file:/obs/obs/oper/memos/pointing_memo.14nov95 (also /rick/point/pointing_memo.14nov95) Dec 4 22:50 1995 memo.14nov95 Page I Pointing notes - 14nov95 - jrf this note discusses radio and optical values obtained for the various terms in the BIMA pointing equations. repeatability, measurement errors, the differences between the optical and radio solutions, and a method for updating the pointing after a move is described. The terms in the radio/optical pointing equation (Mel's equation 4) are: Azimuth terms Elevation terms --------------------------------------------------------------------------- 1 cos (el) encoder offset 1.0 encoder offset 2 sin(el)*sin(az) tilt sin(az) tilt 3 sin (el)*cos(az) tilt cos(az) tilt 4 1 collimation sin(el) sag and other 5 sin (el) axis align cos(el) gravity terms 6 cos (el)*sin(az) l*az sinusoid sin(2*az) 2*az sinusoid 7 cos (el)*cos(az) " cos(2*az) " 8 cos (el)*sin(2az) 2*az sinusoid tan(90-el) refraction 9 cos(el)*cos(2az) " - (only 8 elev terms included) the optical pointing terms in arcmin (~point/optfit.30nov94') are: 1 2 3 4 5 6 7 8 9 1 azim -8.00 -0.13 -0.13 2.00 0.47 -0.37 -3.79 -0.01 -0.06 2 azim 115.21 0.17 0.22 -25.99 -0.46 -0.04 0.04 -0.12 -0.11 3 azim -55.81 -0.16 0.19 -0.47 0.67 0.06 -0.33 0.13 -0.01 4 azim 0.76 0.23 0.12 -3.51 -0.29 -0.85 -0.83 0.00 -0.02 5 azim -53.56 0.22 0.29 —3.05 -0.80 -0.06 -0.04 -0.01 -0.13 6 azim 39.02 0.28 0.09 -3.74 -0.69 -0.04 0.03 0.00 -0.11 7 azim 8.27 0.13 -0.29 -4.53 -0.94') -0.13 0.06 -0.08 0.03 8 azim 10.76 0.15 0.15 -11.07 -n:33 -0.05 0.05 -0.03 -0.05 9 azim 52.45 0.13 -0.22 7.56 -0.03 -0.10 -0.06 -0.07 -0.09 1 elev 39.92 -0.08 -0.71 -0.69 -0.81 0.02 0.09 0.75 0.00 2 elev 36.03 -0.22 0.12 -1.05 -0.49 -0.05 -0.01 0.75 0.00 3 elev -24.10 -0.22 -0.16 -0.38 0.87 -0.02 0.01 0.75 0.00 4 elev 7.20 -0.12 0.27 -0.61 0.36 -0.05 0.05 0.75 0.00 5 elev 27.75 -0.24 0.20 -0.70 0.19 0.09 -0.12 0.75 0.00 6 elev 46.04 -0.09 0.30 -0.53 0.36 0.00 -0.03 0.75 0.00 7 elev -10.81 0.27 0.06 -0.39 0.60 -0.05 -0.15 0.75 0.00 8 elev 84.42 -0.16 0.14 -0.83 -0.01 -0.04 -0.01 0.75 0.00 9 elev 115.12 -0.04 0.09 -0.94 -0.30 -0.05 0.03 0.75 0.00 the residual scatter in the measurements after fitting is about 0.05 arcmin (3") rms for the optical data. this is the same as the ccd pixel size. repeatability for most terms in the pointing fit is also about 3". only pointing terms > 0.05 arcmin are therefore considered significant, the scatter in the radio data are typically 8-10" and is due to lower signal-to-noise. the first 5 pointing terms for all antennas are signicantly different from zero in both az and el. few of the higher-order terms are much greater than 3" except the refraction term (#8 elev) . omitting these terms produces discernable systematics in the pointing residuals of some antennas however, so the full set of parameters is necessary. these higher-order terms probably represent defects in the drives, encoders and mounts. the first term generally has the largest value, and is due mainly to encoder offsets, this term can be reduced to <60" by proper benchmarking of the encoder, but is limited by the 2 deg resolution of the resolver. terms #2 and #3 model antenna tilts. there is good agreement between the antenna tilts determined from the az and el errors independently (#2 az = #3 el; #3 az = -#2 el). these values are similar to the tilts determined from tiltmeter measurements, although predictions of the pointing parameters based on tiltmeter curves tend to be off by around 5". the source of this inconsistency is unclear. ant 9 does not have consistent tilt terms in az and el, and these terms are unstable at a level of about 0.2 arcmin for unknown reasons. repeatability is considerably worse for terms #1, #4 and #5, typical errors being around 0.2 arcmin (12"). these terms involve only a constant or the sin or cos of elevation. since only elevations between 15 and 85 are observed in normal operation, this variation is probably due to coupling among these three terms. there is no problem with coupling among terms dependent on azimuth since the az range covered is -200 to 200 deg in a typical pointing run. a large collimation term is present for antenna 2 (term #4). ant 2 elevation pointing begins to diverge above an elevation of 80 degrees, which may be related to the large collimation error, the pointing error reaches about 30" at an elevation of 85 deg, which is the current observing limit (a 5 deg cone of avoidance was implemented recently to reduce time lost trying to track sources near the zenith and to amieloriate this pointing problem). this error is not expected from the pointing model, and it represents the largest systematic pointing error present. the perpendicular misalignment between the az and el axes (az term #5) is negative for all antennas with an average value ~30". this could be accounted for by a systematic height difference between the yokes of ~0.3 mm, for example. the difference between the radio and optical pointing is (arcmin in nov 95): 1 azim +0.32 -0.20 -0.19 0.88 0.17 0.14 0.25 -0.18 -0.10 2 azim -0.07 -0.02 -0.06 -4.91 -0.27 0.03 0.05 -0.02 -0.02 3 azim 0.01 0.04 0.00 2.32 -0.26 -0.02 -0.08 -0.02 -0.12 4 azim 0.25 0.02 0.03 -3.29 0.03 0.01 0.05 0.00 0.00 5 azim 0.07 0.00 0.05 -4.63 0.12 0.00 -0.07 -0.01 0.04 6 azim 0.04 -0.02 -0.07 -4.42 0.00 0.00 0.10 0.01 -0.03 7 azim -0.07 0.03 -0.01 -5.38 -0.18 -0.07 0.06 0.01 -0.03 8 azim -0.09 -0.06 -0.07 -3.7Q 0.01 0.06 0.08 -0.03 0.01 9 azim 0.03 0.03 -0.09 -4.01 -0.02 0.00 -0.15 -0.07 +0.05 1 elev 2.86 -0.01 -0.64 -1.09 -0.84 -0.06 0.02 -0.20 0.00 2 elev 6.44 0.04 0.05 -0.90 -0.01 -0.01 -0.02 -0.20 0.00 3 elev 2.37 0.01 0.04 -0.62 -0.10 0.02 0.06 -0.20 0.00 4 elev 6.33 -0.04 0.04 -1.11 -0.12 -0.05 -0.01 -0.20 0.00 5 elev 5.85 -0.05 0.03 -1.13 -0.29 -0.05 -0.01 -0.20 0.00 6 elev 6.28 0.03 -0.08 -0.99 0.04 -0.01 0.05 -0.20 0.00 7 elev 5.30 0.01 0.04 -0.99 0.09 -0.06 -0.09 -0.20 0.00 8 elev 4.43 -0.03 -0.03 -0.69 0.01 -0.05 0.04 -0.20 0.00 9 elev 5.98 0.05 -0.14 -1.04 -0.23 -0.07 0.03 -0.20 0.00 the terms which are expected to differ between the radio and optical solutions involve collimation, gravitational deflections and refraction (terms #1, #4, #5 and #8). the only significant differences are in terms #1, #4 and #5 as expected, the -0.2' difference in term #8 elev is due to the fixed refraction terms (0.75 optical and 0.95 radio). since the optical parameters are better determined than the radio due to higher signal to noise, the best radio pointing solution can be taken to be the optical solution plus the above differences in terms #1, #4, #5 and #8. experience has shown that the difference between the radio and optical pointing is constant within the errors, therefore either optical or radio pointing can be used to determine the other. after an antenna move only the first three pointing terms are expected to vary (az skew and tilt terms). since the tiltmeter measurements are incapable of accurately predicting the new pointing tilt terms, all five terms (3 az and 2 el) must be determined by pointing measurements, if antenna tilts could either be kept constant or <3", then only the skew term would need to be measured, unfortunately, this is not generally possible at hat creek. for acceptable accuracy, about 30 points over a large range in azimuth and elevation should be acquired to determine the 5 unknown pointing terms, this can be done in an hour optically, but takes about 6 hours in the radio under good conditions. new pointing constants after a move are therefore most easily measured with the tv cameras, only the first 3 terms in the pointing equation should be fit. the new radio pointing solution is determined from the optical solution using the constant offsets between optical and radio terms, if the sky is cloudy during the calibration period following a move, radio pointing must be used.