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1<html>
2<body>
3<h4>SAS Q Resolution Estimator</h4>
4<ul>
5<li><a href="#Description">Description</a></li>
6<li><a href="#HowTo">HowTo?</a></li>
7<li><a href="#Theory">Theory</a></li>
8<li><a href="#References">References</a></li>
9</ul>
10<h5><a name="Description">Description</a></h5>
11<p>
12This tool is to approximately estimate the resolution of Q based on the
13SAS instrumental parameter values assuming that the detector is flat
14and vertical to the incident beam direction.
15</p>
16
17
18<h5><a name="HowTo">HowTo?</a></h5>
19<p>
201. Select the source and source type (Monochromatic or TOF).
21Note that the computational difference between the sources is
22only the gravitational contribution due to the mass.</p>
23<p>
242. Change the default values of the instrumental parameters as desired.</p>
25<p>
263. The input formats of wavelength and its spread (=FWHM/wavelength) depend on the source type.
27<li>For monochromatic wave, the inputs are just one values as shown with the defaults.</li>
28<li>For TOF, the min and max values should be separated by "-" to describe the wavelength band range.
29Optionally, the input of the wavelength (NOT of the wavelength spread)
30could be extended by adding "; ##" where the ## is the number
31of the bins for the numerical integration.
32Otherwise, the default value "10" bins will be used.
33The same number of bins will be used for the corresponding wavelength spread in either cases.</li>
34</p>
35<p>4. For TOF, the default wavelength spectrum is flat.
36The custom spectrum file (with 2 column text: wavelength(A) vs. intensity)
37can also be loaded by selecting "Add new" in the combobox.</p>
38<p>
395. Once set all the input values, click the compute button.
40Depending on computation loads the calculation time will vary.
41</p>
42<p> 
436. 1D and 2D dQ will be displayed in the text-box at the bottom of
44the panel. Two dimensional resolution weight distribution
45(2D elliptical Gaussian function) will also be
46displayed in the plot panel even if the Q inputs are outside
47of the detector limit.
48The red lines indicate the limits of the detector (if a green lines appear (for TOF),
49it indicates the limits of the maximum q range for the largest wavelength
50due to the size of the detector). Note that the effect from the beam block is ignored,
51so in the small q region near the beam block [ie., q < 2*pi*(beam block diameter) / (sample to detector distance) / lamda_min] 
52the variance is slightly under estimated.</p>
53<p>7. The summary can be accessed by clicking the 'light-bulb' icon
54at the bottom of the SasView main window.
55</p>
56<p><img src="resolution_tutor.gif">
57</p>
58<h5><a name="Theory">Theory</a></h5>
59<p>
60The scattering wave transfer vector is by definition,
61<img src="q.gif">
62</p>
63<p>In the limit of the small angle, the variance of q in the first order approximation is</p>
64<p>
65<img src="sigma_q.gif">
66</p>
67In summary, the geometric and gravitational contributions depending on the shape of each factors can be expressed 
68as shown the table.</p>
69<p>
70<img src="sigma_table.gif">
71</p>
72<p>
73Finally, we use a Gaussian function to describe the 2D weighting distribution of the uncertainty in q.
74</p>
75<p/>
76<h5><a name="References">References</a></h5>
77<p>
78D.F.R. Mildner and J.M. Carpenter, J. Appl. Cryst. 17, 249-256 (1984).</p>
79<p>
80D.F.R. Mildner, J.M. Carpenter and D.L. Worcester, J. Appl. Cryst. 19, 311-319 (1986).</p>
81</body>
82
83</html>
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