[evlatests] Frequency offsets between calibrator & target

[Vivek Dhawan]

Summary of problem: Crystal Brogan reported that in AC904 (6.7GHz,
B array, 2007 Oct 31) where calibrator and target were observed at
slightly different frequencies, phase transfer from calibrator to
target did not work - the images were highly corrupted.

Following discussion with Ken and a test observation, the current
state of understanding is as follows:

VLA and EVLA antennas all show a change of phase between 2 settings
with small frequency offset d_f,  of

d_phi = 2pi * L * d_f / c,

where L is the electrical path length in LO transmission to the
antenna pad. A baseline formed by two antennas equidistant from the
LO distribution point has no phase jump; this has been verified.
Celestial geometry (w term) is not relevant, but L is of the same
order of magnitude.

So, for example, for a 4kHz difference between calibrator scan and
target scan (e.g. on the same source, geometry unchanged), the phase
difference is 50deg at the end of B array (EVLA, glass fiber) or
~30deg for VLA (air).

How the E/VLA differ:

The EVLA does the fine tuning at the antenna (L302) using a reference
that has been distributed over fiber. The VLA does the Doppler tuning
in the Flukes, not in the antenna, and the Fluke reference signal is
not subject to the distribution path length. In the MODCOMP days, the
round-trip phase correction for changes in the LO path was done by
carefully excluding the Fluke part. Now it includes the Fluke and so
the VLA has the same behaviour as the EVLA, and is worse than the old
VLA system. (If cal and target are at the same frequency, this problem
goes away.)

Fixing it:

1. Online: Conceptually the right thing (I think) is to account for
    the LO path length correction as a delay instead of a phase.

2. Post-processing: Knowing the path lengths (pad positions) and
    frequency offset, a post-processing correction should also work.
    I have not yet figured out how to accomplish it in AIPS, but will
    think about it.