| 1 | <html> |
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| 2 | <body> |
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| 3 | <h4>SANS Q Resolution Estimator</h4> |
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| 4 | <ul> |
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| 5 | <li><a href="#Description">Description</a></li> |
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| 6 | <li><a href="#HowTo">HowTo?</a></li> |
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| 7 | <li><a href="#Theory">Theory</a></li> |
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| 8 | <li><a href="#References">References</a></li> |
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| 9 | </ul> |
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| 10 | <h5><a name="Description">Description</a></h5> |
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| 11 | <p> |
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| 12 | This tool is to approximately estimate the resolution of Q based on the |
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| 13 | SANS instrumental parameter values assuming that the detector is flat |
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| 14 | and vertical to the incident beam direction. |
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| 15 | </p> |
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| 16 | |
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| 17 | |
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| 18 | <h5><a name="HowTo">HowTo?</a></h5> |
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| 19 | <p> |
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| 20 | 1. Select the source and source type (Monochromatic or TOF). |
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| 21 | Note that the computational difference between the sources is |
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| 22 | only the gravitational contribution due to the mass.</p> |
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| 23 | <p> |
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| 24 | 2. Change the default values of the instrumental parameters as desired.</p> |
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| 25 | <p> |
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| 26 | 3. The input formats of wavelength and its spread (=FWHM/wavelength) depend on the source type. |
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| 27 | <li>For monochromatic wave, the inputs are just one values as shown with the defaults.</li> |
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| 28 | <li>For TOF, the min and max values should be separated by "-" to describe the wavelength band range. |
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| 29 | Optionally, the input of the wavelength (NOT of the wavelength spread) |
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| 30 | could be extended by adding "; ##" where the ## is the number |
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| 31 | of the bins for the numerical integration. |
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| 32 | Otherwise, the default value "10" bins will be used. |
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| 33 | The same number of bins will be used for the corresponding wavelength spread in either cases.</li> |
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| 34 | </p> |
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| 35 | <p>4. For TOF, the default wavelength spectrum is flat. |
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| 36 | The custom spectrum file (with 2 column text: wavelength(A) vs. intensity) |
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| 37 | can also be loaded by selecting "Add new" in the combobox.</p> |
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| 38 | <p> |
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| 39 | 5. Once set all the input values, click the compute button. |
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| 40 | Depending on computation loads the calculation time will vary. |
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| 41 | </p> |
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| 42 | <p> |
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| 43 | 6. 1D and 2D dQ will be displayed in the text-box at the bottom of |
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| 44 | the panel. Two dimensional resolution weight distribution |
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| 45 | (2D elliptical Gaussian function) will also be |
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| 46 | displayed in the plot panel even if the Q inputs are outside |
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| 47 | of the detector limit. |
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| 48 | The red lines indicate the limits of the detector (if a green lines appear (for TOF), |
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| 49 | it indicates the limits of the maximum q range for the largest wavelength |
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| 50 | due to the size of the detector). Note that the effect from the beam block is ignored, |
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| 51 | so in the small q region near the beam block [ie., q < 2*pi*(beam block diameter) / (sample to detector distance) / lamda_min] |
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| 52 | the variance is slightly under estimated.</p> |
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| 53 | <p>7. The summary can be accessed by clicking the 'light-bulb' icon |
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| 54 | at the bottom of the SansView main window. |
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| 55 | </p> |
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| 56 | <p><img src="resolution_tutor.gif"> |
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| 57 | </p> |
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| 58 | <h5><a name="Theory">Theory</a></h5> |
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| 59 | <p> |
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| 60 | The scattering wave transfer vector is by definition, |
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| 61 | <img src="q.gif"> |
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| 62 | </p> |
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| 63 | <p>In the limit of the small angle, the variance of q in the first order approximation is</p> |
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| 64 | <p> |
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| 65 | <img src="sigma_q.gif"> |
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| 66 | </p> |
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| 67 | In summary, the geometric and gravitational contributions depending on the shape of each factors can be expressed |
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| 68 | as shown the table.</p> |
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| 69 | <p> |
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| 70 | <img src="sigma_table.gif"> |
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| 71 | </p> |
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| 72 | <p> |
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| 73 | Finally, we use a Gaussian function to describe the 2D weighting distribution of the uncertainty in q. |
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| 74 | </p> |
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| 75 | <p/> |
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| 76 | <h5><a name="References">References</a></h5> |
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| 77 | <p> |
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| 78 | D.F.R. Mildner and J.M. Carpenter, J. Appl. Cryst. 17, 249-256 (1984).</p> |
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| 79 | <p> |
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| 80 | D.F.R. Mildner, J.M. Carpenter and D.L. Worcester, J. Appl. Cryst. 19, 311-319 (1986).</p> |
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| 81 | </body> |
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| 82 | |
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| 83 | </html> |
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