1 | #pragma rtGlobals=1 // Use modern global access method. |
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2 | #pragma IgorVersion = 6.0 |
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3 | |
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4 | //////////////////////////////////////////////// |
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5 | // GaussUtils.proc and PlotUtils.proc MUST be included for the smearing calculation to compile |
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6 | // Adopting these into the experiment will insure that they are always present |
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7 | //////////////////////////////////////////////// |
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8 | // this function is for the form factor of a right circular cylinder with uniform scattering length density |
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9 | // |
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10 | // 06 NOV 98 SRK |
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11 | //////////////////////////////////////////////// |
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12 | |
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13 | Proc PlotHollowCylinderForm(num,qmin,qmax) |
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14 | Variable num=128,qmin=0.001,qmax=0.7 |
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15 | Prompt num "Enter number of data points for model: " |
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16 | Prompt qmin "Enter minimum q-value (^-1) for model: " |
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17 | Prompt qmax "Enter maximum q-value (^-1) for model: " |
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18 | |
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19 | Make/O/D/n=(num) xwave_Hcyl,ywave_Hcyl |
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20 | xwave_Hcyl = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
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21 | Make/O/D coef_Hcyl = {1.,20.,30.,400,3.0e-6,0.01} |
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22 | make/o/t parameters_Hcyl = {"scale","core radius (A)","shell radius (A)","length (A)","contrast (A^-2)","incoh. bkg (cm^-1)"} |
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23 | Edit parameters_Hcyl,coef_Hcyl |
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24 | Variable/G root:g_hcyl |
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25 | g_Hcyl := HollowCylinder(coef_Hcyl,ywave_Hcyl,xwave_Hcyl) |
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26 | // ywave_Hcyl := HollowCylinder(coef_Hcyl,xwave_Hcyl) |
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27 | Display ywave_Hcyl vs xwave_Hcyl |
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28 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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29 | Label bottom "q (\\S-1\\M)" |
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30 | Label left "Intensity (cm\\S-1\\M)" |
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31 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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32 | End |
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33 | |
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34 | /////////////////////////////////////////////////////////// |
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35 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
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36 | Proc PlotSmearedHollowCylinderForm(str) |
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37 | String str |
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38 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
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39 | |
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40 | // if any of the resolution waves are missing => abort |
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41 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
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42 | Abort |
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43 | endif |
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44 | |
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45 | SetDataFolder $("root:"+str) |
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46 | |
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47 | // Setup parameter table for model function |
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48 | Make/O/D smear_coef_Hcyl = {1.,20.,30.,400,3.0e-6,0.01} |
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49 | make/o/t smear_parameters_Hcyl = {"scale","core radius (A)","shell radius (A)","length (A)","contrast (A^-2)","incoh. bkg (cm^-1)"} |
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50 | Edit smear_parameters_Hcyl,smear_coef_Hcyl |
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51 | |
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52 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
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53 | // make extra copy of experimental q-values for easy plotting |
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54 | Duplicate/O $(str+"_q") smeared_Hcyl,smeared_qvals |
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55 | SetScale d,0,0,"1/cm",smeared_Hcyl |
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56 | |
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57 | Variable/G gs_Hcyl=0 |
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58 | gs_Hcyl := fSmearedHollowCylinder(smear_coef_Hcyl,smeared_Hcyl,smeared_qvals) //this wrapper fills the STRUCT |
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59 | |
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60 | Display smeared_Hcyl vs smeared_qvals |
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61 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
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62 | Label bottom "q (\\S-1\\M)" |
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63 | Label left "Intensity (cm\\S-1\\M)" |
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64 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
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65 | |
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66 | SetDataFolder root: |
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67 | End |
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68 | |
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69 | |
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70 | //AAO version |
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71 | Function HollowCylinder(cw,yw,xw) : FitFunc |
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72 | Wave cw,yw,xw |
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73 | |
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74 | #if exists("HollowCylinderX") |
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75 | yw = HollowCylinderX(cw,xw) |
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76 | #else |
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77 | yw = fHollowCylinder(cw,xw) |
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78 | #endif |
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79 | return(0) |
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80 | End |
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81 | /////////////////////////////////////////////////////////////// |
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82 | // unsmeared model calculation |
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83 | /////////////////////////// |
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84 | Function fHollowCylinder(w,x) : FitFunc |
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85 | Wave w |
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86 | Variable x |
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87 | |
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88 | //The input variables are (and output) |
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89 | //[0] scale |
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90 | //[1] cylinder CORE RADIUS (A) |
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91 | //[2] cylinder shell radius (A) |
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92 | //[3] total cylinder LENGTH (A) |
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93 | //[4] contrast (A^-2) |
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94 | //[5] background (cm^-1) |
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95 | Variable scale,length,delrho,bkg,rcore,rshell,contrast |
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96 | scale = w[0] |
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97 | rcore = w[1] |
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98 | rshell = w[2] |
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99 | length = w[3] |
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100 | contrast = w[4] |
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101 | bkg = w[5] |
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102 | // |
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103 | // the OUTPUT form factor is <f^2>/Vcyl [cm-1] |
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104 | // |
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105 | |
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106 | // local variables |
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107 | Variable nord,ii,va,vb,contr,vcyl,nden,summ,yyy,zi,qq,halfheight |
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108 | Variable answer |
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109 | String weightStr,zStr |
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110 | |
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111 | weightStr = "gauss76wt" |
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112 | zStr = "gauss76z" |
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113 | |
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114 | |
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115 | // if wt,z waves don't exist, create them |
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116 | // 20 Gauss points is not enough for cylinder calculation |
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117 | |
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118 | if (WaveExists($weightStr) == 0) // wave reference is not valid, |
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119 | Make/D/N=76 $weightStr,$zStr |
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120 | Wave w76 = $weightStr |
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121 | Wave z76 = $zStr // wave references to pass |
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122 | Make76GaussPoints(w76,z76) |
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123 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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124 | else |
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125 | if(exists(weightStr) > 1) |
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126 | Abort "wave name is already in use" // execute if condition is false |
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127 | endif |
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128 | Wave w76 = $weightStr |
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129 | Wave z76 = $zStr // Not sure why this has to be "declared" twice |
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130 | // printf "w[0],z[0] = %g %g\r", w76[0],z76[0] |
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131 | endif |
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132 | |
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133 | |
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134 | // set up the integration |
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135 | // end points and weights |
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136 | nord = 76 |
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137 | va = 0 |
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138 | vb = 1 |
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139 | halfheight = length/2.0 |
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140 | |
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141 | // evaluate at Gauss points |
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142 | // remember to index from 0,size-1 |
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143 | |
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144 | qq = x //current x point is the q-value for evaluation |
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145 | summ = 0.0 // initialize integral |
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146 | ii=0 |
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147 | do |
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148 | // Using 76 Gauss points |
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149 | zi = ( z76[ii]*(vb-va) + vb + va )/2.0 |
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150 | yyy = w76[ii] * Hollowcyl(qq, rcore, rshell, length, zi) |
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151 | summ += yyy |
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152 | |
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153 | ii+=1 |
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154 | while (ii<nord) // end of loop over quadrature points |
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155 | // |
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156 | // calculate value of integral to return |
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157 | |
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158 | answer = (vb-va)/2.0*summ |
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159 | |
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160 | // multiply by the contrast |
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161 | answer *= contrast*contrast |
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162 | |
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163 | //normalize by cylinder volume |
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164 | //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
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165 | vcyl=Pi*(rshell^2-rcore^2)*length |
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166 | answer *= vcyl |
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167 | //convert to [cm-1] |
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168 | answer *= 1.0e8 |
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169 | //Scale |
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170 | answer *= scale |
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171 | // add in the background |
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172 | answer += bkg |
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173 | |
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174 | Return (answer) |
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175 | |
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176 | End //End of function HollowCylinderForm() |
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177 | |
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178 | /////////////////////////////////////////////////////////////// |
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179 | Function Hollowcyl(qq,r2,r1,h,theta) |
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180 | Variable qq,r2,r1,h,theta |
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181 | |
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182 | // qq is the q-value for the calculation (1/A) |
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183 | // r2 is the core radius of the cylinder (A) |
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184 | //r1 is the shell raduis |
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185 | // rho(n) are the respective SLD's |
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186 | // h is the total-LENGTH of the cylinder = L (A) |
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187 | // theta is the dummy variable for the integration (x in Feigin's notation) |
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188 | |
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189 | //Local variables |
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190 | Variable gamma,besarg1,besarg2,lam1,lam2,t2,retval,psi,sinarg |
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191 | |
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192 | gamma = r2/r1 |
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193 | besarg1 = qq*r1*sqrt(1-theta^2) |
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194 | besarg2 = qq*r2*sqrt(1-theta^2) |
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195 | lam1 = 2*bessJ(1,besarg1)/besarg1 |
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196 | lam2 = 2*bessJ(1,besarg2)/besarg2 |
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197 | psi = 1/(1-gamma^2)*(lam1 - gamma^2*lam2) //SRK 10/19/00 |
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198 | |
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199 | sinarg = qq*h*theta/2 |
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200 | t2 = sin(sinarg)/sinarg |
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201 | |
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202 | retval = psi*psi*t2*t2 |
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203 | |
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204 | return retval |
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205 | |
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206 | End //Function Hollowcyl() |
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207 | |
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208 | |
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209 | // this is all there is to the smeared calculation! |
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210 | Function SmearedHollowCylinder(s) :FitFunc |
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211 | Struct ResSmearAAOStruct &s |
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212 | |
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213 | ////the name of your unsmeared model is the first argument |
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214 | Smear_Model_20(HollowCylinder,s.coefW,s.xW,s.yW,s.resW) |
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215 | |
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216 | return(0) |
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217 | End |
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218 | |
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219 | //wrapper to calculate the smeared model as an AAO-Struct |
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220 | // fills the struct and calls the ususal function with the STRUCT parameter |
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221 | // |
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222 | // used only for the dependency, not for fitting |
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223 | // |
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224 | Function fSmearedHollowCylinder(coefW,yW,xW) |
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225 | Wave coefW,yW,xW |
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226 | |
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227 | String str = getWavesDataFolder(yW,0) |
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228 | String DF="root:"+str+":" |
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229 | |
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230 | WAVE resW = $(DF+str+"_res") |
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231 | |
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232 | STRUCT ResSmearAAOStruct fs |
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233 | WAVE fs.coefW = coefW |
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234 | WAVE fs.yW = yW |
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235 | WAVE fs.xW = xW |
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236 | WAVE fs.resW = resW |
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237 | |
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238 | Variable err |
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239 | err = SmearedHollowCylinder(fs) |
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240 | |
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241 | return (0) |
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242 | End |
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