Changeset 87f8971 in sasview for sansmodels/src/sans/models/media/smear_computation.html
- Timestamp:
- Dec 18, 2012 2:27:07 PM (12 years ago)
- 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:
- 9714ff5
- Parents:
- 5b07138
- File:
-
- 1 edited
Legend:
- Unmodified
- Added
- Removed
-
sansmodels/src/sans/models/media/smear_computation.html
r318b5bbb r87f8971 30 30 31 31 <p class=MsoNormal><img 32 src=" ./img/sm_image002.gif" align=left hspace=12></p>32 src="img/sm_image002.gif" align=left hspace=12></p> 33 33 34 34 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'> … … 36 36 <span style='font-family:"Times New Roman","serif"'>where Norm = <span 37 37 style='position:relative;top:15.0pt'><img 38 src=" ./img/sm_image003.gif"></span>.</span></p>38 src="img/sm_image003.gif"></span>.</span></p> 39 39 <br> 40 40 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>The 41 41 functions <span style='position:relative;top:6.0pt'><img 42 src=" ./img/sm_image004.gif"></span> and <span style='position:42 src="img/sm_image004.gif"></span> and <span style='position: 43 43 relative;top:6.0pt'><img 44 src=" ./img/sm_image005.gif"></span> refer to the slit width weighting44 src="img/sm_image005.gif"></span> refer to the slit width weighting 45 45 function and the slit height weighting determined at the q point, respectively. 46 46 Here, we assumes that the weighting function is described by a rectangular … … 48 48 49 49 <p class=MsoNormal><span style='position:relative;top:7.0pt'><img 50 src=" ./img/sm_image006.gif">50 src="img/sm_image006.gif"> 51 51 </span><span style='font-family:"Times New Roman","serif";position:relative; 52 52 top:7.0pt'> ---- 2)</span></p> … … 55 55 56 56 <p class=MsoNormal><span style='position:relative;top:7.0pt'><img 57 src=" ./img/sm_image007.gif"></span>,57 src="img/sm_image007.gif"></span>, 58 58 <span style='font-family:"Times New Roman","serif"'> ---- 3)</span></p> 59 59 60 60 <p>so that <img 61 src=" ./img/sm_image008.gif"> <img src="./img/sm_image009.gif"> for <img62 src=" ./img/sm_image010.gif"> and <i>u</i>. The <img src="./img/sm_image011.gif">63 and <img src=" ./img/sm_image012.gif"> stand for the slit height (FWHM/2) and the slit61 src="img/sm_image008.gif"> <img src="img/sm_image009.gif"> for <img 62 src="img/sm_image010.gif"> and <i>u</i>. The <img src="img/sm_image011.gif"> 63 and <img src="img/sm_image012.gif"> stand for the slit height (FWHM/2) and the slit 64 64 width (FWHM/2) in the q space. Now the integral of Eq. (1) is simplified to</span></p> 65 65 66 66 <p class=MsoNormal><img 67 src=" ./img/sm_image013.gif" align=left hspace=12><span67 src="img/sm_image013.gif" align=left hspace=12><span 68 68 style='font-family:"Times New Roman","serif"'> 69 69 ---- 4)</span></p> … … 80 80 </span></span><span style='font-family:"Times New Roman","serif"'>For </span><span 81 81 style='position:relative;top:6.0pt'><img 82 src=" ./img/sm_image012.gif"></span>= 0 <span style='font-family:82 src="img/sm_image012.gif"></span>= 0 <span style='font-family: 83 83 "Times New Roman","serif"'>and </span><span style='position:relative; 84 top:6.0pt'><img src=" ./img/sm_image011.gif"></span> =84 top:6.0pt'><img src="img/sm_image011.gif"></span> = 85 85 <span style='font-family:"Times New Roman","serif"'>constant:</span></p> 86 86 87 87 <p> 88 <img src=" ./img/sm_image016.gif"></p>88 <img src="img/sm_image016.gif"></p> 89 89 90 90 <p> For discrete q values, at the q 91 91 values from the data points and at the q values extended up to q<sub>N</sub>= 92 q<sub>i</sub> + <img src=" ./img/sm_image011.gif"> , the smeared intensity can be92 q<sub>i</sub> + <img src="img/sm_image011.gif"> , the smeared intensity can be 93 93 calculated approximately, </p> 94 94 95 95 <p><img 96 src=" ./img/sm_image017.gif">.96 src="img/sm_image017.gif">. 97 97 ---- 5)</p> 98 98 99 99 <p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'><span 100 100 style='position:relative;top:7.0pt'><img 101 src=" ./img/sm_image018.gif"></span> <span style='font-family:101 src="img/sm_image018.gif"></span> <span style='font-family: 102 102 "Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 103 103 style='font-family:"Times New Roman","serif"'>j < i</span></i><span … … 111 111 </span></span><span style='font-family:"Times New Roman","serif"'>For </span><span 112 112 style='position:relative;top:6.0pt'><img 113 src=" ./img/sm_image012.gif"></span>= <span style='font-family:113 src="img/sm_image012.gif"></span>= <span style='font-family: 114 114 "Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 115 115 </span><span style='position:relative;top:6.0pt'><img 116 src=" ./img/sm_image011.gif"></span> = <span style='font-family:116 src="img/sm_image011.gif"></span> = <span style='font-family: 117 117 "Times New Roman","serif"'>0:</span></p> 118 118 … … 121 121 122 122 <p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'> 123 <img src=" ./img/sm_image019.gif">123 <img src="img/sm_image019.gif"> 124 124 <span style='font-family:"Times New Roman","serif"'> ---- 6)</span></p> 125 125 … … 127 127 style='font-family:"Times New Roman","serif"'>for q<sub>p</sub> = q<sub>i</sub> 128 128 - </span><span style='position:relative;top:6.0pt'><img 129 src=" ./img/sm_image012.gif"></span><span style='font-family:129 src="img/sm_image012.gif"></span><span style='font-family: 130 130 "Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 131 131 = q<sub>i</sub> + </span><span style='position:relative;top:6.0pt'><img 132 src=" ./img/sm_image012.gif"></span>. <span132 src="img/sm_image012.gif"></span>. <span 133 133 style='position:relative;top:7.0pt'><img 134 src=" ./img/sm_image018.gif"></span> <span style='font-family:134 src="img/sm_image018.gif"></span> <span style='font-family: 135 135 "Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 136 136 style='font-family:"Times New Roman","serif"'>j < p</span></i><span … … 143 143 </span></span><span style='font-family:"Times New Roman","serif"'>For </span><span 144 144 style='position:relative;top:6.0pt'><img 145 src=" ./img/sm_image011.gif"></span>= <span style='font-family:145 src="img/sm_image011.gif"></span>= <span style='font-family: 146 146 "Times New Roman","serif"'>constant </span> <span style='font-family:"Times New Roman","serif"'>and 147 147 </span><span style='position:relative;top:6.0pt'><img 148 src=" ./img/sm_image011.gif"></span> = <span style='font-family:148 src="img/sm_image011.gif"></span> = <span style='font-family: 149 149 "Times New Roman","serif"'>constant:</span></p> 150 150 … … 163 163 164 164 <p class=MsoListParagraphCxSpMiddle style='margin-left:.25in'> 165 <img src=" ./img/sm_image020.gif"> <span style='font-family:165 <img src="img/sm_image020.gif"> <span style='font-family: 166 166 "Times New Roman","serif"'> ---- (7)</span></p> 167 167 … … 169 169 style='font-family:"Times New Roman","serif"'>for q<sub>p</sub> = q<sub>i</sub> 170 170 - </span><span style='position:relative;top:6.0pt'><img 171 src=" ./img/sm_image012.gif"></span><span style='font-family:171 src="img/sm_image012.gif"></span><span style='font-family: 172 172 "Times New Roman","serif"'> and</span> <span style='font-family:"Times New Roman","serif"'>q<sub>N</sub> 173 173 = q<sub>i</sub> + </span><span style='position:relative;top:6.0pt'><img 174 src=" ./img/sm_image012.gif"></span>. <span174 src="img/sm_image012.gif"></span>. <span 175 175 style='position:relative;top:7.0pt'><img 176 src=" ./img/sm_image018.gif"></span> <span style='font-family:176 src="img/sm_image018.gif"></span> <span style='font-family: 177 177 "Times New Roman","serif"'>= 0 for <i>I<sub>s</sub></i> in</span> <i><span 178 178 style='font-family:"Times New Roman","serif"'>j < p</span></i><span … … 193 193 case becomes</span></p> 194 194 195 <p class=MsoNormal><img src=" ./img/sm_image021.gif"><span195 <p class=MsoNormal><img src="img/sm_image021.gif"><span 196 196 style='font-family:"Times New Roman","serif"'> ---- (8)</span></p> 197 197 … … 214 214 except that the weight function used was the 2D elliptical Gaussian function</span></p> 215 215 216 <p class=MsoNormal><img src=" ./img/sm_image022.gif"><span216 <p class=MsoNormal><img src="img/sm_image022.gif"><span 217 217 style='font-family:"Times New Roman","serif"'> ---- (9)</span></p> 218 218 … … 232 232 <p class=MsoNormal align=center style='text-align:center'><span 233 233 style='font-family:"Times New Roman","serif"'><img 234 id="Object 1" src=" ./img/sm_image023.gif"></span></p>234 id="Object 1" src="img/sm_image023.gif"></span></p> 235 235 236 236 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'> </span></p> … … 244 244 assumed that I(x, y) is constant within the bins which in turn becomes</span></p> 245 245 246 <p class=MsoNormal><img src=" ./img/sm_image024.gif"></p>246 <p class=MsoNormal><img src="img/sm_image024.gif"></p> 247 247 248 248 <p class=MsoNormal> <span … … 254 254 around z axis). Then, for the polar symmetric smear,</span></p> 255 255 256 <p class=MsoNormal><img src=" ./img/sm_image025.gif"><span256 <p class=MsoNormal><img src="img/sm_image025.gif"><span 257 257 style='position:relative;top:35.0pt'> </span> ---- (11)</p> 258 258 259 259 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>where,</span></p> 260 260 261 <p class=MsoNormal><img src=" ./img/sm_image026.gif">,</p>261 <p class=MsoNormal><img src="img/sm_image026.gif">,</p> 262 262 263 263 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>while 264 264 for the x-y symmetric smear,</span></p> 265 265 266 <p class=MsoNormal><img src=" ./img/sm_image027.gif"><span266 <p class=MsoNormal><img src="img/sm_image027.gif"><span 267 267 style='font-family:"Times New Roman","serif"'> ---- (12)</span></p> 268 268 269 269 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>where,</span></p> 270 270 271 <p class=MsoNormal><img src=" ./img/sm_image028.gif"></p>271 <p class=MsoNormal><img src="img/sm_image028.gif"></p> 272 272 273 273 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>Here, the
Note: See TracChangeset
for help on using the changeset viewer.
