source: sans/Analysis/trunk/Put in User Procedures/SANS_Models_v3.00/CoreShellCylinder.ipf @ 42

#pragma rtGlobals=1             // Use modern global access method.

////////////////////////////////////////////////
// GaussUtils.proc and PlotUtils.proc MUST be included for the smearing calculation to compile
// Adopting these into the experiment will insure that they are always present
////////////////////////////////////////////////
// this function is for the form factor of a right circular cylinder with core/shell scattering length density profile
//
// the core dimensions are given and a constant shell thickness is added to the radius and to dach and of the length
// this way, the scattering amplitude is simply the difference between two cylinders of different dimensions
//
// 06 NOV 98 SRK
////////////////////////////////////////////////

Proc PlotCoreShellCylinderForm(num,qmin,qmax)
        Variable num=128,qmin=0.001,qmax=0.7
        Prompt num "Enter number of data points for model: "
        Prompt qmin "Enter minimum q-value (^-1) for model: "
        Prompt qmax "Enter maximum q-value (^-1) for model: "
        
        make/o/d/n=(num) xwave_cscyl,ywave_cscyl
        xwave_cscyl =  alog(log(qmin) + x*((log(qmax)-log(qmin))/num))
        make/o/d coef_cscyl = {1.,20.,10.,400,1.0e-6,4.0e-6,1.0e-6,0.01}
        make/o/t parameters_cscyl = {"scale","core radius (A)","shell THICKNESS (A)","CORE length (A)","SLD core (A^-2)","SLD shell (A^-2)","SLD solvent (A^-2)","incoh. bkg (cm^-1)"}
        Edit parameters_cscyl,coef_cscyl
        ywave_cscyl := CoreShellCylinderForm(coef_cscyl,xwave_cscyl)
        Display ywave_cscyl vs xwave_cscyl
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End
///////////////////////////////////////////////////////////

Proc PlotSmearedCSCylinderForm()        
        //no input parameters necessary, it MUST use the experimental q-values
        // from the experimental data read in from an AVE/QSIG data file
        
        // if no gQvals wave, data must not have been loaded => abort
        if(ResolutionWavesMissing())
                Abort
        endif
        
        // Setup parameter table for model function
        make/o/d smear_coef_cscyl =  {1.,20.,10.,400,1.0e-6,4.0e-6,1.0e-6,0.01}
        make/o/t smear_parameters_cscyl = {"scale","core radius (A)","shell radius (A)","length (A)","SLD core (A^-2)","SLD shell (A^-2)","SLD solvent (A^-2)","incoh. bkg (cm^-1)"}
        Edit smear_parameters_cscyl,smear_coef_cscyl
        
        // output smeared intensity wave, dimensions are identical to experimental QSIG values
        // make extra copy of experimental q-values for easy plotting
        Duplicate/O $gQvals smeared_cscyl,smeared_qvals
        SetScale d,0,0,"1/cm",smeared_cscyl     

        smeared_cscyl := SmearedCoreShellCylinderForm(smear_coef_cscyl,$gQvals)
        Display smeared_cscyl vs smeared_qvals
        ModifyGraph log=1,marker=29,msize=2,mode=4
        Label bottom "q (\\S-1\\M)"
        Label left "Intensity (cm\\S-1\\M)"
        AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2)
End

///////////////////////////////////////////////////////////////
// unsmeared model calculation
///////////////////////////
Function CoreShellCylinderForm(w,x) : FitFunc
        Wave w
        Variable x

//The input variables are (and output)
        //[0] scale
        //[1] cylinder CORE RADIUS (A)
        //[2] shell Thickness (A)
        //[3]  cylinder CORE LENGTH (A)
        //[4] core SLD (A^-2)
        //[5] shell SLD (A^-2)
        //[6] solvent SLD (A^-2)
        //[7] background (cm^-1)
        Variable scale,length,delrho,bkg,rcore,thick,rhoc,rhos,rhosolv
        scale = w[0]
        rcore = w[1]
        thick = w[2]
        length = w[3]
        rhoc = w[4]
        rhos = w[5]
        rhosolv = w[6]
        bkg = w[7]
//
// the OUTPUT form factor is <f^2>/Vcyl [cm-1]
//

// local variables
        Variable nord,ii,va,vb,contr,vcyl,nden,summ,yyy,zi,qq,halfheight
        Variable answer
        String weightStr,zStr
        
        weightStr = "gauss76wt"
        zStr = "gauss76z"

        
//      if wt,z waves don't exist, create them
// 20 Gauss points is not enough for cylinder calculation
        
        if (WaveExists($weightStr) == 0) // wave reference is not valid, 
                Make/D/N=76 $weightStr,$zStr
                Wave w76 = $weightStr
                Wave z76 = $zStr                // wave references to pass
                Make76GaussPoints(w76,z76)      
        //                  printf "w[0],z[0] = %g %g\r", w76[0],z76[0]
        else
                if(exists(weightStr) > 1) 
                         Abort "wave name is already in use"    // execute if condition is false
                endif
                Wave w76 = $weightStr
                Wave z76 = $zStr                // Not sure why this has to be "declared" twice
        //          printf "w[0],z[0] = %g %g\r", w76[0],z76[0] 
        endif


// set up the integration
        // end points and weights
        nord = 76
        va = 0
        vb = Pi/2
      halfheight = length/2.0

// evaluate at Gauss points 
        // remember to index from 0,size-1

        qq = x          //current x point is the q-value for evaluation
      summ = 0.0                // initialize integral
      ii=0
      do
                // Using 76 Gauss points
                zi = ( z76[ii]*(vb-va) + vb + va )/2.0          
                yyy = w76[ii] * CoreShellcyl(qq, rcore, thick, rhoc,rhos,rhosolv, halfheight, zi)
                summ += yyy 

                ii+=1
        while (ii<nord)                         // end of loop over quadrature points
//   
// calculate value of integral to return

      answer = (vb-va)/2.0*summ
      
// contrast is now explicitly included in the core-shell calculation

//normalize by cylinder volume
//NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl
//calculate TOTAL volume
// length is the total core length 
        vcyl=Pi*(rcore+thick)*(rcore+thick)*(length+2*thick)
        answer /= vcyl
//convert to [cm-1]
        answer *= 1.0e8
//Scale
        answer *= scale
// add in the background
        answer += bkg

        Return (answer)
        
End             //End of function CoreShellCylinderForm()

///////////////////////////////////////////////////////////////
// F(qq, rcore, thick, rhoc,rhos,rhosolv, length, zi)
//
Function CoreShellcyl(qq, rcore, thick, rhoc,rhos,rhosolv, length, dum)
        Variable qq, rcore, thick, rhoc,rhos,rhosolv, length, dum
        
// qq is the q-value for the calculation (1/A)
// rcore is the core radius of the cylinder (A)
//thick is the uniform thickness
// rho(n) are the respective SLD's

// length is the *Half* CORE-LENGTH of the cylinder = L (A)

// dum is the dummy variable for the integration (x in Feigin's notation)

   //Local variables 
        Variable dr1,dr2,besarg1,besarg2,vol1,vol2,sinarg1,sinarg2,t1,t2,retval
        
        dr1 = rhoc-rhos
        dr2 = rhos-rhosolv
        vol1 = Pi*rcore*rcore*(2*length)
        vol2 = Pi*(rcore+thick)*(rcore+thick)*(2*length+2*thick)
        
        besarg1 = qq*rcore*sin(dum)
        besarg2 = qq*(rcore+thick)*sin(dum)
        sinarg1 = qq*length*cos(dum)
        sinarg2 = qq*(length+thick)*cos(dum)
        
        t1 = 2*vol1*dr1*sin(sinarg1)/sinarg1*bessJ(1,besarg1)/besarg1
        t2 = 2*vol2*dr2*sin(sinarg2)/sinarg2*bessJ(1,besarg2)/besarg2
        
        retval = ((t1+t2)^2)*sin(dum)
        
    return retval
    
End     //Function CoreShellcyl()

// this is all there is to the smeared calculation!
Function SmearedCoreShellCylinderForm(w,x) :FitFunc
        Wave w
        Variable x
        
        Variable ans
        SVAR sq = gSig_Q
        SVAR qb = gQ_bar
        SVAR sh = gShadow
        SVAR gQ = gQVals
        
        //the name of your unsmeared model is the first argument
        ans = Smear_Model_20(CoreShellCylinderForm,$sq,$qb,$sh,$gQ,w,x)

        return(ans)
End