Index: invariantview/media/invariant_help.html
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 <div class=Section1>
-<ul>
-<li><a class=section1 style='mso-outline-level:1' href="#Scattering Invariant">Scattering Invariant</a></li>
-<li><a class=section1 style='mso-outline-level:1' href="#Volume Fraction">Volume Fraction</a></li>
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-<li><a class=section1 style='mso-outline-level:1'href="#How to Compute Invariant?">How to Compute Invariant?</a></li>
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-<a name="Scattering Invariant" class=section1><b style='mso-bidi-font-weight:normal'>The Scattering Invariant<o:p></o:p></b></a>
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-  DrawAspect="Content" ObjectID="_1333134530">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='font-family:TimesNewRoman;mso-bidi-font-family:
-TimesNewRoman'><span style='mso-spacerun:yes'> </span></span>. This model
-independent quantity (Q*) is calculated from the scattering data can be used to
-determine the volume fraction and the specific area of the sample under
-consideration. &nbsp;These quantities&nbsp;are useful in their own right and
-can be used in&nbsp;further analysis. With this scattering invariant module
+
+<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;line-height:normal'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><b><span style='font-family:"Times New Roman","serif"'><a
+href="#invariant">Scattering Invariant</a></span></b></p>
+
+<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;line-height:normal'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><a href="#volume"><b><span style='font-family:"Times New Roman","serif"'>Volume
+Fraction</span></b></a></p>
+
+<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;line-height:normal'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><a href="#surface"><b><span style='font-family:"Times New Roman","serif"'>Specific
+Surface Area</span></b></a></p>
+
+<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;line-height:normal'><span
+style='font-family:Symbol'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><a href="#howto"><b><span style='font-family:"Times New Roman","serif"'>How
+to Compute</span></b></a></p>
+
+<p class=MsoNormal style='line-height:normal'><b><span style='font-family:"Times New Roman","serif"'>The
+scattering <a name=invariant>invariant</a> (Q*)</span></b><span
+style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>The
+scattering invariant (Q*) is a model-independent quantity that can be easily
+calculated from </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>scattering
+data. For two phase systems, the scattering invariant, Q*, is defined as the
+integral of</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'> the
+square of the wave transfer (q) multiplied by the scattering cross section over
+the full range of q. </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>Q*
+is given by the following equation, </span></p>
+
+<p class=MsoNormal style='line-height:normal'>
+
+<table cellpadding=0 cellspacing=0 align=left>
+ <tr>
+  <td width=2 height=4></td>
+ </tr>
+ <tr>
+  <td></td>
+  <td><img width=127 height=35 src="image001.gif"></td>
+ </tr>
+</table>
+
+<span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:150%'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<br clear=ALL>
+
+<p class=MsoNormal style='line-height:150%'><span style='font-family:"Times New Roman","serif"'>This
+model independent quantity (Q*) is calculated from the scattering data that can
+be used to determine the volume fraction and the specific area of the sample
+under consideration. &nbsp;These quantities&nbsp;are useful in their own right
+and can be used in&nbsp;further analysis. With this scattering invariant module
 users will also be able to determine the consistency of those properties
 between data.&nbsp; There is no real data defined from zero to infinity, there
 usually have limited range. Q* is not really computed from zero to infinity.
-Methods to deal with this limitation will be addressed.</p>
-
-<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
-margin-left:.25in;margin-bottom:.0001pt;line-height:normal'><span
-style='font-size:12.0pt;font-family:"Times New Roman"'>&nbsp;<o:p></o:p></span></p>
-
-<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;text-indent:
-22.5pt;line-height:normal'><span style='font-size:12.0pt;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<p class=ListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>The
-scattering invariant is derived as follow:<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l13 level1 lfo10;
-tab-stops:list .5in'><![if !supportLists]><span style='font-size:12.0pt;
-line-height:115%;font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
-Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>I(q)</span></i><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'> =<span
-style='mso-spacerun:yes'>  </span><i style='mso-bidi-font-style:normal'>I(q)</i>-
-background for data without background<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l8 level1 lfo11;
-tab-stops:list .5in'><![if !supportLists]><span style='font-size:12.0pt;
-line-height:115%;font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
-Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><i style='mso-bidi-font-style:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>I(q) </span></i><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>= <i
-style='mso-bidi-font-style:normal'>I(q)* scaling factor </i>, </span><span
-lang=IT style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman";
-mso-ansi-language:IT'><sub><!--[if gte vml 1]><v:shape id="_x0000_i1026"
- type="#_x0000_t75" style='width:11.25pt;height:14.25pt' o:ole="">
- <v:imagedata src="../media/image003.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1026"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026"
-  DrawAspect="Content" ObjectID="_1333134531">
- </o:OLEObject>
-</xml><![endif]--></span><i style='mso-bidi-font-style:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>I(q) = </span></i><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><span
-style='mso-spacerun:yes'> </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1027"
- type="#_x0000_t75" style='width:11.25pt;height:14.25pt' o:ole="">
- <v:imagedata src="../media/image005.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1027"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027"
-  DrawAspect="Content" ObjectID="_1333134532">
- </o:OLEObject>
-</xml><![endif]--><i style='mso-bidi-font-style:normal'>I(q)*scaling factor</i><o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l8 level1 lfo11;
-tab-stops:list .5in'><![if !supportLists]><span style='font-size:12.0pt;
-line-height:115%;font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
-Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><sub><span style='font-size:12.0pt;line-height:
-115%;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape id="_x0000_i1028"
- type="#_x0000_t75" style='width:96pt;height:26.25pt' o:ole="">
- <v:imagedata src="../media/image001.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=128 height=35
-src="../media/image047.gif" v:shapes="_x0000_i1028"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028"
-  DrawAspect="Content" ObjectID="_1333134533">
- </o:OLEObject>
-</xml><![endif]--></span></sub><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'><span style='mso-spacerun:yes'> </span><span
-class=GramE>where</span> g =q for the pinhole geometry and g =<sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1029" type="#_x0000_t75" style='width:11.25pt;height:12.75pt'
- o:ole="">
- <v:imagedata src="../media/image006.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=17
-src="../media/image049.gif" v:shapes="_x0000_i1029"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029"
-  DrawAspect="Content" ObjectID="_1333134534">
- </o:OLEObject>
-</xml><![endif]--><span class=SpellE>q<sub>v</sub></span>(the slit height) for
-the slit geometry which can be given in data or as a value.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo3'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-font-family:
-Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>Numerical approach: <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1030" type="#_x0000_t75" style='width:87pt;height:33.75pt' o:ole="">
- <v:imagedata src="../media/image008.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=116 height=45
-src="../media/image050.gif" v:shapes="_x0000_i1030"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030"
-  DrawAspect="Content" ObjectID="_1333134535">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='mso-spacerun:yes'> </span>where N = number
-of the data points, <span class=SpellE>q<sub>i</sub></span><sub> </sub>= wave transfer,
-I<sub>i</sub> = Scattering intensity at <span class=SpellE>q<sub>i</sub></span>
-, and <sub><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75"
- style='width:11.25pt;height:14.25pt' o:ole="">
- <v:imagedata src="../media/image010.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="invariant_help_files/image048.gif" v:shapes="_x0000_i1031"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031"
-  DrawAspect="Content" ObjectID="_1333134536">
- </o:OLEObject>
-</xml><![endif]--><span class=SpellE>q<sub>i</sub></span><sub> </sub><span
-style='mso-spacerun:yes'> </span>= (q<sub>i+1</sub>  q<sub>i-1</sub>)/2 (;
-note that<span style='mso-spacerun:yes'>  </span><sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1032" type="#_x0000_t75" style='width:11.25pt;height:14.25pt'
- o:ole="">
- <v:imagedata src="../media/image011.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1032"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"
-  DrawAspect="Content" ObjectID="_1333134537">
- </o:OLEObject>
-</xml><![endif]-->q<sub>0 </sub>= (q<sub>1</sub>- q<sub>0</sub>)/2<span
-style='mso-spacerun:yes'>  </span>and <sub><span
-style='mso-spacerun:yes'> </span></sub><span style='mso-spacerun:yes'> </span><sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1033" type="#_x0000_t75" style='width:11.25pt;height:14.25pt'
- o:ole="">
- <v:imagedata src="../media/image012.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1033"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033"
-  DrawAspect="Content" ObjectID="_1333134538">
- </o:OLEObject>
-</xml><![endif]--><span class=SpellE>q<sub>N</sub></span><sub> </sub><span
-style='mso-spacerun:yes'> </span>=<sub><!--[if gte vml 1]><v:shape id="_x0000_i1034"
- type="#_x0000_t75" style='width:11.25pt;height:14.25pt' o:ole="">
- <v:imagedata src="../media/image013.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1034"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"
-  DrawAspect="Content" ObjectID="_1333134539">
- </o:OLEObject>
-</xml><![endif]-->q<sub>N-1</sub> /2).<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo3'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-font-family:
-Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>Uncertainty:<span style='mso-spacerun:yes'> 
-</span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75"
- style='width:137.25pt;height:38.25pt' o:ole="">
- <v:imagedata src="../media/image014.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=183 height=51
-src="../media/image051.gif" v:shapes="_x0000_i1035"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"
-  DrawAspect="Content" ObjectID="_1333134540">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='mso-spacerun:yes'> </span>assuming that
-there is no correlation between each <sub><!--[if gte vml 1]><v:shape id="_x0000_i1036"
- type="#_x0000_t75" style='width:11.25pt;height:14.25pt' o:ole="">
- <v:imagedata src="../media/image016.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=15 height=19
-src="../media/image048.gif" v:shapes="_x0000_i1036"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"
-  DrawAspect="Content" ObjectID="_1333134541">
- </o:OLEObject>
-</xml><![endif]-->I<sub>i</sub> (uncertainty of I, say <span class=SpellE><span
-class=GramE>dy</span></span>).<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l6 level1 lfo3'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-font-family:
-Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>Higher q-region (&gt;= <span class=SpellE>qmax</span>
-of data): <o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:63.9pt;mso-add-space:auto'><span
-class=SpellE><span style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>Porod</span></span><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'> (w/o
-background term) function = C/q<sup>4</sup> will be used where the constant <span
-class=GramE>C(</span>=2<sub><!--[if gte vml 1]><v:shape id="_x0000_i1037"
- type="#_x0000_t75" style='width:24pt;height:15.75pt' o:ole="">
- <v:imagedata src="../media/image017.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=32 height=21
-src="../media/image052.gif" v:shapes="_x0000_i1037"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"
-  DrawAspect="Content" ObjectID="_1333134542">
- </o:OLEObject>
-</xml><![endif]--><span class=SpellE>S<sub>v</sub></span>) is to be found by
-fitting part of data with the range of <span class=SpellE>q<sub>N</sub></span><sub>-m</sub>
-to <span class=SpellE>q<sub>N</sub></span> (m&lt;N).<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>The
-contribution to Q<sup>*</sup> from this region is described in an explicit
-form, and thus numerical integration is not required (w/ no background is
-assumed): <o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:99.9pt;mso-add-space:auto;
-text-indent:-.25in;mso-list:l7 level1 lfo4'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>For pinhole: <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1038" type="#_x0000_t75" style='width:180pt;height:27.75pt' o:ole="">
- <v:imagedata src="../media/image019.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=240 height=37
-src="../media/image053.gif" v:shapes="_x0000_i1038"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038"
-  DrawAspect="Content" ObjectID="_1333134543">
- </o:OLEObject>
-</xml><![endif]--></sub>,<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:99.9pt;mso-add-space:auto;
-text-indent:-.25in;mso-list:l7 level1 lfo4'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>(Also numerical integration can be considered
-for this case).<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:99.9pt;mso-add-space:auto;
-text-indent:-.25in;mso-list:l7 level1 lfo4'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>For slit smear: <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1039" type="#_x0000_t75" style='width:216.75pt;height:38.25pt'
- o:ole="">
- <v:imagedata src="../media/image021.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=289 height=51
-src="../media/image054.gif" v:shapes="_x0000_i1039"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039"
-  DrawAspect="Content" ObjectID="_1333134545">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='mso-spacerun:yes'> </span>where </span><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol'>D</span><span
-class=SpellE><span style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>q<sub>v</sub></span></span><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'> is
-given in data, <span class=SpellE>q<sub>N</sub></span> = maximum q (<span
-class=SpellE>q<sub>max</sub></span>) in <span class=GramE>data<span
-style='mso-spacerun:yes'>  </span>and</span> C is obtained by the fitting data
-in larger q region as described above.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:99.9pt;mso-add-space:auto;
-text-indent:-.25in;mso-list:l7 level1 lfo4'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>Note that the number of points for fitting is to
-be given by users and should be larger than 2 from the point of <span
-class=SpellE>qmax</span>.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:.95in;mso-add-space:auto;
-text-indent:-.25in;mso-list:l12 level1 lfo5'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-font-family:
-Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>Lower q-region:<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:.95in;mso-add-space:auto'><span
-class=SpellE><span style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>Guinier</span></span><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>
-function = <span class=GramE><i style='mso-bidi-font-style:normal'>I<sub>0</sub>exp(</i></span><i
-style='mso-bidi-font-style:normal'>-R<sub>g</sub><sup>2</sup>q<sup>2</sup>/3)</i>
-where I<sub>0</sub> and <span class=SpellE>R<sub>g</sub></span> are obtained by
-fitting, similarly to the high q region above.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:1.45in;mso-add-space:auto;
-text-indent:-.25in;mso-list:l14 level1 lfo6'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>For pinhole: <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1040" type="#_x0000_t75" style='width:158.25pt;height:27.75pt'
- o:ole="">
- <v:imagedata src="../media/image023.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=211 height=37
-src="../media/image055.gif" v:shapes="_x0000_i1040"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040"
-  DrawAspect="Content" ObjectID="_1333134546">
- </o:OLEObject>
-</xml><![endif]--></sub><o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:1.45in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>Numerically<span
-style='mso-spacerun:yes'>  </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1041"
- type="#_x0000_t75" style='width:158.25pt;height:33.75pt' o:ole="">
- <v:imagedata src="../media/image025.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=211 height=45
-src="../media/image056.gif" v:shapes="_x0000_i1041"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041"
-  DrawAspect="Content" ObjectID="_1333134547">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='mso-spacerun:yes'> </span>where <span
-class=SpellE>q<sub>N</sub></span> &lt;= <span class=SpellE>q<sub>min</sub></span>
-in data points, q<sub>0</sub> will be set to 1e-04 (1/A) and N =1000(<span
-class=GramE>?,</span> linear binning?).<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:1.45in;mso-add-space:auto;
-text-indent:-.25in;mso-list:l14 level1 lfo6'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Wingdings;mso-fareast-font-family:
-Wingdings;mso-bidi-font-family:Wingdings'><span style='mso-list:Ignore'>§<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'>For slit smear: <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1042" type="#_x0000_t75" style='width:161.25pt;height:27.75pt'
- o:ole="">
- <v:imagedata src="../media/image027.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=215 height=37
-src="../media/image057.gif" v:shapes="_x0000_i1042"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042"
-  DrawAspect="Content" ObjectID="_1333134548">
- </o:OLEObject>
-</xml><![endif]--></sub><o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpLast style='margin-left:207.9pt;mso-add-space:auto'><sub><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
- id="_x0000_i1043" type="#_x0000_t75" style='width:117pt;height:36.75pt' o:ole="">
- <v:imagedata src="../media/image029.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=156 height=49
-src="../media/image058.gif" v:shapes="_x0000_i1043"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043"
-  DrawAspect="Content" ObjectID="_1333134549">
- </o:OLEObject>
-</xml><![endif]--></span></sub><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'><span style='mso-spacerun:yes'>  </span><span
-class=GramE>where</span> <span class=SpellE>q<sub>min</sub></span> is the
-smallest q value in data points.<o:p></o:p></span></p>
-
-<p class=MsoNormal><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'><span style='mso-tab-count:3'>                                    </span>(Also
-numerical integration can be considered for this case)<o:p></o:p></span></p>
-
-<p class=section1><o:p>&nbsp;</o:p></p>
-<a name="Volume Fraction" class=ListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'><b
-style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;line-height:
-115%;font-family:"Times New Roman"'>Volume <span class=GramE>Fraction<span
-style='font-weight:normal'> </span></span></span></b><span style='font-size:
-12.0pt;line-height:115%;font-family:"Times New Roman"'><sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1044" type="#_x0000_t75" style='width:9.75pt;height:15.75pt'
- o:ole="">
- <v:imagedata src="../media/image031.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=13 height=21
-src="../media/image059.gif" v:shapes="_x0000_i1044"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"
-  DrawAspect="Content" ObjectID="_1333134550">
- </o:OLEObject>
-</xml><![endif]-->: <o:p></o:p></span></a>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:27.9pt;mso-add-space:auto'><sub><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
- id="_x0000_i1045" type="#_x0000_t75" style='width:125.25pt;height:36pt' o:ole="">
- <v:imagedata src="../media/image033.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=167 height=48
-src="../media/image060.gif" v:shapes="_x0000_i1045"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045"
-  DrawAspect="Content" ObjectID="_1333134551">
- </o:OLEObject>
-</xml><![endif]--></span></sub><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'><span style='mso-spacerun:yes'>  </span><span
-class=GramE>where</span> <sub><!--[if gte vml 1]><v:shape id="_x0000_i1046"
- type="#_x0000_t75" style='width:18.75pt;height:15.75pt' o:ole="">
- <v:imagedata src="../media/image035.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=25 height=21
-src="../media/image061.gif" v:shapes="_x0000_i1046"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1046"
-  DrawAspect="Content" ObjectID="_1333134552">
- </o:OLEObject>
-</xml><![endif]-->is the SLD contrast of which value is given by users.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:27.9pt;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>Thus,<span
-style='mso-spacerun:yes'>  </span><sub><!--[if gte vml 1]><v:shape id="_x0000_i1047"
- type="#_x0000_t75" style='width:78pt;height:33.75pt' o:ole="">
- <v:imagedata src="../media/image037.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=104 height=45
-src="../media/image062.gif" v:shapes="_x0000_i1047"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047"
-  DrawAspect="Content" ObjectID="_1333134553">
- </o:OLEObject>
-</xml><![endif]--></sub><span style='mso-spacerun:yes'> </span>where 0 =&lt; A
-=&lt;1/4 in order for these values to be physically valid.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:27.9pt;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<a name="Surface Area" class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><b
-style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;line-height:
-115%;font-family:"Times New Roman"'>Specific Surface Area</span> <sub><!--[if gte vml 1]><v:shape
- id="_x0000_i1048" type="#_x0000_t75" style='width:14.25pt;height:18pt' o:ole="">
- <v:imagedata src="../media/image039.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=19 height=24
-src="../media/image063.gif" v:shapes="_x0000_i1048"><![endif]></sub><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1048"
-  DrawAspect="Content" ObjectID="_1333134554">
- </o:OLEObject>
-</xml><![endif]--></b><b style='mso-bidi-font-weight:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p></o:p></span></b></a>
-
-<p class=ListParagraphCxSpLast style='margin-left:27.9pt;mso-add-space:auto'><sub><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
- id="_x0000_i1049" type="#_x0000_t75" style='width:143.25pt;height:36pt' o:ole="">
- <v:imagedata src="../media/image041.wmz" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=191 height=48
-src="../media/image064.gif" v:shapes="_x0000_i1049"><![endif]><!--[if gte mso 9]><xml>
- <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049"
-  DrawAspect="Content" ObjectID="_1333134555">
- </o:OLEObject>
-</xml><![endif]--></span></sub><span style='font-size:12.0pt;line-height:115%;
-font-family:"Times New Roman"'><span style='mso-spacerun:yes'> </span><span
-class=GramE>where</span> A and Q<sup>*</sup> are obtained from 1) and 2), and
-the <span class=SpellE>Porod</span> constant C<sub>p</sub> is given by users. <o:p></o:p></span></p>
-
-<p class=MsoNormal style='mso-margin-top-alt:auto;line-height:normal;
-mso-outline-level:1'><span style='font-size:12.0pt;font-family:"Times New Roman";
-mso-bidi-font-weight:bold'>Definitions<o:p></o:p></span></p>
-
-<p class=MsoNormal style='margin-left:45.9pt;text-indent:-.25in;line-height:
-normal;mso-list:l3 level1 lfo8;tab-stops:list 45.9pt'><![if !supportLists]><span
-style='font-size:12.0pt;font-family:Symbol;mso-fareast-font-family:Symbol;
-mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span class=GramE><span style='font-size:12.0pt;
-font-family:"Times New Roman"'>Q&nbsp;:</span></span><span style='font-size:
-12.0pt;font-family:"Times New Roman"'> the magnitude of neutron (or X-ray) momentum
-transfer vector.<o:p></o:p></span></p>
-
-<p class=MsoNormal style='mso-margin-bottom-alt:auto;margin-left:45.9pt;
-text-indent:-.25in;line-height:normal;mso-list:l3 level1 lfo8;tab-stops:list 45.9pt'><![if !supportLists]><span
-style='font-size:12.0pt;font-family:Symbol;mso-fareast-font-family:Symbol;
-mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span class=GramE><span style='font-size:12.0pt;
-font-family:"Times New Roman"'>I(</span></span><span style='font-size:12.0pt;
-font-family:"Times New Roman"'>Q): the scattering intensity as a function of
-the momentum transfer Q.<o:p></o:p></span></p>
-
-<p class=ListParagraph style='margin-left:45.9pt;mso-add-space:auto;text-indent:
--.25in;mso-list:l3 level1 lfo8;tab-stops:list 45.9pt'><![if !supportLists]><span
-style='font-size:12.0pt;line-height:115%;font-family:Symbol;mso-fareast-font-family:
-Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'>·<span
-style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-</span></span></span><![endif]><span class=GramE><span style='font-size:12.0pt;
-line-height:115%;font-family:"Times New Roman"'>the</span></span><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>
-invariant total is the sum of the<span style='mso-spacerun:yes'> 
-</span>invariant from datas q range, invariant resulting from extrapolation at
-low q range and high q range.<o:p></o:p></span></p>
-
-<a name="How to Compute Invariant?" class=section1 style='mso-outline-level:1'><b style='mso-bidi-font-weight:
-normal'>How to Compute Invariant?<o:p></o:p></b></a>
-
-<p class=ListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><b
-style='mso-bidi-font-weight:normal'><span style='font-size:12.0pt;line-height:
-115%;font-family:"Times New Roman"'>Step1:</span></b><span style='font-size:
-12.0pt;line-height:115%;font-family:"Times New Roman"'> Load data file.<o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<p class=ListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
- id="_x0000_i1050" type="#_x0000_t75" style='width:395.25pt;height:180pt'>
- <v:imagedata src="../media/image043.png" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=527 height=240
-src="../media/image065.jpg" v:shapes="_x0000_i1050"><![endif]><o:p></o:p></span></p>
-
-<p class=ListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
-
-<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>Step2:</span></b><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'> Select
-loaded data from a plot panel by highlighting that it until its color turns
-yellow. Then right click on that the data and selects the option Compute
-Invariant. The application automatically computes the invariant value if the
-data loaded is valid.</span></p>
-
-<p class=MsoNormal><o:p>&nbsp;</o:p></p>
-
-<p class=MsoNormal><o:p>&nbsp;</o:p></p>
-
-<p class=MsoNormal><o:p>&nbsp;</o:p></p>
-
-<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75"
- style='width:431.25pt;height:262.5pt'>
- <v:imagedata src="../media/image045.png" o:title=""/>
-</v:shape><![endif]--><![if !vml]><img width=575 height=350
-src="../media/image066.jpg" v:shapes="_x0000_i1051"><![endif]></p>
-
-<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
-style='font-size:12.0pt;line-height:115%;font-family:"Times New Roman"'>More
-options</span></b><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'>:<o:p></o:p></span></p>
-
-<p class=MsoNormal><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'>To compute the volume, the user must enter a numerical value
-for the contrast.<o:p></o:p></span></p>
-
-<p class=MsoNormal><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'>To compute the surface area, the user must enter numerical
-values for contrast and <span class=SpellE>Porod</span> constant.<o:p></o:p></span></p>
-
-<p class=MsoNormal><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'>The user can enable extrapolation with check buttons
-available and change options necessary for computations.<o:p></o:p></span></p>
-
-<p class=MsoNormal><span style='font-size:12.0pt;line-height:115%;font-family:
-"Times New Roman"'>A <b style='mso-bidi-font-weight:normal'>detail</b> button
-is also available to explain how the total value of the invariant is computed.</span></p>
+Our maximum q range is 1e-5 ~ 10 (1/A). The lower and/or higher q range than
+data given can be extrapolated by fitting some data nearby.</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>The
+scattering invariant is computed as follow:</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;line-height:normal'><span
+style='font-family:"Arial","sans-serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><i><span style='font-family:"Times New Roman","serif"'>I(q)</span></i><span
+style='font-family:"Times New Roman","serif"'> =  <i>I(q)</i> w/o background :
+If the data includes a background, user sets the value to subtract the background
+for the Q* computation.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;line-height:normal'><span
+style='font-family:"Arial","sans-serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>Reset<i>
+I(q)  </i></span><span style='font-family:"Times New Roman","serif"'>= <i>I(q)*
+scaling factor </i>, delta<i>I(q) =  </i>delta<i>I(q)*scaling factor</i> : If
+non-zero scaling factor is given, it will be considered.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;line-height:normal'><span
+style='font-family:"Arial","sans-serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'> Invariant:</span></p>
+
+<p class=MsoNormal style='margin-left:.25in;line-height:normal'>
+
+<table cellpadding=0 cellspacing=0 align=left>
+ <tr>
+  <td width=45 height=12></td>
+ </tr>
+ <tr>
+  <td></td>
+  <td><img width=127 height=35 src="image001.gif"></td>
+ </tr>
+</table>
+
+<span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<br clear=ALL>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'>            where, <i>g =q</i>
+for the pinhole geometry and <i>g =<sub> </sub>q<sub>v</sub></i>(the slit
+height) for the slit geometry which can be given in data or as a value.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;line-height:normal'><span
+style='font-family:"Arial","sans-serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>&nbsp;Higher
+q-region (&gt;= qmax in data): </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>            Power
+law (w/o background term) function = C/q<sup>4</sup> will be used </span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'>            where the constant
+C(=2pi(delta(rho))S<sub>v</sub>) is to be found by fitting part of data with
+the range of q<sub>N-m</sub>  to q<sub>N</sub> (m&lt;N).</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;line-height:normal'><span
+style='font-family:"Arial","sans-serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'> Lower
+q-region (&lt;= qmin in data): </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>            Guinier
+function = <i>I<sub>0</sub>exp(-R<sub>g</sub><sup>2</sup>q<sup>2</sup>/3)</i>
+where I<sub>0</sub> and R<sub>g</sub> are obtained by fitting, </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>            similarly
+to the high q region above.</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>            Power
+law can also be used.</span></p>
+
+<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>&nbsp;</span><b>The
+<a name=volume>volume </a>fraction</b>: </p>
+
+<p class=MsoNormal style='line-height:normal'><span style='position:absolute;
+z-index:3;margin-left:1px;margin-top:9px;width:161px;height:47px'><img
+width=161 height=47 src="image002.gif"></span><span
+style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>where
+delta(rho) is the SLD contrast of which value is given by users.</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='position:absolute;
+z-index:4;margin-left:1px;margin-top:29px;width:101px;height:45px'><img
+width=101 height=45 src="image003.gif"></span><span
+style='font-family:"Times New Roman","serif"'>Thus,  </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'> where
+0 =&lt; <i>A</i> =&lt;1/4 in order for these values to be physically valid.</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><b><span style='font-family:"Times New Roman","serif"'>The
+<a name=surface>specific surface area </a>:</span></b></p>
+
+<p class=MsoNormal style='line-height:normal'>
+
+<table cellpadding=0 cellspacing=0 align=left>
+ <tr>
+  <td width=1 height=3></td>
+ </tr>
+ <tr>
+  <td></td>
+  <td><img width=184 height=47 src="image004.gif"></td>
+ </tr>
+</table>
+
+<b><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></b></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<br clear=ALL>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'> where
+<i>A</i> and <i>Q<sup>*</sup></i> are obtained from previous sections, and the
+Porod constant <i>C<sub>p</sub></i> is given by users. </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><b><span style='font-family:"Times New Roman","serif"'>Definitions:</span></b><span
+style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>Q&nbsp;:
+the magnitude of neutron (or X-ray) momentum transfer vector.</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>I(Q):
+the scattering intensity as a function of the momentum transfer Q.</span></p>
+
+<p class=MsoNormal style='line-height:150%'><span style='font-family:"Times New Roman","serif"'>Invariant
+total is the sum of the invariant calculated from datas q range and the
+invariant resulting from extrapolation at low q range and at high q range if
+considered.</span></p>
+
+<p class=MsoNormal style='line-height:150%'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
+
+<p class=MsoNormal style='line-height:normal'><a name=reference><b><span
+style='font-family:"Times New Roman","serif"'>Reference</span></b></a><b><span
+style='font-family:"Times New Roman","serif"'>: </span></b></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>Porod's
+chapter (2) from  O. Glatter and O. Kratky, &quot;Small Angle X-Ray
+Scattering&quot;, Academic Press, New York, 1982</span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>Otto's
+web page: </span><a href="http://physchem.kfunigraz.ac.at/sm/"><span
+style='font-family:"Times New Roman","serif"'>http://physchem.kfunigraz.ac.at/sm/</span></a><span
+style='font-family:"Times New Roman","serif"'> </span></p>
+
+<p class=MsoNormal style='line-height:normal'><a name=howto><b><span
+style='font-family:"Times New Roman","serif"'>HowTo</span></b></a><b><span
+style='font-family:"Times New Roman","serif"'>:</span></b></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span>i)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>Loading data
+to the panel: Open the data file from File in the menu bar. Select loaded data
+from a plot panel by highlighting that it until its color turns yellow. Then
+right click on that the data and selects the option Compute Invariant. The
+application automatically computes the invariant value if the data loaded is
+valid.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span>ii)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>To subtract a
+background or/and to rescale the data, type the values in Customized Input
+box.  </span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span>iii)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>If you want
+to calculate the volume fraction and the specific surface area, type the
+optional inputs in the customized input box, and then press Compute button.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span>iv)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>The invariant
+can also be calculated including the outside of the data Q range:  To include
+the lower Q and/or the higher Q range, check in the enable extrapolation check
+box in Extrapolation box. If the power low is chosen, the power (exponent)
+can be either held or fitted by checking the corresponding radio button.  The
+Npts that is being used for the extrapolation can be specified.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span>v)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>If the
+invariant calculated from the extrapolated region is too large, it will be warn
+in red at the top of the panel, which means that your data is not proper to
+calculate the invariant.</span></p>
+
+<p class=MsoNormal style='margin-left:.5in;text-indent:-.5in;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
+</span>vi)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+</span></span><span style='font-family:"Times New Roman","serif"'>The details
+of the calculation is available by clicking the Details button in the middle
+of the panel. </span></p>
+
+<p class=MsoNormal align=center style='text-align:center;line-height:normal'><span
+style='font-family:"Times New Roman","serif"'><img border=0 width=572
+height=449 id="Object 4" src="image005.gif"></span></p>
+
+<p class=MsoNormal style='line-height:normal'><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p>
 
 </div>
