Changeset 8956bdb in sasview for sansmodels/src/media
- Timestamp:
- Mar 22, 2011 5:33:59 PM (13 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:
- 05319e2
- Parents:
- 384647dc
- File:
-
- 1 edited
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sansmodels/src/media/smear_computation.html
r6e8b436 r8956bdb 321 321 322 322 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>In Eq 323 (9), x<sub>0</sub> = qcos</span><span style='font-family:Symbol'> q</span><span323 (9), x<sub>0</sub> = qcos</span><span style='font-family:Symbol'>(theta)</span><span 324 324 style='font-family:"Times New Roman","serif"'> and y<sub>0</sub>=qsin</span><span 325 style='font-family:Symbol'> q</span><span style='font-family:"Times New Roman","serif"'>325 style='font-family:Symbol'>(theta)</span><span style='font-family:"Times New Roman","serif"'> 326 326 , and the primed axes are in the coordinate rotated by an angle </span><span 327 style='font-family:Symbol'> q</span><span style='font-family:"Times New Roman","serif"'>327 style='font-family:Symbol'>theta</span><span style='font-family:"Times New Roman","serif"'> 328 328 around z-axis (below) so that x<sub>0</sub> = x<sub>0</sub>cos</span><span 329 style='font-family:Symbol'> q+ </span><span style='font-family:"Times New Roman","serif"'>y<sub>0</sub>330 sin</span><span style='font-family:Symbol'> q</span><span style='font-family:329 style='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: 331 331 "Times New Roman","serif"'>and y<sub>0</sub> = -x<sub>0</sub>sin</span><span 332 style='font-family:Symbol'> q+ </span><span style='font-family:"Times New Roman","serif"'>y<sub>0</sub>333 cos</span><span style='font-family:Symbol'> q.</span><span style='font-family:332 style='font-family:Symbol'>(theta) + </span><span style='font-family:"Times New Roman","serif"'>y<sub>0</sub> 333 cos</span><span style='font-family:Symbol'>(theta) .</span><span style='font-family: 334 334 "Times New Roman","serif"'> Note that the rotation angle is zero for x-y 335 335 symmetric elliptical Gaussian distribution</span><span style='font-family:Symbol'>. … … 345 345 <p class=MsoNormal><span style='font-family:"Times New Roman","serif"'>Now we 346 346 consider a numerical integration where each bins in </span><span 347 style='font-family:Symbol'> Q</span><span style='font-family:"Times New Roman","serif"'>347 style='font-family:Symbol'>THETA</span><span style='font-family:"Times New Roman","serif"'> 348 348 and R are <b>evenly </b>(this is to simplify the equation below) distributed by 349 </span><span style='font-family:Symbol'>D Q</span><span style='font-family:350 "Times New Roman","serif"'>and </span><span style='font-family:Symbol'>D </span><span349 </span><span style='font-family:Symbol'>Delta_THETA </span><span style='font-family: 350 "Times New Roman","serif"'>and </span><span style='font-family:Symbol'>Delta</span><span 351 351 style='font-family:"Times New Roman","serif"'>R, respectively, and it is 352 352 assumed that I(x, y) is constant within the bins which in turn becomes</span></p> … … 361 361 have found the weighting factor on each bin points, it is convenient to 362 362 transform x-y back to x-y coordinate (rotating it by -</span><span 363 style='font-family:Symbol'> q</span><span style='font-family:"Times New Roman","serif"'>363 style='font-family:Symbol'>(theta)</span><span style='font-family:"Times New Roman","serif"'> 364 364 around z axis). Then, for the polar symmetric smear,</span></p> 365 365
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