1 | #pragma TextEncoding = "MacRoman" |
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2 | #pragma rtGlobals=3 // Use modern global access method and strict wave access. |
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3 | |
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4 | |
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5 | // |
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6 | // this is an empirical representation of the White Beam wavelength |
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7 | // distribution. |
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8 | // |
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9 | // using Integrate function -- find the normalization value |
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10 | // |
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11 | // integral = 20926 (cts*A) for "top" |
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12 | // integral = 19933 (cts*A) for "middle" |
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13 | // integration of interpolated data (100 pts) = 20051 (3 A to 9 A) |
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14 | // |
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15 | // |
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16 | // |
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17 | // of the three choices, using the fit to the "top" of the distribution gives the best-looking |
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18 | // result when compared to the AgBeh data |
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19 | // |
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20 | |
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21 | |
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22 | // 9/2019 |
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23 | // added an empirical functional form for the "Super" white beam mode where the deflector is out |
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24 | // and the wavelength is not cut off at the higher wavelength, but extends to 20 |
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25 | // |
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26 | // Integral = 30955 (cts*A) for middle fit |
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27 | // |
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28 | // |
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29 | |
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30 | // White Beam: |
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31 | // mean wavelength = 5.29687 |
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32 | // 3rd moment/2nd moment = 5.741 |
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33 | // |
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34 | // Super White Beam: |
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35 | // mean wavelength = 6.2033 |
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36 | // 3rd moment/2nd moment = 7.93267 |
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37 | // |
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38 | Constant kWhiteBeam_Mean = 5.3 |
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39 | //Constant kWhiteBeam_Mean = 5.7 // mean of lam^2 |
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40 | Constant kWhiteBeam_Normalization = 19933 |
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41 | |
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42 | Constant kSuperWhiteBeam_Mean = 6.2 |
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43 | //Constant kSuperWhiteBeam_Mean = 7.9 //mean of lam^2 |
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44 | Constant kSuperWhiteBeam_Normalization = 30955 |
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45 | |
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46 | |
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47 | |
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48 | |
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49 | Function V_WhiteBeamDist_top(lam) |
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50 | Variable lam |
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51 | |
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52 | if(lam < 3.37) |
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53 | return(0) |
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54 | endif |
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55 | |
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56 | if(lam < 3.69) |
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57 | return(-31013 + 9198*lam) |
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58 | endif |
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59 | |
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60 | if(lam < 3.84) |
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61 | return(23715 - 5649*lam) |
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62 | endif |
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63 | |
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64 | //// the "middle" of the spikes |
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65 | // if(lam < 4.12) |
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66 | // return(-84962 + 22634*lam) |
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67 | // endif |
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68 | // if(lam < 8.37) |
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69 | // return(-2336 + 11422*exp(-( (lam-3.043)/4.234 )^2)) |
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70 | // endif |
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71 | |
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72 | //// the "top" of the spikes |
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73 | if(lam < 4.16) |
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74 | return(-84962 + 22634*lam) |
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75 | endif |
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76 | if(lam < 8.25) |
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77 | return(-2336 + 12422*exp(-( (lam-3.043)/4.034 )^2)) |
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78 | endif |
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79 | |
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80 | // anything larger than 8.37, return 0 |
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81 | return(0) |
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82 | |
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83 | End |
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84 | |
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85 | |
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86 | Function V_WhiteBeamDist_mid(lam) |
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87 | Variable lam |
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88 | |
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89 | if(lam < 3.37) |
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90 | return(0) |
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91 | endif |
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92 | |
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93 | if(lam < 3.69) |
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94 | return(-31013 + 9198*lam) |
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95 | endif |
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96 | |
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97 | if(lam < 3.84) |
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98 | return(23715 - 5649*lam) |
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99 | endif |
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100 | |
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101 | //// the "middle" of the spikes |
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102 | if(lam < 4.12) |
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103 | return(-84962 + 22634*lam) |
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104 | endif |
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105 | if(lam < 8.37) |
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106 | return(-2336 + 11422*exp(-( (lam-3.043)/4.234 )^2)) |
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107 | endif |
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108 | |
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109 | ////// the "top" of the spikes |
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110 | // if(lam < 4.16) |
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111 | // return(-84962 + 22634*lam) |
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112 | // endif |
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113 | // if(lam < 8.25) |
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114 | // return(-2336 + 12422*exp(-( (lam-3.043)/4.034 )^2)) |
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115 | // endif |
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116 | |
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117 | // anything larger than 8.37, return 0 |
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118 | return(0) |
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119 | |
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120 | End |
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121 | |
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122 | // this is not used - there is no improvement in the results when using the "full" shape of the |
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123 | // WB distribution. |
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124 | Function V_WhiteBeamInterp(lam) |
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125 | Variable lam |
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126 | |
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127 | WAVE interp_lam = root:interp_lam |
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128 | WAVE interp_cts = root:interp_cts |
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129 | |
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130 | return(interp(lam,interp_lam,interp_cts)) |
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131 | End |
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132 | |
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133 | // change the x-scaling of cts_for_mean to 3,9 (beg,end) |
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134 | // 3309 is the average value of cts_for_mean |
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135 | // cts_for_mean = interp_cts*x/3309 |
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136 | // |
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137 | // gives an average wavelength of 5.302 A |
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138 | // median ~ 5.97 A |
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139 | // |
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140 | Function V_WB_Mean() |
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141 | |
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142 | WAVE cts_for_mean |
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143 | Variable tot=sum(cts_for_mean) |
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144 | Variable ans |
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145 | |
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146 | cts_for_mean = cts_for_mean*x |
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147 | ans = sum(cts_for_mean)/tot |
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148 | |
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149 | return(ans) |
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150 | End |
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151 | |
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152 | |
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153 | // assumes that the counts and wavelength data for white and superWhite both are loaded and named: |
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154 | // |
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155 | // white_wavelength, counts_white |
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156 | // super_white_wavelength, counts_super_white |
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157 | // |
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158 | // |
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159 | Proc V_WB_Stats() |
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160 | |
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161 | duplicate/O counts_white cts_W, intg_W,intg_W3 |
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162 | duplicate/O counts_super_white cts_SW intg_SW,intg_SW3 |
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163 | |
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164 | Print "White Beam:" |
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165 | intg_W = cts_W*white_wavelength |
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166 | printf "mean wavelength = %g\r",sum(intg_W)/sum(cts_W) |
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167 | intg_W = cts_W*white_wavelength^2 |
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168 | // printf "sqrt(wavelength^2)/N = %g\r",sqrt( sum(intg_W)/sum(cts_W) ) |
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169 | intg_W3 = cts_W*white_wavelength^3 |
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170 | printf "3rd moment/2nd moment = %g\r",sum(intg_W3)/sum(intg_W) |
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171 | |
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172 | Print |
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173 | Print "Super White Beam:" |
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174 | intg_SW = cts_SW*super_white_wavelength |
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175 | printf "mean wavelength = %g\r",sum(intg_SW)/sum(cts_SW) |
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176 | intg_SW = cts_SW*super_white_wavelength^2 |
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177 | // printf "sqrt(wavelength^2)/N = %g\r",sqrt( sum(intg_SW)/sum(cts_SW) ) |
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178 | intg_SW3 = cts_SW*super_white_wavelength^3 |
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179 | printf "3rd moment/2nd moment = %g\r",sum(intg_SW3)/sum(intg_SW) |
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180 | |
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181 | End |
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182 | |
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183 | // |
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184 | // |
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185 | // |
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186 | Function V_SuperWhiteBeamDist_mid(lam) |
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187 | Variable lam |
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188 | |
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189 | if(lam < 3.37) |
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190 | return(0) |
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191 | endif |
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192 | |
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193 | if(lam < 3.72) |
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194 | return(-33536 + 9919*lam) |
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195 | endif |
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196 | |
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197 | if(lam < 3.88) |
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198 | return(28941 - 6848*lam) |
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199 | endif |
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200 | |
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201 | //// the "middle" of the spikes |
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202 | if(lam < 4.16) |
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203 | return(-1.0111e5 + 26689*lam) |
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204 | endif |
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205 | |
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206 | if(lam < 20) |
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207 | return(5 - 10081*exp(-( (lam-4.161)/0.9788 )) + 19776*exp(-( (lam-4.161)/1.921 )) ) |
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208 | endif |
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209 | |
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210 | // anything larger than 20, return 0 |
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211 | return(0) |
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212 | |
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213 | End |
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214 | |
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215 | |
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