Accounting for aberration in plane of sky coordinates #305
Description
I couldn't find where you accounting for aberration in the calculation of lmn coordinates. All the calculations seem to be ignorant of time. These coordinates are conjugate to the uvw coordinates, and thus also have an effect related to motion of the observer relative to the inertial reference frame of the coordinate system. For the UVW there are two inertial reference frames often used: Solar system barycentre, and Earth's barycentre. CASA use's Earth's barycentre in the UVW calculation, VLBI uses solar system's. In both cases, the orientation of the frame exactly matches ICRS coordinate frame, so that l/u points along RA and m/v points along DEC.
What this means is that if you convert RA/DEC into l and m without taking into account motion, i.e. time, you'll get wrong results.
To illustrate this here I plot the astrometry error over the plane of sky (l,m coords) induced by aberration (and what happens when you ignore time).
separation(lm_to_icrs(l, m, phase_centre, t0 + offset), lm_to_icrs(l, m, phase_centre, t0))
Notice, after exactly 1 year the difference is again minimal, because the Earth is (nearly) in the same spot. The peak error is reached around 6 months.
Here's the error v.s. sqrt(l^2 + m^2) over the course of a year's offset.
Of course, as is usual, for narrow fields of view it's negligible. But, for wide field of view it's good to take into account, and not too hard either.