Measurement of roughness based on the Talbot effect in reflection from rough surfaces
In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the lig...
Gespeichert in:
Veröffentlicht in: | Applied Optics 2015-06, Vol.54 (16), p.5210-5215 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 5215 |
---|---|
container_issue | 16 |
container_start_page | 5210 |
container_title | Applied Optics |
container_volume | 54 |
creator | Dashtdar, Masoomeh Mohammadzade, Ali Hosseini-Saber, S Mohammad-Ali |
description | In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface. If the argument of the height difference function is larger than twice the surface correlation length, the height difference function is constant for different spatial frequencies. Therefore, the square wave is reproduced with smaller contrast. The surface roughness can be obtained by measuring the contrast at different incident angles. It is also shown that the contrast measurements in both reflection and transmission, provide the refractive index of transparent samples with a rough surface. In experimental studies, the roughness of three metal standard rough surfaces are determined at different angles of incidence. Also, the refractive index of a sheet glass with a rough surface is obtained. The results are quite consistent. |
doi_str_mv | 10.1364/ao.54.005210 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1808101108</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1698022526</sourcerecordid><originalsourceid>FETCH-LOGICAL-c460t-42f8b9eb217ce0d5ccc562b64e945fd5ad46b565ea8d70431df63e9220f95e953</originalsourceid><addsrcrecordid>eNqFkD1PwzAQhi0EoqWwMSOPDKT469x4rBBfUlGXdrYc50yDkrjEycC_J6iFlenudM890r2EXHM251KrexfnoOaMgeDshEwFB8gk13BKpowxmWkjYUIuUvoYJ1BmcU4mQnMjdA5Tsn1Dl4YOG2x7GgPt4vC-azElWriEJY0t7XdIN64uYk8xBPQ9rVraYajHthr3oYvN4Y6OpuA8pktyFlyd8OpYZ2T79Lh5eMlW6-fXh-Uq80qzPlMi5IXBQvCFR1aC9x60KLRCoyCU4EqlC9CALi8XTEleBi3RCMGCATQgZ-T24N138XPA1NumSh7r2rUYh2R5znLOOGf5_6g2ORMChB7RuwPqu5jS-Kndd1Xjui_Lmf3J3C7XFpQ9ZD7iN0fzUDRY_sG_IctvlLB78A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1698022526</pqid></control><display><type>article</type><title>Measurement of roughness based on the Talbot effect in reflection from rough surfaces</title><source>Alma/SFX Local Collection</source><source>Optica Publishing Group Journals</source><creator>Dashtdar, Masoomeh ; Mohammadzade, Ali ; Hosseini-Saber, S Mohammad-Ali</creator><creatorcontrib>Dashtdar, Masoomeh ; Mohammadzade, Ali ; Hosseini-Saber, S Mohammad-Ali</creatorcontrib><description>In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface. If the argument of the height difference function is larger than twice the surface correlation length, the height difference function is constant for different spatial frequencies. Therefore, the square wave is reproduced with smaller contrast. The surface roughness can be obtained by measuring the contrast at different incident angles. It is also shown that the contrast measurements in both reflection and transmission, provide the refractive index of transparent samples with a rough surface. In experimental studies, the roughness of three metal standard rough surfaces are determined at different angles of incidence. Also, the refractive index of a sheet glass with a rough surface is obtained. The results are quite consistent.</description><identifier>ISSN: 0003-6935</identifier><identifier>ISSN: 1559-128X</identifier><identifier>EISSN: 2155-3165</identifier><identifier>EISSN: 1539-4522</identifier><identifier>DOI: 10.1364/ao.54.005210</identifier><identifier>PMID: 26192685</identifier><language>eng</language><publisher>United States</publisher><subject>Angle of incidence ; Coefficients ; Luminous intensity ; Reflection ; Refractive index ; Refractivity ; Roughness ; Talbot effect</subject><ispartof>Applied Optics, 2015-06, Vol.54 (16), p.5210-5215</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c460t-42f8b9eb217ce0d5ccc562b64e945fd5ad46b565ea8d70431df63e9220f95e953</citedby><cites>FETCH-LOGICAL-c460t-42f8b9eb217ce0d5ccc562b64e945fd5ad46b565ea8d70431df63e9220f95e953</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26192685$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Dashtdar, Masoomeh</creatorcontrib><creatorcontrib>Mohammadzade, Ali</creatorcontrib><creatorcontrib>Hosseini-Saber, S Mohammad-Ali</creatorcontrib><title>Measurement of roughness based on the Talbot effect in reflection from rough surfaces</title><title>Applied Optics</title><addtitle>Appl Opt</addtitle><description>In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface. If the argument of the height difference function is larger than twice the surface correlation length, the height difference function is constant for different spatial frequencies. Therefore, the square wave is reproduced with smaller contrast. The surface roughness can be obtained by measuring the contrast at different incident angles. It is also shown that the contrast measurements in both reflection and transmission, provide the refractive index of transparent samples with a rough surface. In experimental studies, the roughness of three metal standard rough surfaces are determined at different angles of incidence. Also, the refractive index of a sheet glass with a rough surface is obtained. The results are quite consistent.</description><subject>Angle of incidence</subject><subject>Coefficients</subject><subject>Luminous intensity</subject><subject>Reflection</subject><subject>Refractive index</subject><subject>Refractivity</subject><subject>Roughness</subject><subject>Talbot effect</subject><issn>0003-6935</issn><issn>1559-128X</issn><issn>2155-3165</issn><issn>1539-4522</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNqFkD1PwzAQhi0EoqWwMSOPDKT469x4rBBfUlGXdrYc50yDkrjEycC_J6iFlenudM890r2EXHM251KrexfnoOaMgeDshEwFB8gk13BKpowxmWkjYUIuUvoYJ1BmcU4mQnMjdA5Tsn1Dl4YOG2x7GgPt4vC-azElWriEJY0t7XdIN64uYk8xBPQ9rVraYajHthr3oYvN4Y6OpuA8pktyFlyd8OpYZ2T79Lh5eMlW6-fXh-Uq80qzPlMi5IXBQvCFR1aC9x60KLRCoyCU4EqlC9CALi8XTEleBi3RCMGCATQgZ-T24N138XPA1NumSh7r2rUYh2R5znLOOGf5_6g2ORMChB7RuwPqu5jS-Kndd1Xjui_Lmf3J3C7XFpQ9ZD7iN0fzUDRY_sG_IctvlLB78A</recordid><startdate>20150601</startdate><enddate>20150601</enddate><creator>Dashtdar, Masoomeh</creator><creator>Mohammadzade, Ali</creator><creator>Hosseini-Saber, S Mohammad-Ali</creator><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20150601</creationdate><title>Measurement of roughness based on the Talbot effect in reflection from rough surfaces</title><author>Dashtdar, Masoomeh ; Mohammadzade, Ali ; Hosseini-Saber, S Mohammad-Ali</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c460t-42f8b9eb217ce0d5ccc562b64e945fd5ad46b565ea8d70431df63e9220f95e953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Angle of incidence</topic><topic>Coefficients</topic><topic>Luminous intensity</topic><topic>Reflection</topic><topic>Refractive index</topic><topic>Refractivity</topic><topic>Roughness</topic><topic>Talbot effect</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dashtdar, Masoomeh</creatorcontrib><creatorcontrib>Mohammadzade, Ali</creatorcontrib><creatorcontrib>Hosseini-Saber, S Mohammad-Ali</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</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><jtitle>Applied Optics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dashtdar, Masoomeh</au><au>Mohammadzade, Ali</au><au>Hosseini-Saber, S Mohammad-Ali</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Measurement of roughness based on the Talbot effect in reflection from rough surfaces</atitle><jtitle>Applied Optics</jtitle><addtitle>Appl Opt</addtitle><date>2015-06-01</date><risdate>2015</risdate><volume>54</volume><issue>16</issue><spage>5210</spage><epage>5215</epage><pages>5210-5215</pages><issn>0003-6935</issn><issn>1559-128X</issn><eissn>2155-3165</eissn><eissn>1539-4522</eissn><abstract>In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface. If the argument of the height difference function is larger than twice the surface correlation length, the height difference function is constant for different spatial frequencies. Therefore, the square wave is reproduced with smaller contrast. The surface roughness can be obtained by measuring the contrast at different incident angles. It is also shown that the contrast measurements in both reflection and transmission, provide the refractive index of transparent samples with a rough surface. In experimental studies, the roughness of three metal standard rough surfaces are determined at different angles of incidence. Also, the refractive index of a sheet glass with a rough surface is obtained. The results are quite consistent.</abstract><cop>United States</cop><pmid>26192685</pmid><doi>10.1364/ao.54.005210</doi><tpages>6</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0003-6935 |
ispartof | Applied Optics, 2015-06, Vol.54 (16), p.5210-5215 |
issn | 0003-6935 1559-128X 2155-3165 1539-4522 |
language | eng |
recordid | cdi_proquest_miscellaneous_1808101108 |
source | Alma/SFX Local Collection; Optica Publishing Group Journals |
subjects | Angle of incidence Coefficients Luminous intensity Reflection Refractive index Refractivity Roughness Talbot effect |
title | Measurement of roughness based on the Talbot effect in reflection from rough surfaces |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T14%3A56%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Measurement%20of%20roughness%20based%20on%20the%20Talbot%20effect%20in%20reflection%20from%20rough%20surfaces&rft.jtitle=Applied%20Optics&rft.au=Dashtdar,%20Masoomeh&rft.date=2015-06-01&rft.volume=54&rft.issue=16&rft.spage=5210&rft.epage=5215&rft.pages=5210-5215&rft.issn=0003-6935&rft.eissn=2155-3165&rft_id=info:doi/10.1364/ao.54.005210&rft_dat=%3Cproquest_cross%3E1698022526%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1698022526&rft_id=info:pmid/26192685&rfr_iscdi=true |