source: sasview/src/sas/sasgui/perspectives/fitting/media/pd_help.rst @ 1b9a367

Last change on this file since 1b9a367 was b64b87c, checked in by smk78, 8 years ago

Word 'perspective' removed as per #513

  • Property mode set to 100644
File size: 5.9 KB
RevLine 
[da53353]1.. pd_help.rst
2
3.. This is a port of the original SasView html help file to ReSTructured text
4.. by S King, ISIS, during SasView CodeCamp-III in Feb 2015.
5
6.. |inlineimage004| image:: sm_image004.gif
7.. |inlineimage005| image:: sm_image005.gif
8.. |inlineimage008| image:: sm_image008.gif
9.. |inlineimage009| image:: sm_image009.gif
10.. |inlineimage010| image:: sm_image010.gif
11.. |inlineimage011| image:: sm_image011.gif
12.. |inlineimage012| image:: sm_image012.gif
13.. |inlineimage018| image:: sm_image018.gif
14.. |inlineimage019| image:: sm_image019.gif
15
16
17.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
18
19Polydispersity Distributions
20----------------------------
21
[f256d9b]22With some models SasView can calculate the average form factor for a population
23of particles that exhibit size and/or orientational polydispersity. The resultant
24form factor is normalized by the average particle volume such that
[da53353]25
[f256d9b]26*P(q) = scale* * \ <F*\F> / *V + bkg*
[da53353]27
[f256d9b]28where F is the scattering amplitude and the \<\> denote an average over the size
29distribution.
[da53353]30
[f256d9b]31Users should note that this computation is very intensive. Applying polydispersion
32to multiple parameters at the same time, or increasing the number of *Npts* values
33in the fit, will require patience! However, the calculations are generally more
34robust with more data points or more angles.
[da53353]35
[f256d9b]36SasView uses the term *PD* for a size distribution (and not to be confused with a
37molecular weight distributions in polymer science) and the term *Sigma* for an
38angular distribution.
39
40The following five distribution functions are provided:
[da53353]41
[a0637de]42*  *Rectangular Distribution*
43*  *Gaussian Distribution*
44*  *Lognormal Distribution*
45*  *Schulz Distribution*
[f256d9b]46*  *Array Distribution*
[da53353]47
[a910c788]48These are all implemented in SasView as *number-average* distributions.
49
[a0637de]50.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[da53353]51
52Rectangular Distribution
[892a2cc]53^^^^^^^^^^^^^^^^^^^^^^^^
[da53353]54
[f256d9b]55The Rectangular Distribution is defined as
56
[da53353]57.. image:: pd_image001.png
58
[f256d9b]59where *xmean* is the mean of the distribution, *w* is the half-width, and *Norm* is a
60normalization factor which is determined during the numerical calculation.
61
62Note that the standard deviation and the half width *w* are different!
[da53353]63
64The standard deviation is
65
66.. image:: pd_image002.png
67
[f256d9b]68whilst the polydispersity is
[da53353]69
70.. image:: pd_image003.png
71
72.. image:: pd_image004.jpg
73
[a0637de]74.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[da53353]75
76Gaussian Distribution
[892a2cc]77^^^^^^^^^^^^^^^^^^^^^
[da53353]78
[f256d9b]79The Gaussian Distribution is defined as
80
[da53353]81.. image:: pd_image005.png
82
[f256d9b]83where *xmean* is the mean of the distribution and *Norm* is a normalization factor
[da53353]84which is determined during the numerical calculation.
85
[f256d9b]86The polydispersity is
[da53353]87
88.. image:: pd_image003.png
89
[f256d9b]90
[da53353]91.. image:: pd_image006.jpg
92
[a0637de]93.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[da53353]94
95Lognormal Distribution
[892a2cc]96^^^^^^^^^^^^^^^^^^^^^^
[da53353]97
[f256d9b]98The Lognormal Distribution is defined as
99
[da53353]100.. image:: pd_image007.png
101
[f256d9b]102where |mu|\ =ln(*xmed*), *xmed* is the median value of the distribution, and
103*Norm* is a normalization factor which will be determined during the numerical
104calculation.
105
106The median value for the distribution will be the value given for the respective
[b64b87c]107size parameter in the *FitPage*, for example, radius = 60.
[da53353]108
[f256d9b]109The polydispersity is given by |sigma|
[da53353]110
111.. image:: pd_image008.png
112
113For the angular distribution
114
115.. image:: pd_image009.png
116
[f256d9b]117The mean value is given by *xmean*\ =exp(|mu|\ +p\ :sup:`2`\ /2). The peak value
118is given by *xpeak*\ =exp(|mu|-p\ :sup:`2`\ ).
[da53353]119
120.. image:: pd_image010.jpg
121
[f256d9b]122This distribution function spreads more, and the peak shifts to the left, as *p*
123increases, requiring higher values of Nsigmas and Npts.
[da53353]124
[a0637de]125.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[da53353]126
127Schulz Distribution
[892a2cc]128^^^^^^^^^^^^^^^^^^^
[da53353]129
[f256d9b]130The Schulz distribution is defined as
131
[da53353]132.. image:: pd_image011.png
133
[f256d9b]134where *xmean* is the mean of the distribution and *Norm* is a normalization factor
135which is determined during the numerical calculation, and *z* is a measure of the
136width of the distribution such that
[da53353]137
[f256d9b]138z = (1-p\ :sup:`2`\ ) / p\ :sup:`2`
[da53353]139
[f256d9b]140The polydispersity is
[da53353]141
142.. image:: pd_image012.png
143
[f256d9b]144Note that larger values of PD might need larger values of Npts and Nsigmas.
145For example, at PD=0.7 and radius=60 |Ang|, Npts>=160 and Nsigmas>=15 at least.
[da53353]146
147.. image:: pd_image013.jpg
148
[f256d9b]149For further information on the Schulz distribution see:
150M Kotlarchyk & S-H Chen, *J Chem Phys*, (1983), 79, 2461.
151
[da53353]152.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
[f256d9b]153
154Array Distribution
155^^^^^^^^^^^^^^^^^^
156
157This user-definable distribution should be given as as a simple ASCII text file
158where the array is defined by two columns of numbers: *x* and *f(x)*. The *f(x)*
159will be normalized by SasView during the computation.
160
161Example of what an array distribution file should look like:
162
163====  =====
164 30    0.1
165 32    0.3
166 35    0.4
167 36    0.5
168 37    0.6
169 39    0.7
170 41    0.9
171====  =====
172
173SasView only uses these array values during the computation, therefore any mean
[b64b87c]174value of the parameter represented by *x* present in the *FitPage*
[f256d9b]175will be ignored.
176
177.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
178
179Note about DLS polydispersity
180^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
181
182Many commercial Dynamic Light Scattering (DLS) instruments produce a size
183polydispersity parameter, sometimes even given the symbol *p*! This parameter is
184defined as the relative standard deviation coefficient of variation of the size
185distribution and is NOT the same as the polydispersity parameters in the Lognormal
186and Schulz distributions above (though they all related) except when the DLS
187polydispersity parameter is <0.13.
188
189For more information see:
190S King, C Washington & R Heenan, *Phys Chem Chem Phys*, (2005), 7, 143
191
192.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
193
194.. note::  This help document was last changed by Steve King, 01May2015
Note: See TracBrowser for help on using the repository browser.