Example:Poinging

Latest revision as of 21:24, 10 September 2016

In this example we demonstrate how the task lfit in the FITSH package can be used to fit and evaluate isotropic and/or anisotropic pointing model coefficients as described in this paper.

[edit] Determination of pointing model coefficients

The script below expects a data file (named pointing.txt) which contains four columns: the first two are the encoder readouts for the two axes (here, hour angle and declination) while the third and fourth columns contains the respective first equatorial celestial coordinates derived from astrometry and after the correction for the refraction. Note that this example does not include codes that converts J2000 coordinates to first equatorial coordinates (i.e. does not perform corrections for precession, nutation, aberration and does not compute the local true sidereal time). These computations must be done prior the determination of the model coefficients, i.e. during the preparation of the pointing.txt (or any other equivalent) file.

#!/bin/bash

ct="(cos(tau*pi()/180.0))"
st="(sin(tau*pi()/180.0))"
cd="(cos(dec*pi()/180.0))"
sd="(sin(dec*pi()/180.0))"

ct0="(cos(tt*pi()/180.0))"
st0="(sin(tt*pi()/180.0))"
cd0="(cos(dd*pi()/180.0))"
sd0="(sin(dd*pi()/180.0))"

fx="           +b0*$sd    -c0*$cd*$st+d0*$sd*$st+e0*$sd*$ct-f0*$st"
fy="-a0*$sd               +c0*$cd*$ct-d0*$sd*$ct+e0*$sd*$st+f0*$ct"
fz="+a0*$cd*$st-b0*$cd*$ct                      -e0*$cd"

# $cd*$st, $cd*$ct, $sd

y1="($cd*$st)"
y2="($sd)"
y3="($cd*$ct)"

fx="$fx+b1*$y1*$sd-c1*$y1*$cd*$st+d1*$y1*$sd*$st+e1*$y1*$sd*$ct-f1*$y1*$st"
fy="$fy-a1*$y1*$sd+c1*$y1*$cd*$ct-d1*$y1*$sd*$ct+e1*$y1*$sd*$st+f1*$y1*$ct"
fz="$fz+a1*$y1*$cd*$st-b1*$y1*$cd*$ct-e1*$y1*$cd"

fx="$fx+b2*$y2*$sd-c2*$y2*$cd*$st+d2*$y2*$sd*$st+e2*$y2*$sd*$ct-0*$y2*$st"
fy="$fy-a2*$y2*$sd+c2*$y2*$cd*$ct-d2*$y2*$sd*$ct+e2*$y2*$sd*$st+0*$y2*$ct"
fz="$fz+a2*$y2*$cd*$st-b2*$y2*$cd*$ct-e2*$y2*$cd"

fx="$fx+b3*$y3*$sd-c3*$y3*$cd*$st+d3*$y3*$sd*$st+e3*$y3*$sd*$ct-f3*$y3*$st"
fy="$fy- 0*$y3*$sd+c3*$y3*$cd*$ct-d3*$y3*$sd*$ct+e3*$y3*$sd*$st+f3*$y3*$ct"
fz="$fz+ 0*$y3*$cd*$st-b3*$y3*$cd*$ct-e3*$y3*$cd"

yx="($cd0*$ct0-$cd*$ct)"
yy="($cd0*$st0-$cd*$st)"
yz="($sd0-$sd)"

cdef=tau:1,dec:2,tt:3,dd:4


# change 0 to 1 in ( ... || 0 ) below in order to include the points
# after pole crossing (i.e. having an encoder declination larger than 90).

# first, check the residual of the pointing without any pointing model:
if false; then
	cat	pointing.txt | \
	awk '{ if ( $2 <= 90 || 0 ) print; }' | \
	lfit	-c $cdef -f "$yx^2+$yy^2+$yz^2" | \
	awk '{ sum+=$1;n++; } END { printf("%10.6f\n",sqrt(sum/n)); }'
fi

cat	pointing.txt | \
awk '{ if ( $2 <= 90 || 1 ) print; }' | \
lfit	-v a0,b0,c0,d0,e0,f0,a1,b1,c1,d1,e1,f1,a2,b2,c2,d2,e2,b3,c3,d3,e3,f3 \
	-F a0=%9.6f,b0=%9.6f,c0=%9.6f,d0=%9.6f,e0=%9.6f,f0=%9.6f \
	-F a1=%9.6f,b1=%9.6f,c1=%9.6f,d1=%9.6f,e1=%9.6f,f1=%9.6f \
	-F a2=%9.6f,b2=%9.6f,c2=%9.6f,d2=%9.6f,e2=%9.6f \
	-F b3=%9.6f,c3=%9.6f,d3=%9.6f,e3=%9.6f,f3=%9.6f \
	-ix - -cx $cdef -fx "$fx" -yx "$yx" -ex 0.000013 \
	-iy - -cy $cdef -fy "$fy" -yy "$yy" -ey 0.000013 \
	-iz - -cz $cdef -fz "$fz" -yz "$yz" -ez 0.000013 \
	--err --residual | tee pointing.fit

if true; then
	A=($(cat pointing.fit))
	cat	pointing.txt | \
	lfit	-v a0=${A[0]},b0=${A[1]},c0=${A[2]},d0=${A[3]},e0=${A[4]},f0=${A[5]} \
                -v a1=${A[6]},b1=${A[7]},c1=${A[8]},d1=${A[9]},e1=${A[10]},f1=${A[11]} \
                -v a2=${A[12]},b2=${A[13]},c2=${A[14]},d2=${A[15]},e2=${A[16]} \
                -v b3=${A[17]},c3=${A[18]},d3=${A[19]},e3=${A[20]},f3=${A[21]} \
		-c $cdef \
		-f "tau,dec,sqrt(($fx-$yx)^2+($fy-$yy)^2+($fz-$yz)^2),$fx-$yx,$fy-$yy,$fz-$yz" \
		-F %10.5f,%10.5f,%10.6f,%10.6f,%10.6f,%10.6f \
		-o pointing.res
fi

This script can also be downloaded directly: run-2-fit-y1.sh. The data file is also available for download: pointing.txt.

[edit] Evaluation of the pointing model coefficients

The evaluation of the pointing model can also be done by incorporating the lfit task of the package. However, in most of the cases, the respective implementation regarding to the evaluation is integrated in a telescope control system software stack since it is relatively deeply nested in the computational backends.

[edit] Supporting files