An enhanced HPIV configuration for flow measurement through thick distorting windows
Identifieur interne : 000417 ( Istex/Corpus ); précédent : 000416; suivant : 000418An enhanced HPIV configuration for flow measurement through thick distorting windows
Auteurs : R D Alcock ; C P Garner ; N A Halliwell ; J M CouplandSource :
- Measurement Science and Technology [ 0957-0233 ] ; 2004.
Abstract
This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.
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DOI: 10.1088/0957-0233/15/4/004
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title><author><name sortKey="Alcock, R D" sort="Alcock, R D" uniqKey="Alcock R" first="R D" last="Alcock">R D Alcock</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Garner, C P" sort="Garner, C P" uniqKey="Garner C" first="C P" last="Garner">C P Garner</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Halliwell, N A" sort="Halliwell, N A" uniqKey="Halliwell N" first="N A" last="Halliwell">N A Halliwell</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Coupland, J M" sort="Coupland, J M" uniqKey="Coupland J" first="J M" last="Coupland">J M Coupland</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:0E55D563F327F1316CDDF98E4415656ABF7AC90E</idno><date when="2004" year="2004">2004</date><idno type="doi">10.1088/0957-0233/15/4/004</idno><idno type="url">https://api.istex.fr/document/0E55D563F327F1316CDDF98E4415656ABF7AC90E/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000417</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">An enhanced HPIV configuration for flow measurement through thick distorting windows</title><author><name sortKey="Alcock, R D" sort="Alcock, R D" uniqKey="Alcock R" first="R D" last="Alcock">R D Alcock</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Garner, C P" sort="Garner, C P" uniqKey="Garner C" first="C P" last="Garner">C P Garner</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Halliwell, N A" sort="Halliwell, N A" uniqKey="Halliwell N" first="N A" last="Halliwell">N A Halliwell</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author><author><name sortKey="Coupland, J M" sort="Coupland, J M" uniqKey="Coupland J" first="J M" last="Coupland">J M Coupland</name><affiliation><mods:affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Measurement Science and Technology</title><title level="j" type="abbrev">Meas. 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Technol.</title><idno type="ISSN">0957-0233</idno><idno type="eISSN">1361-6501</idno><imprint><publisher>Institute of Physics Publishing</publisher><date type="published" when="2004">2004</date><biblScope unit="volume">15</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="631">631</biblScope><biblScope unit="page" to="638">638</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint><idno type="ISSN">0957-0233</idno></series><idno type="istex">0E55D563F327F1316CDDF98E4415656ABF7AC90E</idno><idno type="DOI">10.1088/0957-0233/15/4/004</idno><idno type="PII">S0957-0233(04)66429-0</idno><idno type="articleID">166429</idno><idno type="articleNumber">004</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0957-0233</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>R D Alcock</name><affiliations><json:string>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</json:string></affiliations></json:item><json:item><name>C P Garner</name><affiliations><json:string>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</json:string></affiliations></json:item><json:item><name>N A Halliwell</name><affiliations><json:string>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</json:string></affiliations></json:item><json:item><name>J M Coupland</name><affiliations><json:string>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>fluid dynamics instrumentation</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>holographic particle image velocimetry</value></json:item></subject><language><json:string>eng</json:string></language><abstract>This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.</abstract><qualityIndicators><score>5.72</score><pdfVersion>1.3</pdfVersion><pdfPageSize>595 x 842 pts (A4)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>2</keywordCount><abstractCharCount>850</abstractCharCount><pdfWordCount>4172</pdfWordCount><pdfCharCount>24962</pdfCharCount><pdfPageCount>8</pdfPageCount><abstractWordCount>129</abstractWordCount></qualityIndicators><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title><genre.original><json:string>paper</json:string></genre.original><pii><json:string>S0957-0233(04)66429-0</json:string></pii><genre><json:string>research-article</json:string></genre><host><volume>15</volume><publisherId><json:string>MST</json:string></publisherId><pages><total>8</total><last>638</last><first>631</first></pages><issn><json:string>0957-0233</json:string></issn><issue>4</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1361-6501</json:string></eissn><title>Measurement Science and Technology</title></host><publicationDate>2004</publicationDate><copyrightDate>2004</copyrightDate><doi><json:string>10.1088/0957-0233/15/4/004</json:string></doi><id>0E55D563F327F1316CDDF98E4415656ABF7AC90E</id><fulltext><json:item><original>true</original><mimetype>application/pdf</mimetype><extension>pdf</extension><uri>https://api.istex.fr/document/0E55D563F327F1316CDDF98E4415656ABF7AC90E/fulltext/pdf</uri></json:item><json:item><original>false</original><mimetype>application/zip</mimetype><extension>zip</extension><uri>https://api.istex.fr/document/0E55D563F327F1316CDDF98E4415656ABF7AC90E/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/0E55D563F327F1316CDDF98E4415656ABF7AC90E/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">An enhanced HPIV configuration for flow measurement through thick distorting windows</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Institute of Physics Publishing</publisher><availability><p>IOP</p></availability><date>2004</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">An enhanced HPIV configuration for flow measurement through thick distorting windows</title><author><persName><forename type="first">R D</forename><surname>Alcock</surname></persName><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation></author><author><persName><forename type="first">C P</forename><surname>Garner</surname></persName><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation></author><author><persName><forename type="first">N A</forename><surname>Halliwell</surname></persName><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation></author><author><persName><forename type="first">J M</forename><surname>Coupland</surname></persName><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation></author></analytic><monogr><title level="j">Measurement Science and Technology</title><title level="j" type="abbrev">Meas. Sci. Technol.</title><idno type="pISSN">0957-0233</idno><idno type="eISSN">1361-6501</idno><imprint><publisher>Institute of Physics Publishing</publisher><date type="published" when="2004"></date><biblScope unit="volume">15</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="631">631</biblScope><biblScope unit="page" to="638">638</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint></monogr><idno type="istex">0E55D563F327F1316CDDF98E4415656ABF7AC90E</idno><idno type="DOI">10.1088/0957-0233/15/4/004</idno><idno type="PII">S0957-0233(04)66429-0</idno><idno type="articleID">166429</idno><idno type="articleNumber">004</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2004</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.</p></abstract><textClass><keywords scheme="keyword"><list><head>keywords</head><item><term>fluid dynamics instrumentation</term></item><item><term>holographic particle image velocimetry</term></item></list></keywords></textClass><textClass><classCode scheme="">47.80.v</classCode><classCode scheme="">06.30.Gv</classCode><classCode scheme="">42.40.i</classCode></textClass></profileDesc><revisionDesc><change when="2004">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/0E55D563F327F1316CDDF98E4415656ABF7AC90E/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_4_6.dtd" name="istex:docType"></istex:docType><istex:document><article artid="mst166429"><article-metadata><jnl-data jnlid="mst"><jnl-fullname>Measurement Science and Technology</jnl-fullname><jnl-abbreviation>Meas. Sci. Technol.</jnl-abbreviation><jnl-shortname>MST</jnl-shortname><jnl-issn>0957-0233</jnl-issn><jnl-coden>MSTCEP</jnl-coden><jnl-imprint>Institute of Physics Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/MST</jnl-web-address></jnl-data><volume-data><year-publication>2004</year-publication><volume-number>15</volume-number></volume-data><issue-data><issue-number>4</issue-number><coverdate>April 2004</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper" artnum="004">4</type-number><article-number>166429</article-number><first-page>631</first-page><last-page>638</last-page><length>8</length><pii>S0957-0233(04)66429-0</pii><doi>10.1088/0957-0233/15/4/004</doi><copyright>2004 IOP Publishing Ltd</copyright><ccc>0957-0233/04/040631+08$30.00</ccc><printed>Printed in the UK</printed><features colour="none" mmedia="no" suppdata="no"></features></article-data></article-metadata><header><title-group><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title><short-title>An enhanced HPIV configuration for flow measurement through thick distorting windows</short-title><ej-title>An enhanced HPIV configuration for flow measurement through thick distorting windows</ej-title></title-group><author-group><author address="mst166429ad1"><first-names>R D</first-names><second-name>Alcock</second-name></author><author address="mst166429ad1"><first-names>C P</first-names><second-name>Garner</second-name></author><author address="mst166429ad1"><first-names>N A</first-names><second-name>Halliwell</second-name></author><author address="mst166429ad1"><first-names>J M</first-names><second-name>Coupland</second-name></author></author-group><address-group><address id="mst166429ad1" showid="no"><orgname>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University</orgname>, Loughborough, Leicestershire, LE11 3TU, <country>UK</country></address></address-group><history received="17 July 2003" finalform="16 January 2004" online="19 March 2004"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.</p></abstract></abstract-group><classifications><class-codes scheme="pacs"><code>47.80.+v</code><code>06.30.Gv</code><code>42.40.−i</code></class-codes><keywords print="yes"><keyword>fluid dynamics instrumentation</keyword><keyword>holographic particle image velocimetry</keyword></keywords></classifications></header><body numbering="bysection"><sec-level1 id="mst166429s1" label="1"><heading>Introduction</heading><p indent="no">The analysis of the double exposure holographic recordings of seeded flow by correlation of the complex amplitude was originally proposed by Coupland and Halliwell [<cite linkend="mst166429bib01">1</cite>] as a means of making three-component (3C) velocity measurements throughout a three-dimensional flow field. This holographic particle image velocimetry (HPIV) technique was further enhanced using the method of optical conjugate reconstruction [<cite linkend="mst166429bib02">2</cite>] allowing an image shift to be encoded into the hologram. Furthermore, by utilizing a scanning fibre probe to determine the region of interest within the flow, OCR has the practical advantage of reconstructing the recorded particle images at a fixed point in space.</p><p>In its original form, the OCR technique was based upon a reflection hologram geometry that was placed in close proximity to the flow to be measured, increasing the numerical aperture (NA) to give high resolution 3C measurements. However, the reflection geometry required a holographic optical element (HOE) to correct for distortion introduced by the window, and the aperture of the reconstructed wavefront was partially obstructed by the fibre probe, reducing the signal to noise ratio of the process. In fact, neither the HOE nor the reflection geometry are fundamental requirements of OCR, and for this reason, the OCR holographic geometry has been simplified to a large extent as follows.</p><p>An enhanced OCR geometry applied to the problem of measuring fluid flows within a diesel engine is shown in figure <figref linkend="mst166429fig01">1</figref>. A double exposure transmission hologram is orientated so that two collimated reference beams enter from the same side as the scattered light from particles suspended in the flow. The flow is contained behind two thick concentric cylindrical windows, the inner cylinder encapsulating the combustion chamber and reciprocating with the piston. It is worth noting that since the window geometry changes with crankshaft angle, a separate HOE would be necessary if the original reflection geometry OCR were to be used.
<figure id="mst166429fig01"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig01.eps" width="20.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig01.jpg"></graphic-file></graphic><caption id="mst166429fc01" label="Figure 1"><p indent="no">Diesel engine HPIV optical system. (<italic>a</italic>) Recording set-up. (<italic>b</italic>) Replay of hologram in a surrogate engine.</p></caption></figure></p><p>Reconstruction of the developed hologram takes place using a single mode optical fibre probe positioned at the desired particle location as shown in figure <figref linkend="mst166429fig01" override="yes">1(<italic>b</italic>)</figref>. The transmission hologram effectively reconstructs multiple images of the two reference beams, which by virtue of the OCR method are focused by the Fourier transform lens to form pairs of shifted images in and around the (sampling) pinhole aperture. These images correspond to the particles located in the fibre probe region at the time of each exposure [<cite linkend="mst166429bib02">2</cite>]. In this way, the fibre probe determines where (relative to the hologram) measurements are made, and the size of the aperture and numerical aperture of the hologram weight the effect of light scattered by particles in the flow field, hence determining the effective measurement volume.</p><p>The process by which particle displacement was originally determined from the measurement of OCR particle images is quite complex, resulting in a linear mapping of image and particle displacement as a function of probe position [<cite linkend="mst166429bib03">3</cite>]. In the present case, with no HOE, it is clear that account must be taken of the distortion of the scattered field introduced by the window. For this reason, the analysis method has been reconsidered from first principles as outlined below.</p><p>The fundamental aim of the analysis procedure is to calculate the 3D correlation of the optical field scattered by a group of particles that were in a region of interest within the fluid at the times of each exposure. It is shown elsewhere [<cite linkend="mst166429bib04">4</cite>], that the 3D auto-correlation of an optical field <bold>U</bold>(<underline><italic>r</italic></underline>) is given by
<display-eqn id="mst166429ueq01" number="no" eqnalign="center"></display-eqn>where <italic>P</italic>(<underline><italic>k</italic></underline>) is the power spectral density expressed in this notation as a function of the wave vector <underline><italic>k</italic></underline> with orthogonal components of <italic>k<sub>x</sub></italic>, <italic>k<sub>y</sub></italic> and <italic>k<sub>z</sub></italic> and magnitude |<italic>k</italic>| = 1/λ. The power spectral density is defined in terms of the plane wave spectrum <bold>S</bold>(<underline><italic>k</italic></underline>) as, <italic>P</italic>(<underline><italic>k</italic></underline>) = ∣ <bold>S</bold>(<underline><italic>k</italic></underline>)∣<sup>2</sup>, which is subsequently related to the optical field by
<display-eqn id="mst166429ueq02" number="no" eqnalign="center"></display-eqn></p><p>For the case of HPIV using OCR we obtain an optical field that (locally) is the sum of two identical but shifted optical fields corresponding to the first and second exposure images. In this case it is straightforward to show that [<cite linkend="mst166429bib04">4</cite>],
<display-eqn id="mst166429ueq03" number="no" eqnalign="center"></display-eqn>where <italic>P</italic><sub>1</sub>(<underline><italic>k</italic></underline>) is the power spectral density resulting from the first exposure, <underline><italic>s</italic></underline> is the displacement vector and ϕ is a phase constant. It can be seen that the power spectral density of the double exposure field is a real function corresponding to the power spectral density of the first exposure multiplied by cosinusoidal fringes according to the displacement.</p><p>In terms of ray optics the power spectral density can be considered as the power radiated in the far-field component defined by a ray propagating in the direction of the wave vector <underline><italic>k</italic></underline>. In the absence of any windows the plane wave components of the scattered field would propagate to infinity with no deviation. However, it is clear that thick optical windows cause significant deviation of these components as illustrated in figure <figref linkend="mst166429fig02">2</figref>. It can be seen that rays propagating in the same direction (with identical wave vectors), but from particles in two different locations, are deflected by different amounts by the thick cylindrical window shown, and, arrive at different positions on the CCD array. The problem is, therefore, to determine the mapping between each wave vector and its corresponding image at a given position on the CCD array as a function of probe position. We will refer to this mapping as the <italic>k</italic>-space mapping and is determined using ray tracing as outlined in the following section.
<figure id="mst166429fig02"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig02.eps" width="20.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig02.jpg"></graphic-file></graphic><caption id="mst166429fc02" label="Figure 2"><p indent="no">Ray tracing of distortions introduced by the thick window geometry.</p></caption></figure></p></sec-level1><sec-level1 id="mst166429s2" label="2"><heading>Calculation of <italic><underline>k</underline></italic>-space mapping</heading><p indent="no">Consider a ray emanating from a particle at position <underline><italic>r</italic></underline><sub>0</sub> with normalized wave vector <inline-eqn></inline-eqn> within the fluid flow. The propagation of the ray with distance, <italic>d</italic>, can be described as
<display-eqn id="mst166429ueq04" number="no" eqnalign="center"></display-eqn></p><p>Suppose that the flow is encapsulated by one or more thick windows, and that each window surface can be modelled as a quadric function <italic>F</italic>(<italic>x</italic>, <italic>y</italic>, <italic>z</italic>) in rectangular coordinates such that [<cite linkend="mst166429bib05">5</cite>],
<display-eqn id="mst166429ueq05" lines="multiline" number="no" eqnalign="left"></display-eqn>where α<sub><italic>i</italic></sub> are constants that define the surface. It is straightforward to prove that the ray will intersect with the first surface after travelling a distance <italic>d</italic><sub>1</sub> equal to the minimum positive route of
<display-eqn id="mst166429ueq06" number="no" eqnalign="center"></display-eqn>where the coefficients in terms of the respective orthogonal components of <inline-eqn></inline-eqn> and <underline><italic>r</italic></underline><sub>0</sub> are [<cite linkend="mst166429bib05">5</cite>],
<display-eqn id="mst166429ueq07" number="no" eqnalign="center"></display-eqn><display-eqn id="mst166429ueq08" number="no" eqnalign="center"></display-eqn>and
<display-eqn id="mst166429ueq09" lines="multiline" number="no" eqnalign="left"></display-eqn></p><p>The intersect location <underline><italic>r</italic></underline><sub><italic>i</italic></sub> is thus calculated as
<display-eqn id="mst166429ueq10" number="no" eqnalign="center"></display-eqn></p><p>Once the intersect location has been calculated, the ray will undergo refraction at the interface. Finally the unit wave vector <inline-eqn></inline-eqn> of the refracted wave can be calculated using [<cite linkend="mst166429bib05">5</cite>]
<display-eqn id="mst166429ueq11" number="no" eqnalign="center"></display-eqn>where η is the ratio of refractive indices of the incident and transmission media, and the unit normal vector to the surface is <inline-eqn></inline-eqn> where <underline><italic>n</italic></underline> has components given by
<display-eqn id="mst166429ueq12" number="no" eqnalign="center"></display-eqn></p><p>The continuing progress of the ray is traced through other surfaces in exactly the same manner until the ray intersects with the desired surface.</p><p>In the OCR configuration shown in figure <figref linkend="mst166429fig02">2</figref>, the camera effectively records a de-magnified image of the beam reconstructed at the holographic plate—that is an image of the holographic plate projected in the <italic>y</italic>–<italic>z</italic> plane. The mapping between the camera plane and the <italic>k</italic>-space is, therefore, established by tracing rays from the scattering particle location through to the holographic plate. Having ascertained this relationship, the power spectral density can be calculated by linear interpolation [<cite linkend="mst166429bib06">6</cite>] of intensities recorded by the camera at appropriate ray (<italic>y</italic>–<italic>z</italic> plane projection) intercept locations.</p></sec-level1><sec-level1 id="mst166429s3" label="3"><heading>Experiment</heading><p indent="no">Tests of the OCR geometry have been performed using a static mock-up of an optical diesel engine, as illustrated in figure <figref linkend="mst166429fig01">1</figref>. To ascertain the overall accuracy and resolution of the technique, a single mode fibre probe has been used to simulate a single scattering particle at several different locations within the engine. These locations were:
<ordered-list id="mst166429ol1" pattern="2"><list-item id="mst166429ol1.1" marker="(i)"><p indent="no">dead centre of the 56 mm diameter bowl;</p></list-item><list-item id="mst166429ol1.2" marker="(ii)"><p indent="no">left of centre, 8 mm from the wall;</p></list-item><list-item id="mst166429ol1.3" marker="(iii)"><p indent="no">right of centre, 8 mm from the wall;</p></list-item><list-item id="mst166429ol1.4" marker="(iv)"><p indent="no">front of centre, 4 mm from the wall, close to hologram;</p></list-item><list-item id="mst166429ol1.5" marker="(v)"><p indent="no">rear of centre, 3 mm from the wall, furthest from hologram.</p></list-item></ordered-list></p><p>Double exposure holograms were taken at these positions using the geometry shown in figure <figref linkend="mst166429fig01" override="yes">1(<italic>a</italic>)</figref>. A CrystaLaser GLC-050-S 50mW Nd-YAG operating at 532 nm was divided approximately equally between the reference beam and the fibre probe. Between exposures an optical wedge was inserted to deflect the reference beam by an angle of 2″ during the second exposure providing an image shift.</p><p>Replay of the holograms was performed using the same glassware and fibre probe arrangement shown schematically in figure <figref linkend="mst166429fig01" override="yes">1(<italic>b</italic>)</figref>. The fibre probe was placed at the position where the exposures were taken. The illuminated hologram reconstructs the reference beams which were then focused by a diffraction limited (<italic>f</italic> = 100 mm, NA = 0.2) doublet lens through a 100 µm pinhole to mask out light recorded from other particles thereby restricting the measurement volume. A second lens (Pentax <italic>f</italic> = 16 mm <italic>f</italic>/1.4 C-Mount camera lens) was then used to image the cross-spectrum onto a PixelLINK PLA-633 MegaPixel CMOS camera.</p><p>A computer program written in MATLAB was subsequently used to calculate the particles displacement. The algorithm proceeded as follows:
<ordered-list id="mst166429ol2" pattern="2"><list-item id="mst166429ol2.1" marker="(i)"><p indent="no">The distorted power spectral density recorded by CCD camera is digitized at a specified probe position.</p></list-item><list-item id="mst166429ol2.2" marker="(ii)"><p indent="no">The CCD pixel to <italic>k</italic>-space mapping is determined and the power spectral density is determined on a regular grid in <italic>k</italic>-space.</p></list-item><list-item id="mst166429ol2.3" marker="(iii)"><p indent="no">The 3D fast Fourier transform (FFT) is computed to give the 3D auto-correlation.</p></list-item><list-item id="mst166429ol2.4" marker="(iv)"><p indent="no">The position of the most significant peak is determined by centroid analysis.</p></list-item></ordered-list></p><p>Following this procedure statistical analysis of particle displacement was performed, calculating the mean and standard deviation of results obtained for several holograms.</p></sec-level1><sec-level1 id="mst166429s4" label="4"><heading>Results</heading><p indent="no">Two sets of holograms were recorded using the set-up described. In the first set, six double exposure holograms were recorded for each of the five probe positions without moving the probe between exposures. The particle (probe) displacements calculated from these holograms allow the resolution and accuracy of particle displacement measurement and the overall spatial resolution of the HPIV technique to be estimated. In the second set of holograms, a motorized micro-positioning stage was used to move the probe set distances in the <italic>x</italic>, <italic>y</italic> and <italic>z</italic> directions. This has allowed the accuracy of the HPIV system to be estimated as a function of position in the combustion chamber.</p><p>For the purpose of illustrating the <italic>k</italic>-space mapping described, some additional power spectral density images have been obtained for three different particle positions and are shown in figure <figref linkend="mst166429fig03">3</figref>. In these cases the optical wedge was not used and as such the holograms have identical reference beams and no image shift is present. The respective power spectral density images calculated using the ray trace mapping are shown in figure <figref linkend="mst166429fig04">4</figref>.
<figure id="mst166429fig03" width="page"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig03.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig03.jpg"></graphic-file></graphic><caption id="mst166429fc03" label="Figure 3"><p indent="no">Fringe data recorded from static HPIV experiments. (<italic>a</italic>) Dead centre of the bowl. (<italic>b</italic>) Front centre, 4 mm from the wall. (<italic>c</italic>) Left of centre, 8 mm from the wall.</p></caption></figure><figure id="mst166429fig04" width="page"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig04.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig04.jpg"></graphic-file></graphic><caption id="mst166429fc04" label="Figure 4"><p indent="no">Removal of optical distortion from fringes. (<italic>a</italic>) Dead centre of the bowl. (<italic>b</italic>) Front centre, 4 mm from the wall. (<italic>c</italic>) Left of centre, 8 mm from the wall.</p></caption></figure></p><p>It can be seen that in general particle displacements along the <italic>x</italic> direction give rise to vertical (<italic>y</italic> direction) fringes on the camera; however these fringes are not parallel and vary significantly in pitch according to the position of the particle. Vertical (<italic>y</italic>-axis) particle displacements, on the other hand, give rise to horizontal fringes having in general a lower spatial frequency than those resulting from the corresponding <italic>x</italic>-axis displacements. Displacements in the <italic>z</italic> direction towards the plate gives rise to bull's eye fringes, which are of course distorted by the thick window. It is clear from the calculated power spectral density images shown in figure <figref linkend="mst166429fig04">4</figref>, that the distortions introduced by the thick window optical geometry can be removed. Furthermore, it can be seen that the fringe pitch for similar displacements in the <italic>x</italic> and <italic>y</italic> directions have been rendered the same independent of the location of the scattering particle in the engine bowl.</p><sec-level2 id="mst166429s4-1" label="4.1"><heading>Measurement resolution</heading><p indent="no">A specimen set of holograms was recorded for five different probe positions within the engine bowl. In total, 30 holograms were taken equally divided between the five probe positions keeping the probe rigidly steady to within 50 nm (measured interferometrically) during and between the exposures. These holograms have been used to establish the overall experimental resolution and dynamic range of the technique applied to a diesel engine bowl.</p><p>Table <tabref linkend="mst166429tab01">1</tabref> shows the mean and standard deviation particle displacements calculated using the ray tracing particle displacement algorithm described. Note that because the probe did not move during exposures, the measured values of Δ<italic>x</italic>, Δ<italic>y</italic> and Δ<italic>z</italic> would ideally be zero at all locations. The overall trends for <italic>x</italic>-, <italic>y</italic>- and <italic>z</italic>-axis resolutions are however as follows:
<itemized-list id="mst166429il1"><list-item id="mst166429il1.1" marker="•"><p indent="no"><italic>x axis</italic>: For particles measured close to the <italic>y</italic>–<italic>z</italic> plane, the particle displacement can be measured reliably to within about ±50 nm. To the left and right of the cell however an offset error is observed systematic with the probe position, and this is combined with an increase in the observed measurement error. It is thought that this is due to holographic film shrinkage since the modulation frequency of these replayed holograms is slightly shifted in comparison with those observed for the <italic>z</italic>-axis displacement holograms (front, dead centre and rear holograms.) The overall experimental error for <italic>x</italic>-axis displacements including systematic error is therefore about 630 nm. Making the assumption that systematic errors can be modelled and compensated for, it is possible to minimize this measurement error to be better than 250 nm.</p></list-item><list-item id="mst166429il1.2" marker="•"><p indent="no"><italic>y axis</italic>: All displacements can be measured to within an error of about 150 nm, irrespective of any systematic error due to probe position. What is notable, however, is that the experimental error is smallest on particle displacements measured at the front of the bowl nearest to the hologram, and is at its largest at the rear of the bowl. This result is in line with the numerical aperture recorded by the hologram being highest for particles at the front of the bowl.</p></list-item><list-item id="mst166429il1.3" marker="•"><p indent="no"><italic>z axis</italic>: The best resolution is observed for particles located at the front of the engine bowl, giving an error of 320 nm. This, again, is due to the large numerical aperture of the hologram for this position. An offset is observed in the mean displacement values, and this seems to be systematic, varying with probe position. The <italic>z</italic> displacement offset error is probably due to a slight wave front curvature introduced by the optical wedge. Without any correction for this offset, the particle displacements along the <italic>z</italic> axis can be measured to within an error of 1.3 µm. Since this offset is systematic with position, this value falls to about 600 nm once compensations have been applied.</p></list-item></itemized-list><table id="mst166429tab01" frame="topbot" indent="no"><caption id="mst166429tc01" label="Table 1"><p indent="no">Stationary probe mean and standard deviation particle displacements.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><thead><row><entry>Probe position</entry><entry>Δ<italic>x</italic> (std) (nm)</entry><entry>Δ<italic>y</italic> (std) (nm)</entry><entry>Δ<italic>z</italic> (std) (nm)</entry></row></thead><tbody><row><entry>Dead centre</entry><entry> 45 (48)</entry><entry>−51 (98)</entry><entry>−706 (587)</entry></row><row><entry>Front</entry><entry> 12 (43)</entry><entry> 45 (44)</entry><entry>−855 (320)</entry></row><row><entry>Rear</entry><entry> 60 (34)</entry><entry>−165 (141)</entry><entry>−1926 (691)</entry></row><row><entry>Left</entry><entry>−609 (252)</entry><entry>−185 (114)</entry><entry>−1567 (569)</entry></row><row><entry>Right</entry><entry> 1155 (229)</entry><entry>−169 (52)</entry><entry>−3857 (1007)</entry></row><row><entry>All positions</entry><entry> 133 (630)</entry><entry>−105 (152)</entry><entry>−1782 (1340)</entry></row></tbody><tfoot>Values within parentheses denote standard deviation.</tfoot></tgroup></table></p><p>The volume element resolution of the technique has also been estimated from the zero displacement holograms. This has been done by scanning the measurement probe along the <italic>x</italic>, <italic>y</italic> and <italic>z</italic> axes across the original probe position monitoring the overall intensity of the reconstructed fringes. The normalized results obtained are shown in figures <figref linkend="mst166429fig05" range="mst166429fig05,mst166429fig06,mst166429fig07">5–7</figref>, for scans across the <italic>x</italic> axis, <italic>y</italic> axis and <italic>z</italic> axis, respectively. The extent of a volume element (a ‘voxel’) at a particular probe position is defined here as the distance between half intensity maxima for the respective <italic>x</italic>, <italic>y</italic> and <italic>z</italic> scans.
<figure id="mst166429fig05"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig05.eps" width="20.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig05.jpg"></graphic-file></graphic><caption id="mst166429fc05" label="Figure 5"><p indent="no">Net intensity of fringes for the scan of the probe along the <italic>x</italic>-axis.</p></caption></figure><figure id="mst166429fig06"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig06.eps" width="20.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig06.jpg"></graphic-file></graphic><caption id="mst166429fc06" label="Figure 6"><p indent="no">Net intensity of fringes for the scan of the probe along the <italic>y</italic>-axis.</p></caption></figure><figure id="mst166429fig07"><graphic><graphic-file version="print" format="EPS" filename="images/mst166429fig07.eps" width="20.5pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/mst166429fig07.jpg"></graphic-file></graphic><caption id="mst166429fc07" label="Figure 7"><p indent="no">Net intensity of fringes for the scan of the probe along the <italic>z</italic>-axis.</p></caption></figure></p><p>Table <tabref linkend="mst166429tab02">2</tabref> shows the voxel dimensions obtained through this analysis. In summary, voxel dimensions measured are between 50 µm and 100 µm in the <italic>x</italic> direction, about 100 µm in the <italic>y</italic> direction and between 300 µm and 1100 µm in the <italic>z</italic> direction. The smallest volume elements (thus representing the highest measurement density) were found to be towards the front of the bowl nearest the hologram, whereas the largest voxels were found to be towards the rear of the engine bowl. In total it has been estimated that for a 50 mm diameter engine bowl, 12 mm high, there are about half a million independent vectors that can be measured using the system assuming that it is possible for the flow volume to be sufficiently densely seeded with scattering particles.
<table id="mst166429tab02" frame="topbot"><caption id="mst166429tc02" label="Table 2"><p indent="no">Volume element (‘voxel’) resolution.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="right"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="right"></colspec><thead><row><entry>Probe position</entry><entry><italic>x</italic> (µm)</entry><entry><italic>y</italic> (µm)</entry><entry><italic>z</italic> (µm)</entry></row></thead><tbody><row><entry>Dead centre</entry><entry>70</entry><entry>100</entry><entry>660</entry></row><row><entry>Front</entry><entry>50</entry><entry>100</entry><entry>300</entry></row><row><entry>Rear</entry><entry>80</entry><entry>130</entry><entry>1100</entry></row><row><entry>Left</entry><entry>80</entry><entry>100</entry><entry>300</entry></row><row><entry>Right</entry><entry>100</entry><entry>100</entry><entry>300</entry></row></tbody></tgroup></table></p><p>The measurable upper limit of the particle displacement range can also be reasonably estimated to be approximately 1/2 that of the probe range over which correlation fringes are detectable above 50% maximum intensity. Table <tabref linkend="mst166429tab03">3</tabref> shows the ranges calculated from this for the engine bowl geometry used. In general, it has been found that the maximum measurable displacement in the <italic>x</italic> and <italic>y</italic> directions is of the order of ±20 µm, and ±75 µm in the <italic>z</italic> direction. A broad trend that can be seen is that the front of the bowl has the smallest <italic>x</italic> and <italic>z</italic> displacement range, whereas the rear of the bowl has the largest <italic>z</italic> range.
<table id="mst166429tab03" frame="topbot"><caption id="mst166429tc03" label="Table 3"><p indent="no">Maximum measurable displacement range.</p></caption><tgroup cols="4"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><thead><row><entry>Probe position</entry><entry>Δ<italic>x</italic> range (µm)</entry><entry>Δ<italic>y</italic> range (µm)</entry><entry>Δ<italic>z</italic> range (µm)</entry></row></thead><tbody><row><entry>Dead centre</entry><entry>35 (±17.5)</entry><entry>50 (±25)</entry><entry>330 (±165)</entry></row><row><entry>Front</entry><entry>25 (±12.5)</entry><entry>50 (±25)</entry><entry>150 (±75)</entry></row><row><entry>Rear</entry><entry>40 (±20)</entry><entry>65 (±32.5)</entry><entry>550 (±250)</entry></row><row><entry>Left</entry><entry>40 (±20)</entry><entry>50 (±25)</entry><entry>150 (±75)</entry></row><row><entry>Right</entry><entry>40 (±20)</entry><entry>50 (±25)</entry><entry>150 (±75)</entry></row></tbody></tgroup></table></p><p>It is important to note, however, that other factors can limit the displacement range of the system, and that the values given are for particles that are effectively static during the exposures. No account has been made here for velocity gradients during the exposures.</p><p>Additional factors that can influence the displacement range include the size of the aperture used in the replay rig (100 µm in this case), the numerical aperture and resolution of the CCD camera system, and the maximum practical size of the fast Fourier transform that can be used in the particle displacement algorithm. Some care has been taken to optimize the latter two of these, so that the aperture size has become the dominant factor in influencing the displacement range. A larger displacement range may well be possible by increasing the aperture size, but at some point either the numerical aperture, resolution of the camera or the FFT size will limit the actual range accomplished. At the same time a larger aperture will give rise to an increase in voxel size, and so there is a trade-off between volume element resolution and displacement range.</p><p>Using the statistical data collected, the dynamic range of the technique has been calculated for different positions within the engine bowl. This is presented in table <tabref linkend="mst166429tab04">4</tabref> using <italic>x</italic> direction error values of ±100 nm for <italic>y</italic>–<italic>z</italic> plane measurements, and ±250 nm for left and right extremes. For <italic>y</italic> and <italic>z</italic> axes error values of ±150 nm and ±600 nm have been used, respectively. These values assume that adequate compensation can be made for systematic errors. In addition, the displacement ranges have been restricted to be the same in all three axes, the range being the maximum achievable simultaneously in all the directions for the respective position within the bowl (in this case the <italic>x</italic>-axis ranges have effectively been used.) In general, the dynamic ranges have been found to be of the order of 1:100 or more for <italic>x</italic> and <italic>y</italic> displacements, whereas in the <italic>z</italic> direction it falls to approximately 1:30.
<table id="mst166429tab04" frame="topbot"><caption id="mst166429tc04" label="Table 4"><p indent="no">Dynamic range.</p></caption><tgroup cols="5"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><thead><row><entry>Probe position</entry><entry>Particle displacement range (µm)</entry><entry>Δ<italic>x</italic> range</entry><entry>Δ<italic>y</italic> range</entry><entry>Δ<italic>z</italic> range</entry></row></thead><tbody><row><entry>Dead centre</entry><entry>35</entry><entry>1:175</entry><entry>1:115</entry><entry>1:29</entry></row><row><entry>Front</entry><entry>25</entry><entry>1:125</entry><entry>1:82</entry><entry>1:21</entry></row><row><entry>Rear</entry><entry>40</entry><entry>1:200</entry><entry>1:130</entry><entry>1:33</entry></row><row><entry>Left</entry><entry>40</entry><entry>1:80</entry><entry>1:130</entry><entry>1:33</entry></row><row><entry>Right</entry><entry>40</entry><entry>1:80</entry><entry>1:130</entry><entry>1:33</entry></row></tbody></tgroup></table></p></sec-level2><sec-level2 id="mst166429s4-2" label="4.2"><heading>Measurement accuracy</heading><p indent="no">A second set of holograms has been taken in which a motorized AeroTech ACCUDEX micro-positioning stage was used to move the probe set distances. Six different independent movements have been recorded, specifically ±10 µm along the <italic>x</italic> axis, ±10 µm along the <italic>y</italic> axis and ±50 µm along the <italic>z</italic> axis. These translations have been verified using a Hewlett Packard 5519A Laser position measurement system to be accurate to within 0.2 µm. The fringes obtained using these holograms have been processed using the ray tracing particle displacement algorithm described, and are shown in table <tabref linkend="mst166429tab05">5</tabref>. Two simple compensations have been made to minimize systematic error, namely:
<ordered-list id="mst166429ol3" pattern="2"><list-item id="mst166429ol3.1" marker="(i)"><p indent="no">The zero displacement (mean) offsets shown in table <tabref linkend="mst166429tab01">1</tabref> have been subtracted from the calculated <italic>y</italic>- and <italic>z</italic>- direction displacements for the respective probe positions measured.</p></list-item><list-item id="mst166429ol3.2" marker="(ii)"><p indent="no">For left and right probe positions, compensation has been made for the shift in the modulation frequency for these holograms, by appropriately adjusting the demodulation shift used in the computer algorithm for these holograms.</p></list-item></ordered-list><table id="mst166429tab05" frame="topbot" indent="no"><caption id="mst166429tc05" label="Table 5"><p indent="no">Measurements of probe displacements (compensated).</p></caption><tgroup cols="7"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="char" char="."></colspec><colspec colnum="3" colname="col3" align="char" char="."></colspec><colspec colnum="4" colname="col4" align="char" char="."></colspec><colspec colnum="5" colname="col5" align="char" char="."></colspec><colspec colnum="6" colname="col6" align="char" char="."></colspec><colspec colnum="7" colname="col7" align="char" char="."></colspec><thead><row><entry>Probe position</entry><entry>Δ<italic>x</italic> = 10 µm</entry><entry>Δ<italic>x</italic> = −10 µm</entry><entry>Δ<italic>y</italic> = 10 µm</entry><entry>Δ<italic>y</italic> = −10 µm</entry><entry>Δ<italic>z</italic> = 50 µm</entry><entry>Δ<italic>z</italic> = −50 µm</entry></row></thead><tbody><row><entry>Dead centre</entry><entry>10.120</entry><entry>−10.071</entry><entry>9.825</entry><entry>−9.834</entry><entry>49.092</entry><entry>−50.877</entry></row><row><entry>Front</entry><entry>9.503</entry><entry>−9.910</entry><entry>9.834</entry><entry>−9.505</entry><entry>49.783</entry><entry>−51.292</entry></row><row><entry>Rear</entry><entry>10.410</entry><entry>−10.335</entry><entry>9.725</entry><entry>−10.369</entry><entry>48.608</entry><entry>−51.062</entry></row><row><entry>Left</entry><entry>10.330</entry><entry>−10.302</entry><entry>10.386</entry><entry>−10.409</entry><entry>47.292</entry><entry>−51.935</entry></row><row><entry>Right</entry><entry>10.456</entry><entry>−10.278</entry><entry>9.724</entry><entry>−10.616</entry><entry>52.014</entry><entry>−48.987</entry></row><row><entry>Worst error</entry><entry>0.497 (5%)</entry><entry>0.335 (3.4%)</entry><entry>0.386 (3.8%)</entry><entry>0.616 (6.1%)</entry><entry>2.708 (5.4%)</entry><entry>1.935 (3.9%)</entry></row><row><entry> recorded</entry><entry></entry><entry></entry><entry></entry><entry></entry><entry></entry><entry></entry></row><row><entry>STD</entry><entry>0.381</entry><entry>0.169</entry><entry>0.256</entry><entry>0.454</entry><entry>1.742</entry><entry>1.030</entry></row></tbody></tgroup></table></p><p>Clearly the results in table <tabref linkend="mst166429tab05">5</tabref> show that the particle displacements calculated agree with the respective translation stage displacements introduced, typically to within an error of about 3%. The standard deviations recorded are 0.28 µm for displacements in the <italic>x</italic> direction, 0.37 µm in the <italic>y</italic> direction and 1.55 µm along the <italic>z</italic> axis. These are larger than those suggested by the static results, but can be entirely accounted for when the 0.2 µm accuracy of the translation stage and the optical stability of the system over the extended period between exposures are taken into consideration.</p></sec-level2></sec-level1><sec-level1 id="mst166429s5" label="5"><heading>Conclusions</heading><p indent="no">This paper has discussed the application of HPIV using OCR to the measurement of flow velocities within the deep-bowl combustion chamber of a diesel engine. A new OCR method that uses a transmission hologram and dispenses with the need to produce an HOE has been developed. The technique uses ray tracing analysis to give a mapping between the scattered wave vectors and position on the CCD camera, thereby removing the effect of window distortion. Particle displacements are subsequently calculated through three-dimensional Fourier analysis of the power spectral density calculated.</p><p>Static experiments have been performed in an optical diesel engine comprising two thick walled concentric glass cylinders. Seeding particles within the flow encapsulated by the cylinders has been simulated using a stabilized single mode fibre arrangement as a scattering source located at several key positions within the measurement volume. Holograms of this geometry have been taken using a frequency doubled Nd-YAG laser, and the same fibre point source has been used to replay the holograms utilizing the OCR approach.</p><p>Results from these experiments have shown that the particle displacement can be calculated to within an error of about 150 nm in the directions parallel to the holographic plate, and to about a wavelength along the orthogonal axis to these using the technique. This is a function of the particle position within the engine, and is affected by the respective numerical aperture of the hologram. By scanning the fibre probe across the measurement volume, the size of the measurement region has been established to be about 100 µm in extent in the lateral directions, and between 300 µm and 1100 µm in the orthogonal direction, depending on the distance from the plate. In a similar manner, the maximum displacement range for the system in the correlation field has been estimated to be about ±25 µm in the lateral directions, and ±75 µm in the orthogonal direction. This gives an overall dynamic range of approximately 1:100 for the technique.</p></sec-level1></body><back><references><heading>References</heading><reference-list type="numeric"><journal-ref id="mst166429bib01"><authors><au><second-name>Coupland</second-name><first-names>J M</first-names></au><au><second-name>Halliwell</second-name><first-names>N A</first-names></au></authors><year>1992</year><art-title>Particle image velocimetry: three dimensional fluid velocimetry measurements using holographic recording and optical correlation</art-title><jnl-title>Appl. Opt.</jnl-title><volume>131</volume><pages>1005–7</pages></journal-ref><journal-ref id="mst166429bib02"><authors><au><second-name>Barnhart</second-name><first-names>D H</first-names></au><au><second-name>Halliwell</second-name><first-names>N A</first-names></au><au><second-name>Coupland</second-name><first-names>J M</first-names></au></authors><year>2002</year><art-title>Object conjugate reconstruction (OCR): a step forward in holographic metrology</art-title><jnl-title>Proc. R. Soc.</jnl-title><part>A</part><volume>458</volume><pages>2083–97</pages></journal-ref><journal-ref id="mst166429bib03"><authors><au><second-name>Barnhart</second-name><first-names>D</first-names></au><au><second-name>Halliwell</second-name><first-names>N A</first-names></au><au><second-name>Coupland</second-name><first-names>J M</first-names></au></authors><year>2000</year><art-title>Holographic particle image velocimetry: analysis using a conjugate reconstruction geometry</art-title><jnl-title>Opt. Laser Technol.</jnl-title><volume>32</volume><pages>527–33</pages></journal-ref><journal-ref id="mst166429bib04"><authors><au><second-name>Yang</second-name><first-names>H</first-names></au><au><second-name>Halliwell</second-name><first-names>N A</first-names></au><au><second-name>Coupland</second-name><first-names>J M</first-names></au></authors><year>2003</year><art-title>A digital shearing method for 3-D data extraction in HPIV</art-title><jnl-title>Appl. Opt.</jnl-title><volume>42</volume><pages>6458–64</pages></journal-ref><book-ref id="mst166429bib05"><authors><au><second-name>Glassner</second-name><first-names>A S</first-names></au></authors><year>1989</year><book-title>An Introduction to Ray Tracing</book-title><publication><place>London</place><publisher>Academic</publisher></publication></book-ref><book-ref id="mst166429bib06"><authors><au><second-name>Press</second-name><first-names>W H</first-names></au><au><second-name>Teukolsky</second-name><first-names>S A</first-names></au><au><second-name>Vetterling</second-name><first-names>W T</first-names></au><au><second-name>Flannery</second-name><first-names>B P</first-names></au></authors><year>1992</year><book-title>Numerical Recipes in FORTRAN—The Art of Scientific Computing</book-title><edition>2nd edn</edition><publication><place>Cambridge</place><publisher>Cambridge University Press</publisher></publication><pages>pp 116–7</pages></book-ref></reference-list></references></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title></titleInfo><titleInfo type="abbreviated"><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title></titleInfo><titleInfo type="alternative"><title>An enhanced HPIV configuration for flow measurement through thick distorting windows</title></titleInfo><name type="personal"><namePart type="given">R D</namePart><namePart type="family">Alcock</namePart><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">C P</namePart><namePart type="family">Garner</namePart><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">N A</namePart><namePart type="family">Halliwell</namePart><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J M</namePart><namePart type="family">Coupland</namePart><affiliation>Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper"></genre><originInfo><publisher>Institute of Physics Publishing</publisher><dateIssued encoding="w3cdtf">2004</dateIssued><copyrightDate encoding="w3cdtf">2004</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><note type="production">Printed in the UK</note></physicalDescription><abstract>This paper reports on a new holographic particle image velocimetry configuration and analysis procedure that can be used to measure particle displacement through thick distorting windows. The technique builds upon the scanning fibre probe based object conjugate reconstruction geometry; however it avoids the requirement of using a holographic optical element to correct for window distortion of the beams. Removal of the distortion is instead accomplished by using a ray trace mapping between the wave vectors scattered by the particles at the time of each exposure and those measured by the interrogation system. The technique is ideally suited to the study of flow structure within the combustion chamber of a diesel engine, and preliminary experimental results that attempt to assess the accuracy of the technique in this situation are presented.</abstract><subject><genre>keywords</genre><topic>fluid dynamics instrumentation</topic><topic>holographic particle image velocimetry</topic></subject><classification authority="pacs">47.80.v</classification><classification authority="pacs">06.30.Gv</classification><classification authority="pacs">42.40.i</classification><relatedItem type="host"><titleInfo><title>Measurement Science and Technology</title></titleInfo><titleInfo type="abbreviated"><title>Meas. Sci. Technol.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0957-0233</identifier><identifier type="eISSN">1361-6501</identifier><identifier type="PublisherID">MST</identifier><identifier type="CODEN">MSTCEP</identifier><identifier type="URL">stacks.iop.org/MST</identifier><part><date>2004</date><detail type="volume"><caption>vol.</caption><number>15</number></detail><detail type="issue"><caption>no.</caption><number>4</number></detail><extent unit="pages"><start>631</start><end>638</end><total>8</total></extent></part></relatedItem><identifier type="istex">0E55D563F327F1316CDDF98E4415656ABF7AC90E</identifier><identifier type="DOI">10.1088/0957-0233/15/4/004</identifier><identifier type="PII">S0957-0233(04)66429-0</identifier><identifier type="articleID">166429</identifier><identifier type="articleNumber">004</identifier><accessCondition type="use and reproduction" contentType="copyright">2004 IOP Publishing Ltd</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>2004 IOP Publishing Ltd</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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