[evlatests] How Fast Can We Step?

[Steven T. Myers]

IMO this is probably fine. I'm not sure what the driver is for resetting the
delay centers on a fast timescale. I think the delay center can be set (and
fixed) to within a distance theta of the primary beam center given by the usual
bandwidth smearing value (Bridle lecture) - essentially

   theta < beta*(Freq/DeltaFreq)*SynBeam_FWHM
         = beta*(Freq/DeltaFreq)*(D/Bmax)*PB_FWHM

where DeltaFreq is the channel width (e.g. 2MHz) and where SynBeam_FWHM is the 
synthesized beam, or equivalently in terms of D=25m and max baseline 
Bmax (36.4km for A config) and the primary beam PB_FWHM.
The usual error limits apply (e.g. no more than beta=0.33 for a 5% error).

Example: 2MHz chans at 3 GHz in Aconfig :

   d/PB_FWHM < beta*(3000/2)*(25/36400) = 1.03*beta

so at S-band you would want to keep the phase center within 1/3 of a PB of a
pointing center (~5'). Note at higher frequencies this is more lenient, and you
will be dominated by the error losses by the PB smearing over a single 
integration (regardless of how you set phase centers).

Example: 15GHz with 2MHz chans, A-config so d/PB_FWHM < 5.1*beta so you can step
phase centers every beam or so without a problem.

Note - the main argument for stepping phase center each integration or two is to
allow imaging using the approximation that FieldCenter = PointingCenter w/o 
creating and using the POINTING table. But I still say that if you step phase 
centers at 0.33 beams and integrations every 0.1 beams you are ok using nstep=3
in the OPT for S-band and L-band, and longer above this.

Barry and Rick - am I missing an effect here?

-Steve

On Mon, 9 Mar 2015, Rick Perley wrote:

>    With the current system, phase/delay stepping is limited to about 0.7 Hz 
> (a step every 1.5 seconds).  This is much to slow for sky surveys done at 
> high frequencies, where the primary beam crossing time can be less than 2 
> seconds.
>
>    The dominant limitation is in the station board.  Bruce made a change to 
> permit faster stepping.
>
>    I ran a short test this morning, using 3C48, and an antenna motion of 1 
> arcminute/second (4 X 'sidereal').  Dump time was 0.1 second.  The 
> phase/delay center was moved at four different rates: 1.5 seconds, 1.0 
> seconds, 0.75 seconds, 0.5 seconds.  The scans were in RA, and utilized the 
> 'back-and-forth' method (for future analysis), going from first null to first 
> null.
>
>    Results:
>
>     1) The three slowest rates are all good.  The system easily keeps up.
>     2) The fastest rate (2 Hz) gave a mixed result:
>           a)  For the W to E motion, the system could not quite keep up -- 
> many of the initial delay/phase models were incorrect.
>           b)  For the E to W motion, all was fine.  No incorrect 
> calculations.
>
>    Bruce says he can speed it up a little more.  Shall we try?
>
>    Rick
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|:| Steven T. Myers                      |:|  Astronomer               |:|
|:| National Radio Astronomy Observatory |:|  Ph:  (575) 835-7294      |:|
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