Calibration

Note: Even if you get this right your astronomical phases may be incorrect if your feedlines aren't the same electrical length.

Use a splitter and some lengths of coax to connect one antenna up to both receivers. You must ensure the lengths of coax are exactly the same (so that the signal from the antenna arrives at both receivers at the same time).

Then tune find a stable carrier signal and tune so that it makes a tone at a few hundred Hz to few kHz as heared on the speaker.

What we want to do is plot the two waveforms so that we can compare the phase of the tone at the output of each receiver. A CRO is good for this but you could equally use the PC sound card and any waveform viewing software. Use the volume knobs to set the audio outputs to the same level. Note- If appropriate, you should remove any speakers from the output of the receivers now since if the receivers are under different loads the phase measurements may be affected.

Even better is an oscilloscope which can plot the waveforms in X versus Y mode. If your phases are properly aligned the display will show a line at 45 degrees:

If your phases are in quadrature and your gains (volumes) are set the same then you will get a perfect circle:

If there is some error in your phases you might get something like this:

If the signals are not in phase they will peak at different times. If you measure the time between when the two waveform peaks (Terr) and also the period of one full cycle of the audio sine wave (Tcyc), you can calculate the current phase error using:

Perr = 360*(Terr/Tcyc) degrees.

You can calculate the required adjustment to your delay line, Ladj, using:

Ladj = (Terr/Tcyc)*(Vf*Lwav)

Where Vf is the velocity factor of the coax and Lwav is one wavelength in free space.

 

Another way to calibrate the phases of your interferometer is to use a real astronomical source. The best calibrator is a small but bright radio source which is near transit when there are no other bright sources in the sky. During periods of solar continuum storming the sun makes an ideal phase calibrator since it is effectively a point source and it outshines everything else. For Southern Hemisphere players Centaurus-A scrapes in as a calibrator with longer baselines. <source name> might make a good calibrator for Northern observatories.

The idea is to compare predictions of the calibrator transit time with the time of the "cental lobe" in the measured interference fringe pattern. If the Local Oscillators of your receivers are in-phase and your antenna feedlines are the same length you should get a fringe maximum at transit (if you have configured your LO phases to be in quadrature then you expect a zero reading).

If the measured fringes are not where you expect, then you can approximate the required change to your LO delay cable using the
following:

Ladj ~= (Vf*Lwave)*(Terr/Tfringe)

Where;
Ladj = Required adjustment to LO delay cable (m).
Lwave = LO frequency wavelength in free space (m).
Vf = Velocity factor of the delay coax (ratio<1.0).
Terr = Time difference between observed central fringe time and predicted source transit time. Tfringe = Time of one complete fringe period, measured from the central lobe to an adjacent fringe.


The following data provides an example. On 2002/05/11 Simple observed the following set of fringes for Centaurus-A (NGC5128, 13:25.5 RA, -43:01 Dec) with a 150m baseline.

CenA is at transit at LST 13:25.5, shown by the purple vertical line in the graph. When we measure the maximum of the central lobe, we find it occurs at more like 13:29.4, giving an time error, Terr, of 3.9 minutes. Oh no, the phases are miscalibrated!

We measure the duration of the complete fringe, Tfringe, to be 30.3 minutes. Its usually worth averaging the duration of both adjacent fringes to improve the measurement. It's also often more practical to measure between zero-crossing times than between fringe maxima.

Say we're observing at 20MHz (Lwave=15m) and we want to use RG58 coax for the delay line with a velocity factor, Vf, of 0.66. Then to obtain a fringe maxima when CenA is at transit we need to adjust the length of the coax delay line by:

Ladj = (0.66*15)*(3.9/30.3) = 9.9*0.1287 = 1.27m


This different example shows a complete set of solar fringes on 5th March 2004. Using a solar ephemeris tool like this web site
(http://arthemis.na.astro.it:6563/themis/owa/solar.ephemeris) it was easy to determine that solar transit at the observing site happened at 13:12 local time (2:12 UT).

The bottom panel shows a closeup of the period during solar transit. On this day the two receivers were configured to be running in quadrature, so we expect a zero interferometer response at transit. At the 13:12 (13.2) transit you can see the system has essentially zero output, suggesting the quadrature LO delay cable is now cut to the right length!

 

Methods - two antennas on one rx etc

Hardware (noise source etc)