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/* |
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*+ |
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* Name: |
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* palRefv |
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* Purpose: |
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* Adjust an unrefracted Cartesian vector to include the effect of atmospheric refraction |
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* Language: |
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* Starlink ANSI C |
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* Type of Module: |
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* Library routine |
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* Invocation: |
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* void palRefv ( double vu[3], double refa, double refb, double vr[3] ); |
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* Arguments: |
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* vu[3] = double (Given) |
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* Unrefracted position of the source (Az/El 3-vector) |
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* refa = double (Given) |
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* tan Z coefficient (radian) |
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* refb = double (Given) |
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* tan**3 Z coefficient (radian) |
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* vr[3] = double (Returned) |
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* Refracted position of the source (Az/El 3-vector) |
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* Description: |
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* Adjust an unrefracted Cartesian vector to include the effect of |
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* atmospheric refraction, using the simple A tan Z + B tan**3 Z |
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* model. |
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* Authors: |
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* TIMJ: Tim Jenness |
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* PTW: Patrick Wallace |
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* {enter_new_authors_here} |
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* Notes: |
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* - This routine applies the adjustment for refraction in the |
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* opposite sense to the usual one - it takes an unrefracted |
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* (in vacuo) position and produces an observed (refracted) |
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* position, whereas the A tan Z + B tan**3 Z model strictly |
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* applies to the case where an observed position is to have the |
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* refraction removed. The unrefracted to refracted case is |
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* harder, and requires an inverted form of the text-book |
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* refraction models; the algorithm used here is equivalent to |
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* one iteration of the Newton-Raphson method applied to the above |
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* formula. |
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* |
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* - Though optimized for speed rather than precision, the present |
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* routine achieves consistency with the refracted-to-unrefracted |
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* A tan Z + B tan**3 Z model at better than 1 microarcsecond within |
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* 30 degrees of the zenith and remains within 1 milliarcsecond to |
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* beyond ZD 70 degrees. The inherent accuracy of the model is, of |
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* course, far worse than this - see the documentation for palRefco |
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* for more information. |
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* |
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* - At low elevations (below about 3 degrees) the refraction |
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* correction is held back to prevent arithmetic problems and |
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* wildly wrong results. For optical/IR wavelengths, over a wide |
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* range of observer heights and corresponding temperatures and |
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* pressures, the following levels of accuracy (arcsec, worst case) |
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* are achieved, relative to numerical integration through a model |
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* atmosphere: |
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* |
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* ZD error |
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* |
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* 80 0.7 |
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* 81 1.3 |
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* 82 2.5 |
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* 83 5 |
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* 84 10 |
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* 85 20 |
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* 86 55 |
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* 87 160 |
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* 88 360 |
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* 89 640 |
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* 90 1100 |
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* 91 1700 } relevant only to |
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* 92 2600 } high-elevation sites |
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* |
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* The results for radio are slightly worse over most of the range, |
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* becoming significantly worse below ZD=88 and unusable beyond |
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* ZD=90. |
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* |
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* - See also the routine palRefz, which performs the adjustment to |
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* the zenith distance rather than in Cartesian Az/El coordinates. |
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* The present routine is faster than palRefz and, except very low down, |
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* is equally accurate for all practical purposes. However, beyond |
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* about ZD 84 degrees palRefz should be used, and for the utmost |
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* accuracy iterative use of palRefro should be considered. |
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* History: |
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* 2014-07-15 (TIMJ): |
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* Initial version. A direct copy of the Fortran SLA implementation. |
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* Adapted with permission from the Fortran SLALIB library. |
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* {enter_further_changes_here} |
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* Copyright: |
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* Copyright (C) 2014 Tim Jenness |
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* Copyright (C) 2004 Patrick Wallace |
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* All Rights Reserved. |
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104
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* Licence: |
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* This program is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU General Public License as |
107
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* published by the Free Software Foundation; either version 3 of |
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* the License, or (at your option) any later version. |
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* |
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* This program is distributed in the hope that it will be |
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* useful, but WITHOUT ANY WARRANTY; without even the implied |
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* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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* PURPOSE. See the GNU General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
116
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, |
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* MA 02110-1301, USA. |
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120
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* Bugs: |
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* {note_any_bugs_here} |
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*- |
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*/ |
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125
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#include "pal.h" |
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#include "palmac.h" |
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#include |
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129
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2
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void palRefv ( double vu[3], double refa, double refb, double vr[3] ) { |
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131
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double x,y,z1,z,zsq,rsq,r,wb,wt,d,cd,f; |
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133
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/* Initial estimate = unrefracted vector */ |
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2
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x = vu[0]; |
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2
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y = vu[1]; |
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2
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z1 = vu[2]; |
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138
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/* Keep correction approximately constant below about 3 deg elevation */ |
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2
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z = DMAX(z1,0.05); |
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/* One Newton-Raphson iteration */ |
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2
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zsq = z*z; |
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2
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rsq = x*x+y*y; |
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2
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r = sqrt(rsq); |
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2
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wb = refb*rsq/zsq; |
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2
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wt = (refa+wb)/(1.0+(refa+3.0*wb)*(zsq+rsq)/zsq); |
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d = wt*r/z; |
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cd = 1.0-d*d/2.0; |
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f = cd*(1.0-wt); |
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151
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/* Post-refraction x,y,z */ |
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2
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vr[0] = x*f; |
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2
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vr[1] = y*f; |
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2
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vr[2] = cd*(z+d*r)+(z1-z); |
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} |