| 1 | #pragma rtGlobals=1 // Use modern global access method. |
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| 2 | |
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| 3 | //////////////////////////////////////////////// |
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| 4 | // GaussUtils.proc and PlotUtils.proc MUST be included for the smearing calculation to compile |
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| 5 | // Adopting these into the experiment will insure that they are always present |
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| 6 | //////////////////////////////////////////////// |
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| 7 | // this function is for the form factor of a right circular cylinder with uniform scattering length density |
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| 8 | // |
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| 9 | // 06 NOV 98 SRK |
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| 10 | //////////////////////////////////////////////// |
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| 11 | |
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| 12 | Proc PlotCylinderForm(num,qmin,qmax) |
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| 13 | Variable num=128,qmin=0.001,qmax=0.7 |
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| 14 | Prompt num "Enter number of data points for model: " |
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| 15 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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| 16 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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| 17 | |
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| 18 | make/o/D/n=(num) xwave_cyl,ywave_cyl |
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| 19 | xwave_cyl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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| 20 | make/o/D coef_cyl = {1.,20.,400,3.0e-6,0.01} |
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| 21 | make/o/t parameters_cyl = {"scale","radius (A)","length (A)","contrast (A^-2)","incoh. bkg (cm^-1)"} |
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| 22 | Edit parameters_cyl,coef_cyl |
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| 23 | ywave_cyl := CylinderForm(coef_cyl,xwave_cyl) |
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| 24 | Display ywave_cyl vs xwave_cyl |
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| 25 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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| 26 | Label bottom "q (\\S-1\\M)" |
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| 27 | Label left "Intensity (cm\\S-1\\M)" |
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| 28 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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| 29 | End |
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| 30 | /////////////////////////////////////////////////////////// |
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| 31 | |
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| 32 | Proc PlotSmearedCylinderForm() |
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| 33 | //no input parameters necessary, it MUST use the experimental q-values |
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| 34 | // from the experimental data read in from an AVE/QSIG data file |
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| 35 | |
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| 36 | // if no gQvals wave, data must not have been loaded => abort |
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| 37 | if(ResolutionWavesMissing()) |
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| 38 | Abort |
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| 39 | endif |
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| 40 | |
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| 41 | // Setup parameter table for model function |
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| 42 | make/o/D smear_coef_cyl = {1.,20.,400,3.0e-6,0.01} |
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| 43 | make/o/t smear_parameters_cyl = {"scale","radius (A)","length (A)","contrast (A^-2)","incoh. bkg (cm^-1)"} |
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| 44 | Edit smear_parameters_cyl,smear_coef_cyl |
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| 45 | |
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| 46 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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| 47 | // make extra copy of experimental q-values for easy plotting |
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| 48 | Duplicate/O $gQvals smeared_cyl,smeared_qvals |
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| 49 | SetScale d,0,0,"1/cm",smeared_cyl |
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| 50 | |
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| 51 | smeared_cyl := SmearedCylinderForm(smear_coef_cyl,$gQvals) |
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| 52 | Display smeared_cyl vs smeared_qvals |
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| 53 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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| 54 | Label bottom "q (\\S-1\\M)" |
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| 55 | Label left "Intensity (cm\\S-1\\M)" |
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| 56 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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| 57 | End |
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| 58 | |
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| 59 | /////////////////////////////////////////////////////////////// |
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| 60 | // unsmeared model calculation |
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| 61 | /////////////////////////// |
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| 62 | Function CylinderForm(w,x) : FitFunc |
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| 63 | Wave w |
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| 64 | Variable x |
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| 65 | |
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| 66 | String funcStr = SelectString(exists("CylinderFormX")==3,"", "CylinderFormX") |
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| 67 | if(strlen(funcStr) > 0) |
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| 68 | FUNCREF SANSModel_proto func=$funcStr |
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| 69 | return func(w,x) |
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| 70 | endif |
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| 71 | |
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| 72 | //The input variables are (and output) |
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| 73 | //[0] scale |
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| 74 | //[1] cylinder RADIUS (A) |
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| 75 | //[2] total cylinder LENGTH (A) |
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| 76 | //[3] contrast (A^-2) |
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| 77 | //[4] background (cm^-1) |
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| 78 | Variable scale, radius,length,delrho,bkg |
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| 79 | scale = w[0] |
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| 80 | radius = w[1] |
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| 81 | length = w[2] |
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| 82 | delrho = w[3] |
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| 83 | bkg = w[4] |
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| 84 | // |
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| 85 | // the OUTPUT form factor is <f^2>/Vcyl [cm-1] |
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| 86 | // |
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| 87 | |
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| 88 | // local variables |
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| 89 | Variable nord,ii,va,vb,contr,vcyl,nden,summ,yyy,zi,qq,halfheight |
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| 90 | Variable answer |
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| 91 | String weightStr,zStr |
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| 92 | |
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| 93 | weightStr = "gauss76wt" |
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| 94 | zStr = "gauss76z" |
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| 95 | |
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| 96 | |
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| 97 | // if wt,z waves don't exist, create them |
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| 98 | // 20 Gauss points is not enough for cylinder calculation |
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| 99 | |
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| 100 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
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| 101 | Make/D/N=76 $weightStr,$zStr |
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| 102 | Wave w76 = $weightStr |
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| 103 | Wave z76 = $zStr // wave references to pass |
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| 104 | Make76GaussPoints(w76,z76) |
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| 105 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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| 106 | else |
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| 107 | if(exists(weightStr) > 1) |
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| 108 | Abort "wave name is already in use" // execute if condition is false |
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| 109 | endif |
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| 110 | Wave w76 = $weightStr |
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| 111 | Wave z76 = $zStr // Not sure why this has to be "declared" twice |
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| 112 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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| 113 | endif |
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| 114 | |
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| 115 | |
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| 116 | // set up the integration |
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| 117 | // end points and weights |
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| 118 | nord = 76 |
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| 119 | va = 0 |
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| 120 | vb = Pi/2.0 |
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| 121 | halfheight = length/2.0 |
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| 122 | |
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| 123 | // evaluate at Gauss points |
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| 124 | // remember to index from 0,size-1 |
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| 125 | |
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| 126 | qq = x //current x point is the q-value for evaluation |
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| 127 | summ = 0.0 // initialize integral |
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| 128 | ii=0 |
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| 129 | do |
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| 130 | // Using 76 Gauss points |
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| 131 | zi = ( z76[ii]*(vb-va) + vb + va )/2.0 |
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| 132 | yyy = w76[ii] * cyl(qq, radius, halfheight, zi) |
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| 133 | summ += yyy |
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| 134 | |
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| 135 | ii+=1 |
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| 136 | while (ii<nord) // end of loop over quadrature points |
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| 137 | // |
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| 138 | // calculate value of integral to return |
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| 139 | |
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| 140 | answer = (vb-va)/2.0*summ |
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| 141 | |
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| 142 | // Multiply by contrast^2 |
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| 143 | answer *= delrho*delrho |
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| 144 | //normalize by cylinder volume |
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| 145 | //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
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| 146 | vcyl=Pi*radius*radius*length |
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| 147 | answer *= vcyl |
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| 148 | //convert to [cm-1] |
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| 149 | answer *= 1.0e8 |
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| 150 | //Scale |
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| 151 | answer *= scale |
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| 152 | // add in the background |
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| 153 | answer += bkg |
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| 154 | |
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| 155 | Return (answer) |
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| 156 | |
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| 157 | End //End of function CylinderForm() |
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| 158 | |
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| 159 | /////////////////////////////////////////////////////////////// |
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| 160 | Function cyl(qq,rr,h,theta) |
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| 161 | Variable qq,rr,h,theta |
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| 162 | |
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| 163 | // qq is the q-value for the calculation (1/A) |
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| 164 | // rr is the radius of the cylinder (A) |
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| 165 | // h is the HALF-LENGTH of the cylinder = L/2 (A) |
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| 166 | |
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| 167 | //Local variables |
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| 168 | Variable besarg,bj,retval,d1,t1,b1,t2,b2 |
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| 169 | besarg = qq*rr*sin(theta) |
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| 170 | |
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| 171 | bj =bessJ(1,besarg) |
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| 172 | |
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| 173 | //* Computing 2nd power */ |
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| 174 | d1 = sin(qq * h * cos(theta)) |
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| 175 | t1 = d1 * d1 |
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| 176 | //* Computing 2nd power */ |
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| 177 | d1 = bj |
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| 178 | t2 = d1 * d1 * 4.0 * sin(theta) |
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| 179 | //* Computing 2nd power */ |
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| 180 | d1 = qq * h * cos(theta) |
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| 181 | b1 = d1 * d1 |
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| 182 | //* Computing 2nd power */ |
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| 183 | d1 = qq * rr * sin(theta) |
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| 184 | b2 = d1 * d1 |
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| 185 | retval = t1 * t2 / b1 / b2 |
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| 186 | |
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| 187 | return retval |
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| 188 | |
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| 189 | End //Function cyl() |
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| 190 | |
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| 191 | // this is all there is to the smeared calculation! |
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| 192 | Function SmearedCylinderForm(w,x) :FitFunc |
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| 193 | Wave w |
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| 194 | Variable x |
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| 195 | |
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| 196 | Variable ans |
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| 197 | SVAR sq = gSig_Q |
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| 198 | SVAR qb = gQ_bar |
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| 199 | SVAR sh = gShadow |
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| 200 | SVAR gQ = gQVals |
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| 201 | |
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| 202 | //the name of your unsmeared model is the first argument |
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| 203 | if(exists("CylinderFormX") == 3) |
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| 204 | ans = Smear_Model_20($"CylinderFormX",$sq,$qb,$sh,$gQ,w,x) |
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| 205 | else |
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| 206 | ans = Smear_Model_20(CylinderForm,$sq,$qb,$sh,$gQ,w,x) |
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| 207 | endif |
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| 208 | |
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| 209 | return(ans) |
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| 210 | End |
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| 211 | |
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