Bima Memoranda No. 23
EFFECT OF ANTENNA TILTS AND ALIGNMENT ERRORS ON POINTING AND PHASE
Melvyn Wright, 14-May-92
SUMMARY
We obtained optical pointing data for antenna No. 5 on 11-12 May 1992 using
the unix operating system. An rms residual of 6 arcsec was obtained with a
sin(2Az) residual pattern in elevation. We investigate the effects of large
tilts and collimation errors on the pointing equations. An antenna tilt, or
an elevation axis mis-alignment of 1', or a collimation error of 5' produce
errors of ~1" rms in the pointing.
INTRODUCTION
Antenna axis mis-alignments and axis offsets produce errors in the antenna
pointing and in the interferometer phase. If the offsets are small then the
the pointing and phase can be easily corrected. We review these corrections
and discuss the accuracy of the antenna alignments required for obtaining good
radio images. The dynamic range is limited principally by phase errors. For
sources which are large compared with the primary beam, pointing errors become
important.
POINTING FITS
The optical pointing data were fitted to the usual pointing equations which
contain parameters to describe the collimation axis, angles between the azimuth
and elevation axes, and antenna tilt. In addition we include parameters to
represent encoder errors, and a refraction parameter:
daz = a(1)*cos(el) + a(2) + a(3)*sin(el) + sin(el)*(a(4)*sin(az)
+ a(5)*cos(az)) + cos(el)*(a(6)*sin(2*az) + a(7)*cos(2*az)) ...(1)
where a(1) - Azimuth encoder + antenna mount offset from the meridian
a(2) - Collimation error of optical or radio axis from the
mechanical axis (orthogonal to the elevation axis). Note that
the optical and radio pointing will differ in this term.
a(3) - Misalignment of elevation axis relative to azimuth axis.
a(4), a(5) - Tilt of azimuth axis.
a(6), a(7) - residuals.
The elevation pointing was fit to:
del = b(1) +b(2)*sin(el) + b(3)*cos(el) + b(4)*sin(az)
+ b(5)*cos(az) + b(6)*sin(2.*az) + b(7)*cot(el) .....(2)
where:
b(1) - Elevation encoder offset.
b(2) and b(3) - Elevation axis errors. The radio pointing may
contain an additional contribution due to subreflector sag.
b(4), b(5) - Tilt of azimuth axis.
b(6) - Fourier analysis residual.
b(7) - Refraction term. Differs for radio and optical pointing.
The functions in these equations are not orthogonal, but the corrections can
be added if the mis-alignments are small.
Antenna 5 has not yet been levelled. The azimuth fit for antenna 5 (Fig 1)
shows a tv camera collimation of 9' and an antenna tilt of 6'. The
elevation fit (Fig 2) is consistent with this tilt but has a residual which has
been fit with a sin(2Az) term. Without this term the fit is significantly
worse (Fig 3).
MODELING
To investigate the effect of large mis-alignments we generated model pointing
data using the MIRIAD task PNTGEN. An antenna tilt was modeled by:
sin(el') = sin(el)*cos(tilt) - cos(el)*sin(tilt)*cos(az)
sin(az') = cos(el')*sin(az)/cos(el) .....(3)
where az' and el' are the apparent azimuth and elevation, and azimuth is
measured from the direction of the tilt. An elevation axis mis-alignment w.r.t.
the azimuth axis has the same effect as an antenna tilt at an azimuth of 90
degrees.
The collimation angle between the telescope (or tv-camera) axis, w.r.t.
the elevation axis was modeled by:
el' = asin( sin(el)/cos(theta) ) + phi
az' = asin( sin(theta)/cos(el) ) + az .....(4)
where theta and phi are the collimation angles parallel and orthogonal to the
elevation axis.
If the tilt and mis-alignments are small then changes in azimuth and elevation
can be added to give the usual linear equations. For large mis-alignments the
equations are non-linear. We generated model data for a collimation of 9' and
tilt of 6' using a random sample of azimuth and elevation. Fig 4 & 5 show the
resulting errors in the pointing constants and pointing residuals. The errors
are much larger close to azimuth 90 and elevation 90 degrees.
OPTICAL POINTING
Table 1 summarizes the current optical pointing. The 'tilt' terms for azimuth
have been modified to model the large encoder errors on antenna 1-3
Table 1. Pointing fit - Thu May 14 15:54:10 1992
Ant Axis Pointing constants (arcmin)
1 azim -41.88 1.43 0.87 -1.26 -3.50 0.11 0.03
2 azim -35.93 0.80 0.97 -3.45 -1.88 0.17 0.36
3 azim 14.65 -0.67 0.60 0.08 -0.55 0.31 0.35
4 azim 33.11 7.16 -0.34 -0.03 0.27 -0.08 -0.01
5 azim 70.41 9.31 -0.40 2.06 -3.39 0.00 0.00
1 elev 9.16 0.35 -0.15 -0.32 -0.12 0.04 0.87
2 elev 73.03 0.43 0.23 -0.08 0.48 0.12 0.87
3 elev -54.73 -0.82 1.38 -0.27 0.16 -0.38 0.87
4 elev 78.86 0.47 0.66 -0.28 0.03 0.02 0.84
5 elev 33.17 -2.06 -2.94 3.87 2.27 0.17 0.85
MIS-ALIGNMENT TOLERANCES
In order to keep the rms pointing errors less than 1 arcsec we need a tilt and
elevation axis alignment better than 1' and a collimation better than 5'. This
corresponds to 1 mm tolerance in the level of the ~ 3 m antenna base, and the
elevation axis support, and ~ 5 mm in the subreflector position. Table 1 shows
that the elevation axis alignment is adequate on all antennae. The antennae are
usually leveled to 10-20" (antenna 5 has not yet been levelled). The tv camera
collimation could be improved on antennas 4 & 5. The radio axis is determined
by the panel alignment with the subreflector. A consideration in the alignment
of the radio axis is the tolerance in the panel mounting points; we need to
leave sufficient space to adjust the panels to the best figure. For optical
pointing, and offset radio pointing from the optical image it is desirable that
the optical and radio collimation are within the field of the tv camera.
PHASE CORRECTION FOR AXIS OFFSETS
Motions of the antennae relative to the source change the interferometer phase.
Motion in the direction of the source change the delay, w, for all sources,
whilst motion along the wavefront change the projected interferometer baseline
(u,v), and hence the visibility for an extended source. It is convenient to
define an interferometer baseline as a fixed vector, b=(u,v,w), between the
intersection of the rotational axes of each antenna. If the axes do not
intersect, then the interferometer phase is also a function of antenna
pointing. Wade (1970) has analysed the phase associated with the large axis
offsets usually present in equatorially mounted antennae. For alt-azimuth
mounts the offset is usually small and the change in projected spacing (u,v)
can be ignored. The extra delay, w, is given by D * cos(El) where D is the
D is the distance between the axes measured perpendicular to the azimuth
axis, and El is the source elevation, corrected for the tilt of the azimuth
axis.
CONCLUSION
Antenna axis mis-alignments and axis offsets produce errors in the antenna
pointing and in the interferometer phase. If the axis errors are large then
cross products need to be taken into account in order to obtain arcsec pointing
and 1 degree phase accuracy. Whilst it is possible to fit the axis errors and
offsets using non-linear fits to pointing and phase data, limited sky coverage
and noise in the data produce considerable coupling between the fitted
parameters. It is preferable to keep the axis errors small and to directly
measure them where possible, rather than to maintain them as parameters to be
fitted from the data. The large azimuth encoder errors on antennae 1-3 are
strongly coupled with antenna tilts and are best measured directly. The
collimation errors due to offset receiver feeds can be calculated and the
antenna coordinates corrected using equation 4. If the antenna tilt is kept
small, then the cross products between tilt and collimation can be ignored.
Slow changes in the antenna tilt will show up as instrumental phase drifts
which can be calibrated from quasar observations. The antenna structure is not
perfectly represented by rotations about rigid axes, and other pointing and
phase errors will be present, for example, due to differential expansion of the
yoke supports for the elevation axis. We can attempt to minimize these by
thermal insulation of the antenna structure.
REFERENCES
Wade, C.M., 1970, Ap.J., 162, 381