[daip] [!6280]: aips - Dispersive delay fitting in AIPS

[Adam T Deller]

Adam T Deller updated #6280
---------------------------

Dispersive delay fitting in AIPS
--------------------------------

           Ticket ID: 6280
                 URL: https://help.nrao.edu/staff/index.php?/Tickets/Ticket/View/6280
           Full Name: Adam T Deller
               Email: deller at astron.nl
             Creator: User
          Department: AIPS Data Processing
       Staff (Owner): -- Unassigned --
                Type: Issue
              Status: Open
            Priority: Default
                 SLA: NRAO E2E
      Template Group: Default
             Created: 02 March 2015 02:34 AM
             Updated: 02 March 2015 02:34 AM
                 Due: 04 March 2015 02:34 AM (2d 0h 0m)
      Resolution Due: 10 March 2015 02:34 AM (8d 0h 0m)



Hi Eric,

As we discussed last week, here is a summary of the feature request for dispersive delay fitting in AIPS.  Broadly speaking, I see two possible ways in which this could be done, and I'll cover both.

Currently, FRING fits delay, delay rate, and phase.  It would be most ideal to extend FRING to also fit dispersive delay and Faraday rotation, as well as the rates of these and a phase rate too.  So 8 parameters in total.  Of these, dispersive delay and its rate are the most important for the use case I have in mind (1000km baselines at 100-200 MHz), but Faraday rotation can become important below 100 MHz.  So if it was the case that incorporating Faraday rotation greatly complicated matters (and I imagine it might), then starting with just dispersive delay and its rate would already be very useful.  Ditto if including a phase rate is problematic.  On the other hand, if you were going to mess with the SN table anyway, then maybe this would be a good opportunity to make sure that all relevant parameters are included.

In the case that all parameters are included, then the visibility phase as a function of frequency f and time t is given by:

RCP phase = (P + t*dP/dt) + (f*N + f*t*dN/dt) + ((1/f)*D + (1/f)*t*dD/dt) + 0.5*((1/f^2)*F + (1/f^2)*t*dF/dt)
LCP phase = (P + t*dP/dt) + (f*N + f*t*dN/dt) + ((1/f)*D + (1/f)*t*dD/dt) - 0.5*((1/f^2)*F + (1/f^2)*t*dF/dt)

where P is phase, N is non-dispersive delay, D is dispersive delay, and F is faraday rotation.  I didn't bother to include any constants because that is a nuisance when typing it out like this, but of course it would probably be nicer to store the values of D and F in sensible units, as is already done for N in the SN table.  Also there's only a 50% chance I got the sign convention right for Faraday rotation.

I could imagine that internally to FRING one would begin with a coarse FFT delay search followed by global optimization of the non-dispersive delay on a per-subband basis as is done now, but then adding a new step which takes these single-band non-dispersive delays and uses them to set a starting guess for dispersive delay and Faraday rotation, and subsequently does a least squares minimization to the single-band phases to fit for all parameters.  This could be further refined if desired by taking this as the starting point for a true global optimization of all 8 parameters, fitting to the actual visibilities again.

The potential to get stuck in local minima is definitely a concern, and it may be useful to force several different least-squares optimizations beginning from different parameters (e.g., you can change the coarse best-fit dispersive delay a little and compensate as best possible with the non-dispersive delay, and use that as a new starting point, and then try again making the change in the other direction).  But with good S/N data it may turn out that these problems are not a big deal.  One would definitely want to be able to set windows for dispersive delay, its rate, Faraday rotation and its rate, just like is possible now for delay and rate.

A related way to attack the problem would be to leave FRING alone and use some variant of MBDLY to fit for dispersive delay, its rate, and optionally Faraday rotation and its rate, using just the FRING outputs: single band delays/rates and phases.  This is probably simpler, and it boils down to exactly the same approach, except that the final optimization (going back to the visibilities) is not possible, so the S/N will be a little lower.  If this is much easier, though, then this would already still be a big improvement over what I do with LOFAR data now (which is to just use narrow-ish subbands and just use FRING as it is available now, essentially doing a piece-wise linear approximation of the phase).

If it was useful, I could definitely provide some LOFAR data which could be used for testing.  If you have any other questions, please let me know.

Cheers,
Adam

------------------------------------------------------
Staff CP:  https://help.nrao.edu/staff