Ignore:
Timestamp:
Aug 14, 2012 6:00:12 PM (13 years ago)
Author:
Jae Cho <jhjcho@…>
Branches:
master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, release_4.0.1, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
5a313a3
Parents:
96277b9
Message:

moving model img files to media/img/

File:
1 edited

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  • sansmodels/src/sans/models/media/smear_computation.html

    r76b5220 r17574ae  
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    907</head> 
    … …  
    9613<p class=MsoNormal><span style='font-size:16.0pt;line-height:115%;font-family: 
    9714"Times New Roman","serif"'><h4>Smear Computation </h4></span></p> 
    98 <p class=MsoNormal>&nbsp;</p> 
     15 
    9916 
    10017<ul style='margin-top:0in' type=disc> 
    … …  
    10623        </li> 
    10724</ul> 
    108 <p class=MsoNormal>&nbsp;</p> 
    109 <p class=MsoNormal>&nbsp;</p> 
     25 
    11026<p class=MsoListParagraph><span style='font-size:14.0pt;line-height:115%; 
    11127font-family:"Times New Roman","serif"'><h5><a name="Slit Smear">Slit Smear</a></h5></span></p> 
    … …  
    11531 
    11632<p class=MsoNormal><img width=349 height=49 
    117 src="sm_image002.gif" align=left hspace=12></p> 
    118  
    119 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>            
    120                                  1)</span><br clear=all> 
     33src="./img/sm_image002.gif" align=left hspace=12></p> 
     34 
     35<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>            
     36                                 1)</span><br clear=all> 
    12137<span style='font-family:"Times New Roman","serif"'>where Norm = <span 
    12238style='position:relative;top:15.0pt'><img width=137 height=49 
    123 src="sm_image003.gif"></span>.</span></p> 
     39src="./img/sm_image003.gif"></span>.</span></p> 
    12440 
    12541<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>The 
    12642functions <span style='position:relative;top:6.0pt'><img width=43 height=25 
    127 src="sm_image004.gif"></span>and <span style='position: 
     43src="./img/sm_image004.gif"></span>and <span style='position: 
    12844relative;top:6.0pt'><img width=43 height=25 
    129 src="sm_image005.gif"></span>refer to the slit width weighting 
     45src="./img/sm_image005.gif"></span>refer to the slit width weighting 
    13046function and the slit height weighting determined at the q point, respectively. 
    131  Here, we assumes that the weighting function is described by a rectangular 
     47 Here, we assumes that the weighting function is described by a rectangular 
    13248function, i.e.,</span></p> 
    13349 
    13450<p class=MsoNormal><span style='position:relative;top:7.0pt'><img width=134 
    135 height=26 src="sm_image006.gif">                                                                                                        
    136   </span><span style='font-family:"Times New Roman","serif";position:relative; 
     51height=26 src="./img/sm_image006.gif">                                                                                                        
     52  </span><span style='font-family:"Times New Roman","serif";position:relative; 
    13753top:7.0pt'>2)</span></p> 
    13854 
    … …  
    14056 
    14157<p class=MsoNormal><span style='position:relative;top:7.0pt'><img width=136 
    142 height=26 src="sm_image007.gif"></span>,                                                                               
    143                          <span style='font-family:"Times New Roman","serif"'>3)</span></p> 
     58height=26 src="./img/sm_image007.gif"></span>,                                                                               
     59                         <span style='font-family:"Times New Roman","serif"'>3)</span></p> 
    14460 
    14561<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>so that </span><span 
    14662style='position:relative;top:6.0pt'><img width=58 height=23 
    147 src="sm_image008.gif"></span> <span style='position:relative; 
    148 top:16.0pt'><img width=76 height=51 src="sm_image009.gif"></span> <span 
    149 style='font-family:"Times New Roman","serif"'>for</span>  <span 
     63src="./img/sm_image008.gif"></span> <span style='position:relative; 
     64top:16.0pt'><img width=76 height=51 src="./img/sm_image009.gif"></span> <span 
     65style='font-family:"Times New Roman","serif"'>for</span>  <span 
    15066style='position:relative;top:3.0pt'><img width=40 height=15 
    151 src="sm_image010.gif"></span> <span style='font-family: 
     67src="./img/sm_image010.gif"></span> <span style='font-family: 
    15268"Times New Roman","serif"'>and <i>u</i>. The </span><span style='position:relative; 
    153 top:6.0pt'><img width=28 height=24 src="sm_image011.gif"></span> <span 
     69top:6.0pt'><img width=28 height=24 src="./img/sm_image011.gif"></span> <span 
    15470style='font-family:"Times New Roman","serif"'>and </span><span 
    15571style='position:relative;top:6.0pt'><img width=28 height=24 
    156 src="sm_image012.gif"> </span><span style='font-family: 
     72src="./img/sm_image012.gif"> </span><span style='font-family: 
    15773"Times New Roman","serif"'>stand for the slit height (FWHM/2) and the slit 
    15874width (FWHM/2) in the q space. Now the integral of Eq. (1) is simplified to</span></p> 
    15975 
    16076<p class=MsoNormal><img width=283 height=52 
    161 src="sm_image013.gif" align=left hspace=12><span 
    162 style='font-family:"Times New Roman","serif"'>                                                   
    163          4)</span></p> 
     77src="./img/sm_image013.gif" align=left hspace=12><span 
     78style='font-family:"Times New Roman","serif"'>                                                   
     79        4)</span></p> 
    16480 
    16581<p class=MsoNormal><span style='font-family:"Times New Roman","serif"; 
    … …  
    17490</span></span><span style='font-family:"Times New Roman","serif"'>For </span><span 
    17591style='position:relative;top:6.0pt'><img width=28 height=24 
    176 src="sm_image014.gif"></span>= 0  <span style='font-family: 
     92src="./img/sm_image014.gif"></span>= 0 <span style='font-family: 
    17793"Times New Roman","serif"'>and </span><span style='position:relative; 
    178 top:6.0pt'><img width=28 height=24 src="sm_image015.gif"></span> = 
     94top:6.0pt'><img width=28 height=24 src="./img/sm_image015.gif"></span> = 
    17995<span style='font-family:"Times New Roman","serif"'>constant:</span></p> 
    18096 
    18197<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'> 
    182 <img  
    183 src="sm_image016.gif"></p> 
     98<img src="./img/sm_image016.gif"></p> 
    18499 
    185100<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 
    186101style='font-family:"Times New Roman","serif"'>For discrete q values, at the q 
    187 values from the data points and at the q values extended up to  q<sub>N</sub>= 
     102values from the data points and at the q values extended up to  q<sub>N</sub>= 
    188103q<sub>i</sub> + </span><span style='position:relative;top:6.0pt'><img width=28 
    189 height=24 src="sm_image011.gif"></span><span 
     104height=24 src="./img/sm_image011.gif"></span><span 
    190105style='font-family:"Times New Roman","serif"'>, the smeared intensity can be 
    191106calculated approximately,</span></p> 
    192107 
    193108<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><img  
    194 src="sm_image017.gif">.                                                           <span 
    195 style='font-family:"Times New Roman","serif"'>5)</span></p> 
     109src="./img/sm_image017.gif">.                                                            
     110<span style='font-family:"Times New Roman","serif"'>5)</span></p> 
    196111 
    197112<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 
    198113style='position:relative;top:7.0pt'><img width=23 height=25 
    199 src="sm_image018.gif"></span> <span style='font-family: 
     114src="./img/sm_image018.gif"></span> <span style='font-family: 
    200115"Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 
    201116style='font-family:"Times New Roman","serif"'>j &lt; i</span></i><span 
    … …  
    207122<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;text-indent:-.25in'><span 
    208123style='font-family:"Times New Roman","serif"'>2)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    209 </span></span><span style='font-family:"Times New Roman","serif"'>For  </span><span 
     124</span></span><span style='font-family:"Times New Roman","serif"'>For  </span><span 
    210125style='position:relative;top:6.0pt'><img width=28 height=24 
    211 src="sm_image014.gif"></span>= <span style='font-family: 
    212 "Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 
     126src="./img/sm_image014.gif"></span>= <span style='font-family: 
     127"Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 
    213128</span><span style='position:relative;top:6.0pt'><img width=28 height=24 
    214 src="sm_image015.gif"></span> = <span style='font-family: 
     129src="./img/sm_image015.gif"></span> = <span style='font-family: 
    215130"Times New Roman","serif"'>0:</span></p> 
    216131 
    … …  
    219134 
    220135<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'> 
    221 <img  
    222 src="sm_image019.gif">                                                                                         
    223 <span 
    224 style='font-family:"Times New Roman","serif"'>6)</span></p> 
    225  
    226 <p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 
    227 style='font-family:"Times New Roman","serif"'>for  q<sub>p</sub> = q<sub>i</sub> 
     136<img src="./img/sm_image019.gif">                                                                                         
     137<span style='font-family:"Times New Roman","serif"'>6)</span></p> 
     138 
     139<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 
     140style='font-family:"Times New Roman","serif"'>for  q<sub>p</sub> = q<sub>i</sub> 
    228141- </span><span style='position:relative;top:6.0pt'><img width=28 height=24 
    229 src="sm_image012.gif"></span><span style='font-family: 
    230 "Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 
     142src="./img/sm_image012.gif"></span><span style='font-family: 
     143"Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 
    231144= q<sub>i</sub> + </span><span style='position:relative;top:6.0pt'><img 
    232 width=28 height=24 src="sm_image012.gif"></span>.  <span 
     145width=28 height=24 src="./img/sm_image012.gif"></span>. <span 
    233146style='position:relative;top:7.0pt'><img width=23 height=25 
    234 src="sm_image018.gif"></span> <span style='font-family: 
     147src="./img/sm_image018.gif"></span> <span style='font-family: 
    235148"Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 
    236149style='font-family:"Times New Roman","serif"'>j &lt; p</span></i><span 
    … …  
    241154<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;text-indent:-.25in'><span 
    242155style='font-family:"Times New Roman","serif"'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
    243 </span></span><span style='font-family:"Times New Roman","serif"'>For  </span><span 
     156</span></span><span style='font-family:"Times New Roman","serif"'>For  </span><span 
    244157style='position:relative;top:6.0pt'><img width=28 height=24 
    245 src="sm_image014.gif"></span>= <span style='font-family: 
    246 "Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 
     158src="./img/sm_image014.gif"></span>= <span style='font-family: 
     159"Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 
    247160</span><span style='position:relative;top:6.0pt'><img width=28 height=24 
    248 src="sm_image015.gif"></span> = <span style='font-family: 
     161src="./img/sm_image015.gif"></span> = <span style='font-family: 
    249162"Times New Roman","serif"'>constant:</span></p> 
    250163 
    … …  
    256169W, which will take minutes and minutes to finish the calculation for a set of 
    257170typical SANS data. An alternative way which is correct for slit width &lt;&lt; 
    258 slit hight, is used in the SANSView:  This method is a mixed method that 
     171slit hight, is used in the SANSView:  This method is a mixed method that 
    259172combines the method 1) with the numerical integration for the slit width.</span></p> 
    260173 
    … …  
    263176 
    264177<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'> 
    265 <img  
    266 src="sm_image020.gif">    <span style='font-family: 
     178<img src="./img/sm_image020.gif">    <span style='font-family: 
    267179"Times New Roman","serif"'>(7)</span></p> 
    268180 
    269181<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 
    270 style='font-family:"Times New Roman","serif"'>for  q<sub>p</sub> = q<sub>i</sub> 
     182style='font-family:"Times New Roman","serif"'>for  q<sub>p</sub> = q<sub>i</sub> 
    271183- </span><span style='position:relative;top:6.0pt'><img width=28 height=24 
    272 src="sm_image012.gif"></span><span style='font-family: 
    273 "Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 
     184src="./img/sm_image012.gif"></span><span style='font-family: 
     185"Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 
    274186= q<sub>i</sub> + </span><span style='position:relative;top:6.0pt'><img 
    275 width=28 height=24 src="sm_image012.gif"></span>.  <span 
     187width=28 height=24 src="./img/sm_image012.gif"></span>. <span 
    276188style='position:relative;top:7.0pt'><img width=23 height=25 
    277 src="sm_image018.gif"></span> <span style='font-family: 
     189src="./img/sm_image018.gif"></span> <span style='font-family: 
    278190"Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 
    279191style='font-family:"Times New Roman","serif"'>j &lt; p</span></i><span 
    … …  
    294206case becomes</span></p> 
    295207 
    296 <p class=MsoNormal><img  
    297 src="sm_image021.gif"><span 
    298 style='font-family:"Times New Roman","serif"'>                                                         (8)</span></p> 
     208<p class=MsoNormal><img src="./img/sm_image021.gif"><span 
     209style='font-family:"Times New Roman","serif"'>                                                         (8)</span></p> 
    299210 
    300211<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>For all 
    … …  
    303214evenly) below (&gt;0) and above the q range of data in order to cover all data 
    304215points of the smearing computation for a given model and for a given slit size. 
    305  The <i>Norm</i> factor is found numerically with the weighting matrix, and 
     216 The <i>Norm</i> factor is found numerically with the weighting matrix, and 
    306217considered on <i>I<sub>s</sub></i> computation.</span></p> 
    307218 
    … …  
    316227except that the weight function used was the 2D elliptical Gaussian function</span></p> 
    317228 
    318 <p class=MsoNormal><img  
    319 src="sm_image022.gif"><span 
    320 style='font-family:"Times New Roman","serif"'>                    (9)</span></p> 
     229<p class=MsoNormal><img src="./img/sm_image022.gif"><span 
     230style='font-family:"Times New Roman","serif"'>                    (9)</span></p> 
    321231 
    322232<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>In Eq 
    … …  
    326236, and the primed axes are in the coordinate rotated by an angle </span><span 
    327237style='font-family:Symbol'>theta</span><span style='font-family:"Times New Roman","serif"'> 
    328 around z-axis (below) so that x’<sub>0</sub> =  x<sub>0</sub>cos</span><span 
     238around z-axis (below) so that x’<sub>0</sub> =  x<sub>0</sub>cos</span><span 
    329239style='font-family:Symbol'>(theta) + </span><span style='font-family:"Times New Roman","serif"'>y<sub>0</sub> 
    330 sin</span><span style='font-family:Symbol'>(theta)  </span><span style='font-family: 
    331 "Times New Roman","serif"'>and y’<sub>0</sub> =  -x<sub>0</sub>sin</span><span 
     240sin</span><span style='font-family:Symbol'>(theta)  </span><span style='font-family: 
     241"Times New Roman","serif"'>and y’<sub>0</sub> =  -x<sub>0</sub>sin</span><span 
    332242style='font-family:Symbol'>(theta) + </span><span style='font-family:"Times New Roman","serif"'>y<sub>0</sub> 
    333243cos</span><span style='font-family:Symbol'>(theta) .</span><span style='font-family: 
    334244"Times New Roman","serif"'> Note that the rotation angle is zero for x-y 
    335245symmetric elliptical Gaussian distribution</span><span style='font-family:Symbol'>. 
    336 </span><span style='font-family:"Times New Roman","serif"'>The  A is a 
     246</span><span style='font-family:"Times New Roman","serif"'>The  A is a 
    337247normalization factor.</span></p> 
    338248 
    339249<p class=MsoNormal align=center style='text-align:center'><span 
    340250style='font-family:"Times New Roman","serif"'><img width=439 height=376 
    341 id="Object 1" src="sm_image023.gif"></span></p> 
     251id="Object 1" src="./img/sm_image023.gif"></span></p> 
    342252 
    343253<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>&nbsp;</span></p> 
    … …  
    352262assumed that I(x’, y’) is constant within the bins which in turn becomes</span></p> 
    353263 
    354 <p class=MsoNormal><img  
    355 src="sm_image024.gif"></p> 
    356  
    357 <p class=MsoNormal>                                                                                                                                                                                <span 
     264<p class=MsoNormal><img src="./img/sm_image024.gif"></p> 
     265 
     266<p class=MsoNormal>                                                                                                                                                                                <span 
    358267style='font-family:"Times New Roman","serif"'>(10)</span></p> 
    359268 
    … …  
    362271transform x’-y’ back to x-y coordinate (rotating it by -</span><span 
    363272style='font-family:Symbol'>(theta)</span><span style='font-family:"Times New Roman","serif"'> 
    364 around z axis).  Then, for the polar symmetric smear,</span></p> 
    365  
    366 <p class=MsoNormal><img  
    367 src="sm_image025.gif"><span 
    368 style='position:relative;top:35.0pt'>                                                         </span>(11)</p> 
     273around z axis).  Then, for the polar symmetric smear,</span></p> 
     274 
     275<p class=MsoNormal><img src="./img/sm_image025.gif"><span 
     276style='position:relative;top:35.0pt'>                                                         </span>(11)</p> 
    369277 
    370278<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>where,</span></p> 
    371279 
    372 <p class=MsoNormal><img  
    373 src="sm_image026.gif"></p> 
     280<p class=MsoNormal><img src="./img/sm_image026.gif"></p> 
    374281 
    375282<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>while 
    376283for the x-y symmetric smear,</span></p> 
    377284 
    378 <p class=MsoNormal><img  
    379 src="sm_image027.gif"><span 
    380 style='font-family:"Times New Roman","serif"'>                                                                                          (12)</span></p> 
     285<p class=MsoNormal><img src="./img/sm_image027.gif"><span 
     286style='font-family:"Times New Roman","serif"'>                                                                                          (12)</span></p> 
    381287 
    382288<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>where,</span></p> 
    383289 
    384 <p class=MsoNormal><img  
    385 src="sm_image028.gif"></p> 
     290<p class=MsoNormal><img src="./img/sm_image028.gif"></p> 
    386291 
    387292<p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>Here, the 
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