Pointing and RT32 Gain

•   Model3 has an azimuth component of –0.013255°/sin(z) ↓ Radiation pattern deviates to the right by 0.013° Subreflector is translated –0.013255/–3.3925 m = +4 mm to the left (as seen from the feeds) → 1.5 % ABERRATION LOSSES ——— or ——— is rotated by –0.013255°/0.1046 = –0.127° (i.e., seen from feeds, its vertex to the right) around prime focus → NO LOSSES •   Data of campaign 2003 against 2004 shifted in azimuth by –0.017° → translation of secondary by 5 mm (direction being consistent with the idea that the above 4 mm is purely due to it)

The losses of about 1.5 % resulting from the translation in case of RT32 cannot be compensated by other subreflector motions.

Distorted power pattern of the RT32 telescope at 30 GHz as expected of lateral shift of its secondary by 4 mm. Here the main lobe has been cut-off at the level of 1 % of the peak power. The sidelobe peak seen on the East (left, when viewed from feeds) side of the main lobe is at the level of about 2 % [figure source: OptiCass output]

Conclusion: a small (4 – 5 mm) correction in the horizontal position of the Cassegrain mirror promises the recovery of about 12 m² of aperture area (5 panels) supposedly lost at 30 GHz after unintentional change during maintenance of the mirror drives in 2003. The pronounced asymmetry of the first side lobe (seen in the above figure) should be observable provided the signal to noise ratio exceeding 50:1 can be achieved for a point source. If observationally detected it would be rather unmistakable indication of the presence of discussed lateral misalignment of the secondary.
In fact similar signature on the first sidelobe could be expected also of a feed displacement, however to get comparable magnitude of the distortion it would require as much as a metre of its lateral offset and another nearly 0.5 m of axial adjustment.

  17 % of 314 measurements in the azimuth coordinate
  36 % of 314 measurements in the zenith distance

After correction for variable astronomical effects of the annual aberration of light and nutation of Earth axis (see these figures) these numbers reduce to:

  8 % in the azimuth
  23 % in the zenith distance

This makes average of 14 % of real 'outliers'.

Of original data (of 2003 and 2004) used to fit the pointing model (the one currently used)

Observed (blue) and corrected (red) pointing errors in the azimuth (upper panel) and zenith distance (lower panel). These plots show that the errors are dominated by still unaccounted systematic effects. Note however that the presence of the 0.02° jump becames discernced in the zenith distance errors after applying corrections for aberration and nutation (see also this figure). The jump seems to be mainly responsible for the standard deviations remaining practically the same before and after applying the corrections

Error distributions for uncorrected (blue) and corrected (red) pointing measurements in the zenith distance. This diagram reveals the presence of 0.02-degree jump in the corrected errors (red bars clearly peaking near +0.02° with the main peak between –0.005 and 0.005°)

The above figure shows that in the zenith distance coordinate there is considerable fraction (about 15 %) of errors in the range +0.0175 to +0.0275°. Attributing them all to the +0.02-degree jump diminishes those 23 % to 8 %, about equal to the other coordinate percentage.

Thus, after correction for the two variable astronomical effects and the jump in elevation coordinate this new series of measurements appears to contain only about 8 % 'outliers'. This favourably compares with the mentioned 11 % of similar outliers in the original data of 2003/2004.
The missed 3 % can easily be explained by preselection effects (data analysed here have been picked, by RF, from a larger set with an eye on 'better' measurements).

Conclusion 1: Analysed measurements confirm that Model3 developed last year for RT32 pointing does not contain significant biases.

Conclusion 2: There is an urgent necessity to improve the present steering system in that at least two variable, but easily predictable, astronomical effects (annual aberration and nutation) be accounted for in addition to the precession of catalogue equatorial coordinates of sources when observed with the OCRA receivers.

A further 2 or 3 % improvement in this regard may be expected from inclusion of the third of most prominent effects, that due to the UT1 – UTC difference. Practical suggestions on implementation of these effects are given in an earlier report.
The zenith distance coordinate pointing apparently is still very much affected by the 0.02° jump.

Can Model3 be improved?

Comparison of 2003/2004 residua from Model3 (in the inset; note the different scale for these residua) with 2005 errors in azimuth coordinate (red dots) reveals weak similarities in the two distributions suggesting a possibility to slightly improve the model in the future, when more conclusive data are collected

Pointing Lookup Table

The plot below shows the largest value of position errors (composed of errors in the two coordinates added quadratically) of all knots at each even degree of elevation starting from the telescope horizon (i.e. elevation of 2°).

Largest errors of lookup table due to sampling of Model3 every 2°

Between altitudes 24 and 86° this pointing error does not exceed 0.002°, and falls below 0.001° for altitudes 50 to 78°.

Conclusion: Anccuracy of current scheme of using lookup table for pointing corrections seems satisfactory for OCRA purposes.

More on Optical Properties

RT32 aperture efficiency losses due to subreflector lateral displacement and defocus of subreflector and feeds. Note the different scale (top) for the subreflector displacements. Downward axial displacements result in similar (although slightly smaller) losses as these presented

An error of 1 mm in the axial position of the subreflector results in similar gain losses (1.4 %) as these due to 50 mm of the feed axial displacement (1.3 %)!

Is this observation consistent with the known fact that the secondary focus is of the order of the magnification squared, M², as deep as the prime focus? Typically the proportionality factor in this rule is estimated to about 0.7 and M of RT32 equals to about 8.7, thus the theoretical ratio of the two depths would be about 53. This number is in very good agreement with the above noted factor of 50. The purpose of this check is to convince the reader that the presented results, though obtained with entirely new software (the OptiCass program), can be relied upon. There are more checks available for inspection in another document. Those there are related to various beam parameters (such as the width and deviations in response to feed and subreflector offsets).

For lateral feed displacements smaller than 10 cm, even in the absence of refocusing, the aberration losses are negligible (staying below 0.02 %).

Postscript: OCRA-F Losses

Next generation of the OCRA array is expected to have 16 closely packed feeds placed at the same height (z-coordinate). Each horn (8.5 cm in diameter) will be directed parallelly to z-axis. This means that the outermost and innermost feeds will be displaced by 18 cm and 6 cm, respectively, from the RT32 optical axis.

OptiCass computes patterns assuming the feed to be directed towards the subreflector centre, but a user can offset this direction as he desires. Making the feed radiation pattern parallel to z-axis in OptiCass is particularly simple since one of normally displayed parameters is the inclination of the feed — subreflector centre direction with respect to the optical axis. Thus it is enough to set one of the two feed angles to the value displayed for the corresponding inclination angle assigning to it an opposite sign. This procedure was used to compute results that follow.

OCRA5 ====> r-offset: max = 0.18 m, min = 0.06 m Feed pattern parallel to optical axis Feed Beam Aberr Spill 1st side z-off angle squint loss loss lobe m deg deg % % % Outer feeds, r_off = 18 cm 0.0 -1.1275 -0.1057 0.1344 0.2834 0.8634 <== Feed toward subrefl. centre 0.0 0.0 -0.1058 0.1128 0.1973 0.8636 <== Feed parallel to z 0.014 -0.0017 -0.1059 0.0192 0.1976 0.8770 <== Optimal z-offset 0.014 0.0000 -0.1059 0.0192 0.1975 0.8771 <== Parallel to z (final) Inner feeds, r_off = 6 cm 0.0 -0.3759 -0.0352 0.0035 0.0847 0.7672 <== Subreflector centre 0.0 0.0 -0.0352 0.0033 0.0752 0.7686 <== Parallel to z 0.002 0.0 -0.0353 0.0021 0.0752 0.7692 <== Optimal position Aberration and added-spillover losses for all the feeds at the same level (z-off, counted from the secondary focus, upwards positive) Feed at r=6cm Feed at r=13.44cm Feed at r=18cm z-off Aberr Spill Aberr Spill Aberr Spill m % % % % % % 0.008 0.0233 0.0753 0.0108 0.1432 0.0357 0.1974 0.009 0.0304 0.0753 0.0115 0.1432 0.0305 0.1974 <== 'best z' 0.010 0.0386 0.0753 0.0133 0.1432 0.0263 0.1975 Complete set of assumed and computed parameters as displayed by OptiCass for the outer feed at optimal z SETTABLE parameters # #0 #1 #2 #3 #4 Cassegrain: D,X_min,f,Xs_max,h2 [m] 0 32.000 -16.000 11.200 1.600 1.000 Subreflector: x,y,z, tx, ty [m,deg] 1 0.000 0.000 0.000 0.000 0.000 Feed offsets: x,y,z, Dtx,Dty [m,deg] 2 0.180 0.000 0.009 1.129 0.000 Ray-tracing: N/R.NxNy,Nu,Nv,maxU,maxV 3 20.00 24. 24. 2.500 2.500 Wavel,Taper,zAprt,pltD,pivot [m,dB,-] 4 0.010 12.000 -8.343 2. -1. COMPUTED param's & x,z_piv,du,v,N 0.000 0.480 0.004 0.000 0.000 Main dish: f/D,f/Dp, D2, G,coordG [m] 6 0.3500 0.3500 32.000 5.714 16.000 angles: t_V,t_H, t_0, t_1, t_2 [deg] 7 142.151 142.151 0.000 -71.075 71.075 Subreflector: Dc,Dm,Ds2,Gs,Xs_min [m] 8 3.2000 3.2000 3.2000 0.5056 -1.6000 feed angles: t_VH,t_c,_0,_1,_2 [deg] 9 18.8256 0.0000 0.0000 -9.4128 9.4128 Cassegrain: f1, f2, fs, F, M [m,-] 10 1.0541 9.1459 10.2000 97.173 8.6762 Hyperbola: a,c,b,e, FSAmpRatio [m,-] 11 4.0459 5.1000 3.1050 1.2605 0.9933 Beam: t_u,t_v, HPBW_u,_v,_0 [deg] 12 -0.1058 0.0000 0.0210 0.0206 0.0208 Squint, phi_X,Y, apert_X,Y [deg,m] 13 0.1058 -1.1286 0.0000 -0.1999 0.0000 Loss: Aberr,Spill,A&S,IllDec,Totl [%] 14 0.0305 0.1974 0.2279 3.0697 3.2905 pathR,ComaLow,-Hi,1stLob,Totl'[m,%] 15 0.0575 -0.0799 1.5544 0.8715 1.232

Note in the above tables the same (in absolute sense) values for feed initial direction to the subreflector centre (phi_X of –1.1286) and feed radiation pattern offset (Dtx of 1.129, which is internal 1.1286 rounded only for display). This ensures parallelism of the feed pattern and the RT32 optical axis.

These computations demonstrate that for the OCRA-F size the losses due to lateral feed displacements and due to the field curvature will not be significant. If the array is placed exactly in the focal plane, the aberration losses (i.e. those usually referred to as coma and astigmatism) will not exceed 0.15 % for the outer feeds (the inner feeds will then experience practically no losses). Lifting the array by about 9 mm above the secondary focus, toward the subreflector, nearly equates the losses for the inner and outer feeds (keeping all the 16 feeds still at marginally low losses of about 0.03 % or less).

Note also: 30 GHz ray-tracing beam of a laterally offset feed deviates from the RT32 optical axis by 35.3' per metre of offset or by 21.2" with each centimetre of the offset. Thus the horn separation of 8.5 cm will correspond to 3', or 0.05°, or 2.4 HPBW separation of beams on the sky.