1 | #include "erfa.h"
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2 |
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3 | void eraRefco(double phpa, double tc, double rh, double wl,
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4 | double *refa, double *refb)
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5 | /*
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6 | ** - - - - - - - - -
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7 | ** e r a R e f c o
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8 | ** - - - - - - - - -
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9 | **
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10 | ** Determine the constants A and B in the atmospheric refraction model
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11 | ** dZ = A tan Z + B tan^3 Z.
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12 | **
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13 | ** Z is the "observed" zenith distance (i.e. affected by refraction)
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14 | ** and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
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15 | ** zenith distance.
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16 | **
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17 | ** Given:
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18 | ** phpa double pressure at the observer (hPa = millibar)
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19 | ** tc double ambient temperature at the observer (deg C)
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20 | ** rh double relative humidity at the observer (range 0-1)
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21 | ** wl double wavelength (micrometers)
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22 | **
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23 | ** Returned:
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24 | ** refa double* tan Z coefficient (radians)
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25 | ** refb double* tan^3 Z coefficient (radians)
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26 | **
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27 | ** Notes:
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28 | **
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29 | ** 1) The model balances speed and accuracy to give good results in
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30 | ** applications where performance at low altitudes is not paramount.
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31 | ** Performance is maintained across a range of conditions, and
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32 | ** applies to both optical/IR and radio.
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33 | **
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34 | ** 2) The model omits the effects of (i) height above sea level (apart
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35 | ** from the reduced pressure itself), (ii) latitude (i.e. the
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36 | ** flattening of the Earth), (iii) variations in tropospheric lapse
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37 | ** rate and (iv) dispersive effects in the radio.
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38 | **
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39 | ** The model was tested using the following range of conditions:
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40 | **
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41 | ** lapse rates 0.0055, 0.0065, 0.0075 deg/meter
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42 | ** latitudes 0, 25, 50, 75 degrees
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43 | ** heights 0, 2500, 5000 meters ASL
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44 | ** pressures mean for height -10% to +5% in steps of 5%
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45 | ** temperatures -10 deg to +20 deg with respect to 280 deg at SL
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46 | ** relative humidity 0, 0.5, 1
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47 | ** wavelengths 0.4, 0.6, ... 2 micron, + radio
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48 | ** zenith distances 15, 45, 75 degrees
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49 | **
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50 | ** The accuracy with respect to raytracing through a model
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51 | ** atmosphere was as follows:
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52 | **
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53 | ** worst RMS
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54 | **
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55 | ** optical/IR 62 mas 8 mas
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56 | ** radio 319 mas 49 mas
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57 | **
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58 | ** For this particular set of conditions:
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59 | **
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60 | ** lapse rate 0.0065 K/meter
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61 | ** latitude 50 degrees
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62 | ** sea level
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63 | ** pressure 1005 mb
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64 | ** temperature 280.15 K
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65 | ** humidity 80%
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66 | ** wavelength 5740 Angstroms
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67 | **
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68 | ** the results were as follows:
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69 | **
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70 | ** ZD raytrace eraRefco Saastamoinen
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71 | **
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72 | ** 10 10.27 10.27 10.27
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73 | ** 20 21.19 21.20 21.19
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74 | ** 30 33.61 33.61 33.60
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75 | ** 40 48.82 48.83 48.81
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76 | ** 45 58.16 58.18 58.16
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77 | ** 50 69.28 69.30 69.27
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78 | ** 55 82.97 82.99 82.95
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79 | ** 60 100.51 100.54 100.50
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80 | ** 65 124.23 124.26 124.20
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81 | ** 70 158.63 158.68 158.61
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82 | ** 72 177.32 177.37 177.31
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83 | ** 74 200.35 200.38 200.32
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84 | ** 76 229.45 229.43 229.42
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85 | ** 78 267.44 267.29 267.41
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86 | ** 80 319.13 318.55 319.10
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87 | **
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88 | ** deg arcsec arcsec arcsec
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89 | **
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90 | ** The values for Saastamoinen's formula (which includes terms
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91 | ** up to tan^5) are taken from Hohenkerk and Sinclair (1985).
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92 | **
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93 | ** 3) A wl value in the range 0-100 selects the optical/IR case and is
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94 | ** wavelength in micrometers. Any value outside this range selects
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95 | ** the radio case.
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96 | **
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97 | ** 4) Outlandish input parameters are silently limited to
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98 | ** mathematically safe values. Zero pressure is permissible, and
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99 | ** causes zeroes to be returned.
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100 | **
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101 | ** 5) The algorithm draws on several sources, as follows:
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102 | **
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103 | ** a) The formula for the saturation vapour pressure of water as
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104 | ** a function of temperature and temperature is taken from
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105 | ** Equations (A4.5-A4.7) of Gill (1982).
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106 | **
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107 | ** b) The formula for the water vapour pressure, given the
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108 | ** saturation pressure and the relative humidity, is from
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109 | ** Crane (1976), Equation (2.5.5).
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110 | **
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111 | ** c) The refractivity of air is a function of temperature,
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112 | ** total pressure, water-vapour pressure and, in the case
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113 | ** of optical/IR, wavelength. The formulae for the two cases are
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114 | ** developed from Hohenkerk & Sinclair (1985) and Rueger (2002).
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115 | **
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116 | ** d) The formula for beta, the ratio of the scale height of the
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117 | ** atmosphere to the geocentric distance of the observer, is
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118 | ** an adaption of Equation (9) from Stone (1996). The
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119 | ** adaptations, arrived at empirically, consist of (i) a small
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120 | ** adjustment to the coefficient and (ii) a humidity term for the
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121 | ** radio case only.
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122 | **
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123 | ** e) The formulae for the refraction constants as a function of
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124 | ** n-1 and beta are from Green (1987), Equation (4.31).
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125 | **
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126 | ** References:
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127 | **
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128 | ** Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
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129 | ** Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
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130 | ** Academic Press, 1976.
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131 | **
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132 | ** Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,
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133 | ** 1982.
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134 | **
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135 | ** Green, R.M., "Spherical Astronomy", Cambridge University Press,
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136 | ** 1987.
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137 | **
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138 | ** Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,
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139 | ** 1985.
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140 | **
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141 | ** Rueger, J.M., "Refractive Index Formulae for Electronic Distance
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142 | ** Measurement with Radio and Millimetre Waves", in Unisurv Report
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143 | ** S-68, School of Surveying and Spatial Information Systems,
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144 | ** University of New South Wales, Sydney, Australia, 2002.
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145 | **
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146 | ** Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.
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147 | **
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148 | ** Copyright (C) 2013-2015, NumFOCUS Foundation.
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149 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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150 | */
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151 | {
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152 | int optic;
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153 | double p, t, r, w, ps, pw, tk, wlsq, gamma, beta;
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154 |
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155 | /* Decide whether optical/IR or radio case: switch at 100 microns. */
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156 | optic = ( wl <= 100.0 );
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157 |
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158 | /* Restrict parameters to safe values. */
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159 | t = ERFA_GMAX ( tc, -150.0 );
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160 | t = ERFA_GMIN ( t, 200.0 );
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161 | p = ERFA_GMAX ( phpa, 0.0 );
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162 | p = ERFA_GMIN ( p, 10000.0 );
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163 | r = ERFA_GMAX ( rh, 0.0 );
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164 | r = ERFA_GMIN ( r, 1.0 );
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165 | w = ERFA_GMAX ( wl, 0.1 );
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166 | w = ERFA_GMIN ( w, 1e6 );
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167 |
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168 | /* Water vapour pressure at the observer. */
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169 | if ( p > 0.0 ) {
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170 | ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) /
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171 | ( 1.0 + 0.00412*t ) ) *
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172 | ( 1.0 + p * ( 4.5e-6 + 6e-10*t*t ) );
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173 | pw = r * ps / ( 1.0 - (1.0-r)*ps/p );
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174 | } else {
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175 | pw = 0.0;
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176 | }
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177 |
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178 | /* Refractive index minus 1 at the observer. */
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179 | tk = t + 273.15;
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180 | if ( optic ) {
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181 | wlsq = w * w;
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182 | gamma = ( ( 77.53484e-6 +
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183 | ( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p
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184 | - 11.2684e-6*pw ) / tk;
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185 | } else {
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186 | gamma = ( 77.6890e-6*p - ( 6.3938e-6 - 0.375463/tk ) * pw ) / tk;
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187 | }
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188 |
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189 | /* Formula for beta from Stone, with empirical adjustments. */
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190 | beta = 4.4474e-6 * tk;
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191 | if ( ! optic ) beta -= 0.0074 * pw * beta;
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192 |
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193 | /* Refraction constants from Green. */
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194 | *refa = gamma * ( 1.0 - beta );
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195 | *refb = - gamma * ( beta - gamma / 2.0 );
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196 |
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197 | /* Finished. */
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198 |
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199 | }
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200 | /*----------------------------------------------------------------------
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201 | **
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202 | **
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203 | ** Copyright (C) 2013-2015, NumFOCUS Foundation.
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204 | ** All rights reserved.
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205 | **
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206 | ** This library is derived, with permission, from the International
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207 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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208 | ** available from http://www.iausofa.org.
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209 | **
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210 | ** The ERFA version is intended to retain identical functionality to
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211 | ** the SOFA library, but made distinct through different function and
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212 | ** file names, as set out in the SOFA license conditions. The SOFA
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213 | ** original has a role as a reference standard for the IAU and IERS,
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214 | ** and consequently redistribution is permitted only in its unaltered
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215 | ** state. The ERFA version is not subject to this restriction and
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216 | ** therefore can be included in distributions which do not support the
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217 | ** concept of "read only" software.
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218 | **
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219 | ** Although the intent is to replicate the SOFA API (other than
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220 | ** replacement of prefix names) and results (with the exception of
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221 | ** bugs; any that are discovered will be fixed), SOFA is not
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222 | ** responsible for any errors found in this version of the library.
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223 | **
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224 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
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225 | ** that you are using a library derived from SOFA, rather than SOFA
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226 | ** itself.
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227 | **
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228 | **
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229 | ** TERMS AND CONDITIONS
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230 | **
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231 | ** Redistribution and use in source and binary forms, with or without
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232 | ** modification, are permitted provided that the following conditions
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233 | ** are met:
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234 | **
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235 | ** 1 Redistributions of source code must retain the above copyright
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236 | ** notice, this list of conditions and the following disclaimer.
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237 | **
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238 | ** 2 Redistributions in binary form must reproduce the above copyright
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239 | ** notice, this list of conditions and the following disclaimer in
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240 | ** the documentation and/or other materials provided with the
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241 | ** distribution.
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242 | **
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243 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
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244 | ** the International Astronomical Union nor the names of its
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245 | ** contributors may be used to endorse or promote products derived
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246 | ** from this software without specific prior written permission.
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247 | **
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248 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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249 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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250 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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251 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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252 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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253 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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254 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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255 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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256 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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257 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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258 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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259 | ** POSSIBILITY OF SUCH DAMAGE.
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260 | **
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261 | */
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