Ignore:
Timestamp:
May 1, 2015 8:58:57 AM (9 years ago)
Author:
smk78
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:
3b67c30
Parents:
a9dc4eb
Message:

Proof read.

File:
1 edited

Legend:

Unmodified
Added
Removed

  • src/sas/perspectives/fitting/media/pd_help.rst

    r892a2cc rf256d9b  
    1111.. |theta| unicode:: U+03B8 
    1212.. |chi| unicode:: U+03C7 
     13.. |Ang| unicode:: U+212B 
    1314 
    1415.. |inlineimage004| image:: sm_image004.gif 
    … …  
    2829---------------------------- 
    2930 
    30 Calculates the form factor for a polydisperse and/or angular population of  
    31 particles with uniform scattering length density. The resultant form factor  
    32 is normalized by the average particle volume such that  
    33  
    34 P(q) = scale*\<F*F\>/Vol + bkg 
    35  
    36 where F is the scattering amplitude and the\<\>denote an average over the size  
    37 distribution.  Users should use PD (polydispersity: this definition is  
    38 different from the typical definition in polymer science) for a size  
    39 distribution and Sigma for an angular distribution (see below). 
    40  
    41 Note that this computation is very time intensive thus applying polydispersion/ 
    42 angular distribution for more than one parameters or increasing Npts values 
    43 might need extensive patience to complete the computation. Also note that  
    44 even though it is time consuming, it is safer to have larger values of Npts  
    45 and Nsigmas. 
    46  
    47 The following five distribution functions are provided 
     31With some models SasView can calculate the average form factor for a population 
     32of particles that exhibit size and/or orientational polydispersity. The resultant 
     33form factor is normalized by the average particle volume such that 
     34 
     35*P(q) = scale* * \ <F*\F> / *V + bkg* 
     36 
     37where F is the scattering amplitude and the \<\> denote an average over the size 
     38distribution. 
     39 
     40Users should note that this computation is very intensive. Applying polydispersion 
     41to multiple parameters at the same time, or increasing the number of *Npts* values 
     42in the fit, will require patience! However, the calculations are generally more 
     43robust with more data points or more angles. 
     44 
     45SasView uses the term *PD* for a size distribution (and not to be confused with a 
     46molecular weight distributions in polymer science) and the term *Sigma* for an 
     47angular distribution. 
     48 
     49The following five distribution functions are provided: 
    4850 
    4951*  *Rectangular Distribution* 
    50 *  *Array Distribution* 
    5152*  *Gaussian Distribution* 
    5253*  *Lognormal Distribution* 
    5354*  *Schulz Distribution* 
     55*  *Array Distribution* 
    5456 
    5557.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    … …  
    5860^^^^^^^^^^^^^^^^^^^^^^^^ 
    5961 
     62The Rectangular Distribution is defined as 
     63 
    6064.. image:: pd_image001.png 
    6165 
    62 The xmean is the mean of the distribution, w is the half-width, and Norm is a  
    63 normalization factor which is determined during the numerical calculation.  
    64 Note that the Sigma and the half width *w*  are different. 
     66where *xmean* is the mean of the distribution, *w* is the half-width, and *Norm* is a 
     67normalization factor which is determined during the numerical calculation. 
     68 
     69Note that the standard deviation and the half width *w* are different! 
    6570 
    6671The standard deviation is 
    … …  
    6873.. image:: pd_image002.png 
    6974 
    70 The PD (polydispersity) is 
     75whilst the polydispersity is 
    7176 
    7277.. image:: pd_image003.png 
    7378 
    7479.. image:: pd_image004.jpg 
     80 
     81.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     82 
     83Gaussian Distribution 
     84^^^^^^^^^^^^^^^^^^^^^ 
     85 
     86The Gaussian Distribution is defined as 
     87 
     88.. image:: pd_image005.png 
     89 
     90where *xmean* is the mean of the distribution and *Norm* is a normalization factor 
     91which is determined during the numerical calculation. 
     92 
     93The polydispersity is 
     94 
     95.. image:: pd_image003.png 
     96 
     97 
     98.. image:: pd_image006.jpg 
     99 
     100.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     101 
     102Lognormal Distribution 
     103^^^^^^^^^^^^^^^^^^^^^^ 
     104 
     105The Lognormal Distribution is defined as 
     106 
     107.. image:: pd_image007.png 
     108 
     109where |mu|\ =ln(*xmed*), *xmed* is the median value of the distribution, and 
     110*Norm* is a normalization factor which will be determined during the numerical 
     111calculation. 
     112 
     113The median value for the distribution will be the value given for the respective 
     114size parameter in the *Fitting Perspective*, for example, radius = 60. 
     115 
     116The polydispersity is given by |sigma| 
     117 
     118.. image:: pd_image008.png 
     119 
     120For the angular distribution 
     121 
     122.. image:: pd_image009.png 
     123 
     124The mean value is given by *xmean*\ =exp(|mu|\ +p\ :sup:`2`\ /2). The peak value 
     125is given by *xpeak*\ =exp(|mu|-p\ :sup:`2`\ ). 
     126 
     127.. image:: pd_image010.jpg 
     128 
     129This distribution function spreads more, and the peak shifts to the left, as *p* 
     130increases, requiring higher values of Nsigmas and Npts. 
     131 
     132.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     133 
     134Schulz Distribution 
     135^^^^^^^^^^^^^^^^^^^ 
     136 
     137The Schulz distribution is defined as 
     138 
     139.. image:: pd_image011.png 
     140 
     141where *xmean* is the mean of the distribution and *Norm* is a normalization factor 
     142which is determined during the numerical calculation, and *z* is a measure of the 
     143width of the distribution such that 
     144 
     145z = (1-p\ :sup:`2`\ ) / p\ :sup:`2` 
     146 
     147The polydispersity is 
     148 
     149.. image:: pd_image012.png 
     150 
     151Note that larger values of PD might need larger values of Npts and Nsigmas. 
     152For example, at PD=0.7 and radius=60 |Ang|, Npts>=160 and Nsigmas>=15 at least. 
     153 
     154.. image:: pd_image013.jpg 
     155 
     156For further information on the Schulz distribution see: 
     157M Kotlarchyk & S-H Chen, *J Chem Phys*, (1983), 79, 2461. 
    75158 
    76159.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    … …  
    79162^^^^^^^^^^^^^^^^^^ 
    80163 
    81 This distribution is to be given by users as a txt file where the array  
    82 should be defined by two columns in the order of x and f(x) values. The f(x)  
     164This user-definable distribution should be given as as a simple ASCII text file 
     165where the array is defined by two columns of numbers: *x* and *f(x)*. The *f(x)* 
    83166will be normalized by SasView during the computation. 
    84167 
    85 Example of an array in the file 
    86  
    87 30        0.1 
    88 32        0.3 
    89 35        0.4 
    90 36        0.5 
    91 37        0.6 
    92 39        0.7 
    93 41        0.9 
    94  
    95 We use only these array values in the computation, therefore the mean value  
    96 given in the control panel, for example ‘radius = 60’, will be ignored. 
    97  
    98 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    99  
    100 Gaussian Distribution 
    101 ^^^^^^^^^^^^^^^^^^^^^ 
    102  
    103 .. image:: pd_image005.png 
    104  
    105 The xmean is the mean of the distribution and Norm is a normalization factor  
    106 which is determined during the numerical calculation. 
    107  
    108 The PD (polydispersity) is 
    109  
    110 .. image:: pd_image003.png 
    111  
    112 .. image:: pd_image006.jpg 
    113  
    114 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    115  
    116 Lognormal Distribution 
    117 ^^^^^^^^^^^^^^^^^^^^^^ 
    118  
    119 .. image:: pd_image007.png 
    120  
    121 The /mu/=ln(xmed), xmed is the median value of the distribution, and Norm is a  
    122 normalization factor which will be determined during the numerical calculation.  
    123 The median value is the value given in the size parameter in the control panel,  
    124 for example, “radius = 60â€ￜ. 
    125  
    126 The PD (polydispersity) is given by /sigma/ 
    127  
    128 .. image:: pd_image008.png 
    129  
    130 For the angular distribution 
    131  
    132 .. image:: pd_image009.png 
    133  
    134 The mean value is given by xmean=exp(/mu/+p2/2). The peak value is given by  
    135 xpeak=exp(/mu/-p2). 
    136  
    137 .. image:: pd_image010.jpg 
    138  
    139 This distribution function spreads more and the peak shifts to the left as the  
    140 p increases, requiring higher values of Nsigmas and Npts. 
    141  
    142 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    143  
    144 Schulz Distribution 
    145 ^^^^^^^^^^^^^^^^^^^ 
    146  
    147 .. image:: pd_image011.png 
    148  
    149 The xmean is the mean of the distribution and Norm is a normalization factor 
    150 which is determined during the numerical calculation. 
    151  
    152 The z = 1/p2– 1. 
    153  
    154 The PD (polydispersity) is 
    155  
    156 .. image:: pd_image012.png 
    157  
    158 Note that the higher PD (polydispersity) might need higher values of Npts and  
    159 Nsigmas. For example, at PD = 0.7 and radisus = 60 A, Npts >= 160, and  
    160 Nsigmas >= 15 at least. 
    161  
    162 .. image:: pd_image013.jpg 
    163  
    164 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     168Example of what an array distribution file should look like: 
     169 
     170====  ===== 
     171 30    0.1 
     172 32    0.3 
     173 35    0.4 
     174 36    0.5 
     175 37    0.6 
     176 39    0.7 
     177 41    0.9 
     178====  ===== 
     179 
     180SasView only uses these array values during the computation, therefore any mean 
     181value of the parameter represented by *x* present in the *Fitting Perspective* 
     182will be ignored. 
     183 
     184.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     185 
     186Note about DLS polydispersity 
     187^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 
     188 
     189Many commercial Dynamic Light Scattering (DLS) instruments produce a size 
     190polydispersity parameter, sometimes even given the symbol *p*! This parameter is 
     191defined as the relative standard deviation coefficient of variation of the size 
     192distribution and is NOT the same as the polydispersity parameters in the Lognormal 
     193and Schulz distributions above (though they all related) except when the DLS 
     194polydispersity parameter is <0.13. 
     195 
     196For more information see: 
     197S King, C Washington & R Heenan, *Phys Chem Chem Phys*, (2005), 7, 143 
     198 
     199.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     200 
     201.. note::  This help document was last changed by Steve King, 01May2015 
Note: See TracChangeset for help on using the changeset viewer.