Proper alignment of a receiver to the telescope is important to ensure maximum efficiency and proper operation of the instrument. One part of the alignment is to ensure that the receiver illuminates the secondary properly. The beam coming from the receiver should be centered on the secondary. We have here used the fact that it often is easier to assume the receiver is a transmitter. For the optical properties it does not matter if we think of the system as transmitting or receiving. The amount of radiation received from a given direction is proportional to the amount that would been transmitted in that direction. This is due to reciprocal properties of Maxwell's equations. We will use this duality frequently below.

The receivers produce beams that have Gaussian shape. When the beam is centered the power density at the edge of the secondary is normally 10% of the value in the center – this would be a 90% edge taper. The radiation missing the secondary is called spillover. If we integrate the spillover power density we find that 10% of the transmitted beam power will bypass the secondary and fall directly on the sky for a 90% edge taper. Hence, due to the reciprocity 10% of the received radiation will come directly for the sky bypassing the main dish and secondary mirror. If the beam not is properly centered the power density will be higher on the side where the beam is pointed. We can use this effect to center the illumination on the secondary mirror. Simply measure the intensity of the spillover past the secondary to the east, west, top and bottom. Then adjust the TMU position until the spillover is equal. Since some receivers produce a slightly elliptical beam it is safest to only compare left with right and top with bottom. Further, if the edge taper is high the spillover amplitude might be very weak when the beam is well centered on the secondary.

The Cassegrain focus in the cabin has a f/12 focal ratio. Hence the angular radius is 2.39 degrees as seen from the cabin. The relative amplitude of this feature is only about one millionth of the response of the main beam. To see this feature we need a source that is very strong and it would also help if it were more extended than the main beam. The Sun is such a source.

Make sure the total power is displayed on the chart recorder through the offset box. The total power comes from the IF2 unit in the wall rack. It is normally already connected to at least the patch panel to the left of the TSS station. You will need the offset box since we are looking at a weak signal of top of a large background consisting of atmospheric and receiver noise. Without the offset box the signal will go out of scale when we increase the sensitivity enough so we can see the spillover.

Use the source command to slew to the Sun. We will make a raster scan across the sun large enough to cover the spillover, which was 2.39 degrees away. The raster is actually +/-4.44 degrees/cos(El). The relative limit between the antenna and carousel is +/-5 degrees. Hence we must make sure the carousel follows the antenna all the time. Normally the carousel only follows the center position of a map. The command to do this is

followed by another source command. It will not work without a new source command since the vset command only changes a default parameter to the source or centre command. Then go off the sun – i.e. more than 900" which is the radius of the Sun. Set up the sensitivity and offset box such that you can start to see the noise on the chart recorder. It is standard to connect the polarity such that higher input signal is to the right i.e. when you go on the Sun the chart recorder should deflect to the right. Assuming this is the case - center the track towards the left of the chart but leave space for drifts in the atmospheric contribution. With an almost 9 degree long raster the atmospheric contribution can change significantly when you scan in elevation at high airmass. We should now be ready to start. The command is

The procedure will make a raster scan across the Sun – first in Azimuth and then in Elevation. Each raster is 80 seconds long, with overheads the procedure takes about 4 minutes so a chart recorder speed off say 2cm/minute is about right. The procedure code listed is appendix 1. Note that the procedure changes the cell to 40 40 Az. This will affected your offset commands if you need to go off the Sun again to make adjustment.

Figure 2 is an idealized version of what the chart recorder output should look like. The arrow shows the direction of time on the chart. The figure does not show what happens during the setup for the raster scan. If you were looking the Sun when you started, the level will drop down to the off Sun level while the antenna is setting up for the raster. The drop might have some structure associated with it but it should settled down. You can see when the raster scan actually start by looking at the on source counter. In the figure we have first a small signal due to the spillover in negative Azimuth direction, then we pass the Sun and the chart recorder is pegged to the right. After the main beam has passed the Sun a much larger spillover in the positive Azimuth direction. After the Azimuth raster has finished we will again go on the Sun while the antenna sets up for the Elevation raster. There might see some structure (small peaks) while this happens. Then the Elevation raster starts. Here we can see a medium peak in the negative Elevation direction followed by a small peak in the positive Elevation direction. The difference in the "sum" of positive and negative amplitudes is due to elliptical beams as mentioned before. Hence, we will not compare the amplitudes between the Azimuth and Elevation raster.

The real complication is the interpretation of the result and computation of the new TMU values. Each TMU step is 0.01 degrees but the beam will move twice this distance. Thus a TMU change of 100 steps will move the beam about the radius of the secondary. Due to the geometry the TMU x motion is even more sensitive. Thus a move of 100 units is large!

The raster always starts with a negative offset – i.e. east in Azimuth and lower in Elevation. Consider the Azimuth raster and look at figure 3. In the figure we are at a westerly i.e. positive offset from the Sun. As you can see from the figure – if the positive Azimuth spillover is larger the receiver is looking to the east of the secondary. Similar if we have a larger spillover at negative Elevation offsets, during the raster, the receiver is looking above the secondary!

Thus, from the relative intensities we can very simply find were the beam is centered on the secondary. If the receiver looks to the east (west) of the secondary the positive (negative) Azimuth peak is highest. Similar if the receiver looks below (above) the secondary the positive (negative) Elevation peak is highest.

The real complication is from this information figure out how to change the TMU position. This will depend on the receiver position in the cabin. To make calculations possible lets introduce an receiver position angle with RxW close to 0, right Nasmyth at 90, RxB3 close to 180 and SCUBA at 270 degrees. After some consideration we get

DAz = K₁cos(f)Dx + K₂sin(f)Dy

DEl = -K₁sin(f)Dx + K₂cos(f)Dy

The K₁ and K₂ factors scale between TMU units and motion of the beam on the secondary, they are different due to geometrical factors. The equation tells you that if we move the TMU x position in the positive direction the beam will move, on the secondary, in Azimuth as K₁cos(f) and in Elevation as - K₁sin(f). If we move the TMU in the positive y direction the beam will move, on the secondary, in Azimuth as K₂sin(f) and in Elevation as K₂cos(f). The position for the input mirrors on the receivers are roughly –10, 20, 170, 250, 270 and 280 for RxW, RxA, RxB, Bonn, SCUBA and RxH3, respectively. We can now make a table for how to estimate the change in TMU position. The table shows in which way to change the TMU x and y position to even out the peaks.

A + means increase and a – decrease. Small effects are denoted by 0 for no impact, i.e. when the cos or sin factor is 0. ~0+/- is used for 10 degrees away from no impact direction while 0+/- is used for an position of 20 degrees away from no impact direction. Note: sin(10)=0.17 and sin(20)=0.34. It is simplest to start to with the Azimuth raster and make the peaks equal and then do the Elevation raster. Otherwise the result might be very confusing. However, there are some interactions between adjusting the Azimuth and Elevation spillover. You might need to go back and fine tune the Azimuth spillover after finishing the Elevation.

The procedure can then be summaries as:

• Cable up the chart recorder and offset box.
• Run up the system and enter vset carousel_track antenna

• Go to the Sun
• Check the polarity of the chart recorder and offset box and set up the sensitivity by going on/off the Sun.
• Run the procedure tmu_test_scan
• Measure the relative amplitude of the Azimuth and Elevation spillover. Go to the table and see how to correct the TMU position. It is simplest to do it for Azimuth first not to cause confusion. Normal starting motion is about 20-30 TMU units.
• Repeat the tmu_test_scan and TMU updates until the spillover is even.

If observing continues afterwards reset the carousel tracking with

vset carousel_track centre

Good Luck.