Index: src/sas/perspectives/fitting/media/fitting_help.rst
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--- src/sas/perspectives/fitting/media/fitting_help.rst	(revision 98b30b46ac241d857a5698740991daae2c25c3c2)
+++ src/sas/perspectives/fitting/media/fitting_help.rst	(revision 4c42410a7267a64ab2b07c60e1bb0ebbc9e3b8f0)
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 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 
-..  _Polydispersity_Distributions:
-
-Polydispersity Distributions
-----------------------------
-
-Calculates the form factor for a polydisperse and/or angular population of 
-particles with uniform scattering length density. The resultant form factor 
-is normalized by the average particle volume such that 
-
-P(q) = scale*\<F*F\>/Vol + bkg
-
-where F is the scattering amplitude and the\<\>denote an average over the size 
-distribution.  Users should use PD (polydispersity: this definition is 
-different from the typical definition in polymer science) for a size 
-distribution and Sigma for an angular distribution (see below).
-
-Note that this computation is very time intensive thus applying polydispersion/
-angular distrubtion for more than one paramters or increasing Npts values 
-might need extensive patience to complete the computation. Also note that 
-even though it is time consuming, it is safer to have larger values of Npts 
-and Nsigmas.
-
-The following five distribution functions are provided
-
-*  *Rectangular_Distribution_*
-*  *Array_Distribution_*
-*  *Gaussian_Distribution_*
-*  *Lognormal_Distribution_*
-*  *Schulz_Distribution_*
-
-.. _Rectangular_Distribution:
-
-Rectangular Distribution
-------------------------
-
-.. image:: pd_image001.png
-
-The xmean is the mean of the distribution, w is the half-width, and Norm is a 
-normalization factor which is determined during the numerical calculation. 
-Note that the Sigma and the half width *w*  are different.
-
-The standard deviation is
-
-.. image:: pd_image002.png
-
-The PD (polydispersity) is
-
-.. image:: pd_image003.png
-
-.. image:: pd_image004.jpg
-
-.. _Array_Distribution:
-
-Array Distribution
-------------------
-
-This distribution is to be given by users as a txt file where the array 
-should be defined by two columns in the order of x and f(x) values. The f(x) 
-will be normalized by SasView during the computation.
-
-Example of an array in the file
-
-30        0.1
-32        0.3
-35        0.4
-36        0.5
-37        0.6
-39        0.7
-41        0.9
-
-We use only these array values in the computation, therefore the mean value 
-given in the control panel, for example Ã¢â¬Ëradius = 60Ã¢â¬â¢, will be ignored.
-
-.. _Gaussian_Distribution:
-
-Gaussian Distribution
----------------------
-
-.. image:: pd_image005.png
-
-The xmean is the mean of the distribution and Norm is a normalization factor 
-which is determined during the numerical calculation.
-
-The PD (polydispersity) is
-
-.. image:: pd_image003.png
-
-.. image:: pd_image006.jpg
-
-.. _Lognormal_Distribution:
-
-Lognormal Distribution
-----------------------
-
-.. image:: pd_image007.png
-
-The /mu/=ln(xmed), xmed is the median value of the distribution, and Norm is a 
-normalization factor which will be determined during the numerical calculation. 
-The median value is the value given in the size parameter in the control panel, 
-for example, Ã¢â¬Åradius = 60Ã¢â¬ï¿œ.
-
-The PD (polydispersity) is given by /sigma/
-
-.. image:: pd_image008.png
-
-For the angular distribution
-
-.. image:: pd_image009.png
-
-The mean value is given by xmean=exp(/mu/+p2/2). The peak value is given by 
-xpeak=exp(/mu/-p2).
-
-.. image:: pd_image010.jpg
-
-This distribution function spreads more and the peak shifts to the left as the 
-p increases, requiring higher values of Nsigmas and Npts.
-
-.. _Schulz_Distribution:
-
-Schulz Distribution
--------------------
-
-.. image:: pd_image011.png
-
-The xmean is the mean of the distribution and Norm is a normalization factor
-which is determined during the numerical calculation.
-
-The z = 1/p2Ã¢â¬â 1.
-
-The PD (polydispersity) is
-
-.. image:: pd_image012.png
-
-Note that the higher PD (polydispersity) might need higher values of Npts and 
-Nsigmas. For example, at PD = 0.7 and radisus = 60 A, Npts >= 160, and 
-Nsigmas >= 15 at least.
-
-.. image:: pd_image013.jpg
-
-.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
-
-.. _Smearing_Computation:
-
-Smearing Computation
---------------------
-
-Slit_Smearing_ 
-
-Pinhole_Smearing_
-
-2D_Smearing_
-
-.. _Slit_Smearing:
-
-Slit Smearing
--------------
-
-The sit smeared scattering intensity for SAS is defined by
-
-.. image:: sm_image002.gif
-
-where Norm =
-
-.. image:: sm_image003.gif
-
-Equation 1
-
-The functions |inlineimage004| and |inlineimage005|
-refer to the slit width weighting function and the slit height weighting 
-determined at the q point, respectively. Here, we assumes that the weighting 
-function is described by a rectangular function, i.e.,
-
-.. image:: sm_image006.gif
-
-Equation 2
-
-and
-
-.. image:: sm_image007.gif
-
-Equation 3
-
-so that |inlineimage008| |inlineimage009| for |inlineimage010| and u.
-
-The |inlineimage011| and |inlineimage012| stand for
-the slit height (FWHM/2) and the slit width (FWHM/2) in the q space. Now the 
-integral of Equation 1 is simplified to
-
-.. image:: sm_image013.gif
-
-Equation 4
-
-Numerical Implementation of Equation 4
---------------------------------------
-
-Case 1
-------
-
-For |inlineimage012| = 0 and |inlineimage011| = constant.
-
-.. image:: sm_image016.gif
-
-For discrete q values, at the q values from the data points and at the q 
-values extended up to qN= qi + |inlineimage011| the smeared 
-intensity can be calculated approximately
-
-.. image:: sm_image017.gif
-
-Equation 5
-
-|inlineimage018| = 0 for *Is* in *j* < *i* or *j* > N-1*.
-
-Case 2
-------
-
-For |inlineimage012| = constant and |inlineimage011| = 0.
-
-Similarly to Case 1, we get
-
-|inlineimage019| for qp= qi- |inlineimage012| and qN= qi+ |inlineimage012|. |inlineimage018| = 0
-for *Is* in *j* < *p* or *j* > *N-1*.
-
-Case 3
-------
-
-For |inlineimage011| = constant and 
-|inlineimage011| = constant.
-
-In this case, the best way is to perform the integration, Equation 1, 
-numerically for both slit height and width. However, the numerical integration 
-is not correct enough unless given a large number of iteration, say at least 
-10000 by 10000 for each element of the matrix, W, which will take minutes and 
-minutes to finish the calculation for a set of typical SAS data. An 
-alternative way which is correct for slit width << slit hight, is used in 
-SasView. This method is a mixed method that combines method 1 with the 
-numerical integration for the slit width.
-
-.. image:: sm_image020.gif
-
-Equation 7
-
-for qp= qi- |inlineimage012| and
-qN= qi+ |inlineimage012|. |inlineimage018| = 0 for
-*Is* in *j* < *p* or *j* > *N-1*.
-
-.. _Pinhole_Smearing:
-
-Pinhole Smearing
-----------------
-
-The pinhole smearing computation is done similar to the case above except 
-that the weight function used is the Gaussian function, so that the Equation 6 
-for this case becomes
-
-.. image:: sm_image021.gif
-
-Equation 8
-
-For all the cases above, the weighting matrix *W* is calculated when the 
-smearing is called at the first time, and it includes the ~ 60 q values 
-(finely binned evenly) below (\>0) and above the q range of data in order 
-to cover all data points of the smearing computation for a given model and 
-for a given slit size. The *Norm*  factor is found numerically with the 
-weighting matrix, and considered on *Is* computation.
-
-.. _2D_Smearing:
-
-2D Smearing
------------ 
-
-The 2D smearing computation is done similar to the 1D pinhole smearing above 
-except that the weight function used was the 2D elliptical Gaussian function
-
-.. image:: sm_image022.gif
-
-Equation 9
-
-In Equation 9, x0 = qcos/theta/ and y0 = qsin/theta/, and the primed axes 
-are in the coordinate rotated by an angle /theta/ around the z-axis (below) 
-so that xÃ¢â¬â¢0= x0cos/theta/+y0sin/theta/ and yÃ¢â¬â¢0= -x0sin/theta/+y0cos/theta/.
-
-Note that the rotation angle is zero for x-y symmetric elliptical Gaussian 
-distribution. The A is a normalization factor.
-
-.. image:: sm_image023.gif
-
-Now we consider a numerical integration where each bins in /theta/ and R are 
-*evenly* (this is to simplify the equation below) distributed by /delta//theta/ 
-and /delta/R, respectively, and it is assumed that I(xÃ¢â¬â¢, yÃ¢â¬â¢) is constant 
-within the bins which in turn becomes
-
-.. image:: sm_image024.gif
-
-Equation 10
-
-Since we have found the weighting factor on each bin points, it is convenient 
-to transform xÃ¢â¬â¢-yÃ¢â¬â¢ back to x-y coordinate (rotating it by -/theta/ around z 
-axis). Then, for the polar symmetric smear
-
-.. image:: sm_image025.gif
-
-Equation 11
-
-where
-
-.. image:: sm_image026.gif
-
-while for the x-y symmetric smear
-
-.. image:: sm_image027.gif
-
-Equation 12
-
-where
-
-.. image:: sm_image028.gif
-
-Here, the current version of the SasView uses Equation 11 for 2D smearing 
-assuming that all the Gaussian weighting functions are aligned in the polar 
-coordinate.
-
-In the control panel, the higher accuracy indicates more and finer binnng 
-points so that it costs more in time.
-
-.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
-
-.. _Polarisation_Magnetic_Scattering:
-
-Polarisation/Magnetic Scattering
---------------------------------
-
-Magnetic scattering is implemented in five (2D) models 
-
-*  *SphereModel*
-*  *CoreShellModel*
-*  *CoreMultiShellModel*
-*  *CylinderModel*
-*  *ParallelepipedModel*
-
-In general, the scattering length density (SLD) in each regions where the 
-SLD (=/beta/) is uniform, is a combination of the nuclear and magnetic SLDs and 
-depends on the spin states of the neutrons as follows. For magnetic scattering, 
-only the magnetization component, *M*perp, perpendicular to the scattering 
-vector *Q* contributes to the the magnetic scattering length.
-
-.. image:: mag_vector.bmp
-
-The magnetic scattering length density is then
-
-.. image:: dm_eq.gif
-
-where /gamma/ = -1.913 the gyromagnetic ratio, /mu/B is the Bohr magneton, r0 
-is the classical radius of electron, and */sigma/* is the Pauli spin. For 
-polarised neutron, the magnetic scattering is depending on the spin states. 
-
-Let's consider that the incident neutrons are polarized parallel (+)/
-anti-parallel (-) to the x' axis (See both Figures above). The possible 
-out-coming states then are + and - states for both incident states
-
-Non-spin flips: (+ +) and (- -)
-Spin flips:     (+ -) and (- +)
-
-.. image:: M_angles_pic.bmp
-
-Now, let's assume that the angles of the *Q*  vector and the spin-axis (x') 
-against x-axis are /phi/ and /theta/up, respectively (See Figure above). Then, 
-depending upon the polarisation (spin) state of neutrons, the scattering length 
-densities, including the nuclear scattering length density (/beta/N) are given 
-as, for non-spin-flips
-
-.. image:: sld1.gif
-
-for spin-flips
-
-.. image:: sld2.gif
-
-where
-
-.. image:: mxp.gif
-
-.. image:: myp.gif
-
-.. image:: mzp.gif
-
-.. image:: mqx.gif
-
-.. image:: mqy.gif
-
-Here, the M0x, M0y and M0z are the x, y and z components of the magnetization 
-vector given in the xyz lab frame. The angles of the magnetization, /theta/M 
-and /phi/M as defined in the Figure (above)
-
-.. image:: m0x_eq.gif
-
-.. image:: m0y_eq.gif
-
-.. image:: m0z_eq.gif
-
-The user input parameters are M0_sld = DMM0, Up_theta = /theta/up, 
-M_theta = /theta/M, and M_phi = /phi/M. The 'Up_frac_i' and 'Up_frac_f' are 
-the ratio
-
-(spin up)/(spin up + spin down)
-
-neutrons before the sample and at the analyzer, respectively.
-
-*Note:* The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range
-between 0 and 1.
-
-.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
-
 .. _Key_Combinations:
 
