Doppler setting

[iancze]

Is your feature request related to a problem or opportunity? Please describe.
ALMA does not "Doppler track" but instead "Doppler sets." This means that the Barycentric correction is calculated at the beginning of the observation, but then every subsequent sample is not corrected for this drift. Instead, it can be calculated offline, since source elevation and track is known, as is the observatory location. The way in which we address the Doppler setting is important, because we'll either need to interpolate the latent space model (at some set of high resolution channels) to the data or vice versa, and the interpolation kernel (nearest neighbor, linear, cubic, sinc) has an impact on the spectral response.

Describe the solution you'd like
One conceptual question I have is where is the (thermal) "noise" introduced into the process of generating the visibility, and how does this affect our ability to interpolate/shift spectral data? TMS Ch 6.2 derives the autocorrelation and potentially has some relevant spectral information.

If we can pre-process the data so that all integration steps have the same LSRK channels, then we can avoid any concerns related to spectral interpolation (though we might still need to deal with spectral covariance #18 ).

Would it be possible to do a Fourier Transform, phase shift, and then process all visibilities to a common channel center? How would we need to treat the noise and its covariances? Can we test this with some mock Gaussian random variables? It seems like this is the idea behind CASA's mstransform interpolation w/ phaseramp.

To start, we should implement some tests using Nyquist sampled spectral data + noise and determine what is critical to the problem. Looking at actual ALMA data, and in particular real observations of the bandpass calibrators, could also help clear up some misconceptions (related to #18 as well).

Update 4/28/21: Leroy+21 has a very useful discussion of the spectral covariances introduced by mstransform linear interpolation (h/t @richteague).

Describe alternatives you've considered
We could interpolate the LSRK model to the TOPO frame, i.e., leave the data in it's natural Doppler-tracked state. This adds in a lot of overhead since we have to perform many spectral interpolations with every model evaluation.

We could also ignore any covariance problems all together by just pre-processing the data with mstransform linear interpolation and modeling the data as is. This is currently supported by the package.

[iancze]

The recommended solution is to pre-process the data using a CASA task like cvel2 such that all visibilities are in the LSRK frame. That way, model can be compared to data at the exact channels of the dataset. Spectral covariance will still need to be treated, but that is a separate issue (#18). Spectral covariance may need to be modified to account for any covariance introduced by a sub-optimal type of interpolation kernel (e.g., linear).

It will be too much of a computational burden for the package to support shifting and interpolation to the BARY frame.