLCXFHobnPE1NczoRB3K5k_rX1eX3fRQEFTen8_zvj4IvaNkTbncfN7u10KtCRFEtK_QilEhGk6leI1W9agbytTPK_Qm50dCuNjo9hJdcSoIV1yu0J_737GxfoKQfQxmxDt4gGAT4DmOhxAnb8aMTV24N9ln7GLCPhRItW5KfYOjw9YUg0vEcS5-8s-Ayy_AOY7LC3C8-5SM9SYMtZxMyHNMBcPTclIx1fzwDPbsFZdgTTrgOcV-hAlXIi_JmQEyLpCLDw9v0YWrzcHNeb9GP75-ub_93uz23-5ut7tm4FSXxg1qQzdgNPSGGEd72VraEyWs1L1updKaMEmdc9rVf5OSWu2oE0NrmZGM8Wv08aRbe3laqnc3-TzAOJoAcckdY0q1jHCmK_rhP_QxLqlOdqRqQIpqLiv16UQNKeacwHVz8lOdtqOkO2babfedUN0p04q_P4su_QT2H_wSIv8Lhc6ghg</recordid><startdate>20190620</startdate><enddate>20190620</enddate><creator>Arriaga-Hernández, J A</creator><creator>Cuevas-Otahola, B</creator><creator>Oliveros-Oliveros, J</creator><creator>Morín-Castillo, M</creator><general>Optical Society of America</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-1046-1500</orcidid><orcidid>https://orcid.org/0000-0002-9121-5917</orcidid><orcidid>https://orcid.org/0000-0001-8059-9399</orcidid><orcidid>https://orcid.org/0000-0002-1715-3631</orcidid></search><sort><creationdate>20190620</creationdate><title>Two-dimensional Legendre polynomials as a basis for interpolation of data to optimize the solution of the irradiance transport equation analyzed as a boundary problem on surfaces testing</title><author>Arriaga-Hernández, J A ; Cuevas-Otahola, B ; Oliveros-Oliveros, J ; Morín-Castillo, M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-fc8414ea9eba0af1b67d1b085d69b9768990261fff9f316661d9f1f5c7d2a6223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Differential equations</topic><topic>Interpolation</topic><topic>Irradiance</topic><topic>Polynomials</topic><topic>Sharpness</topic><topic>Transport equations</topic><topic>Wave fronts</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arriaga-Hernández, J A</creatorcontrib><creatorcontrib>Cuevas-Otahola, B</creatorcontrib><creatorcontrib>Oliveros-Oliveros, J</creatorcontrib><creatorcontrib>Morín-Castillo, M</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Applied optics (2004)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arriaga-Hernández, J A</au><au>Cuevas-Otahola, B</au><au>Oliveros-Oliveros, J</au><au>Morín-Castillo, M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-dimensional Legendre polynomials as a basis for interpolation of data to optimize the solution of the irradiance transport equation analyzed as a boundary problem on surfaces testing</atitle><jtitle>Applied optics (2004)</jtitle><addtitle>Appl Opt</addtitle><date>2019-06-20</date><risdate>2019</risdate><volume>58</volume><issue>18</issue><spage>5057</spage><epage>5066</epage><pages>5057-5066</pages><issn>1559-128X</issn><eissn>2155-3165</eissn><eissn>1539-4522</eissn><abstract>In this paper, we give a solution to the irradiance transport equation (ITE) using the two-dimensional (2D) Legendre polynomials (LPs) and an interpolator (i-LP) based on the LP. In the first place, we analyze the experimental data; subsequently, we proceed to fit the most probable 2D LPs' surface to the data in order to obtain the wavefront surface (
(
,
) of the elements under test) as a solution of the ITE differential equation associated with a boundary problem; and finally, we interpolate the resulting fitting. The interpolation is built from LP to increase the resolution and sharpness of the data. We apply the ITE to these results in order to obtain the wavefront as a nondeterministic solution that increases the resolution of the ITE as an optical test, and we compare our results regarding the obtained aberration surfaces (
(
,
)).</abstract><cop>United States</cop><pub>Optical Society of America</pub><pmid>31503836</pmid><doi>10.1364/AO.58.005057</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-1046-1500</orcidid><orcidid>https://orcid.org/0000-0002-9121-5917</orcidid><orcidid>https://orcid.org/0000-0001-8059-9399</orcidid><orcidid>https://orcid.org/0000-0002-1715-3631</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1559-128X |
| ispartof | Applied optics (2004), 2019-06, Vol.58 (18), p.5057-5066 |
| issn | 1559-128X 2155-3165 1539-4522 |
| language | eng |
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| source | Alma/SFX Local Collection; Optica Publishing Group Journals |
| subjects | Differential equations Interpolation Irradiance Polynomials Sharpness Transport equations Wave fronts |
| title | Two-dimensional Legendre polynomials as a basis for interpolation of data to optimize the solution of the irradiance transport equation analyzed as a boundary problem on surfaces testing |
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