rms values from uvplt uvstat

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rms values from uvplt uvstat

Postby mikepracy » Tue Jul 16, 2013 2:27 pm

Hi Everyone,

I've been having trouble working out what the rms and theoretical rms values mean from uvplt and uvstat. In short I have some snap shot data which has a noise level (as determined from imaging or the original integration time estimates) of about 1mJy. When I output and plot things like amplitude or real component values for the visibilities they have a scatter between them consistent with this i.e. a few mJy. However if I output the rms for these same visibilities from either uvplt or uvstat and either theoretical or empirical estimates I get values in the 100s of mJy. This cant be the rms expected in the amplitudes because the scatter is 100 times smaller so I'd like to know what these values mean?

Thanks
Mike
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Re: rms values from uvplt uvstat

Postby ste616 » Tue Jul 16, 2013 3:33 pm

Hi Mike,

What you are actually getting from uvplt or uvstat when you ask for rms is the scatter within that individual visibility. The "noise level" continuum observers usually care about is the scatter in the average amplitudes of each visibility.

To be more explicit, each visibility in CABB (for the 1 MHz wideband IFs) has 2048 channels. The amplitude in each of these channels is (assuming you've done gain and bandpass correction) the combination of the correct amplitude and some Gaussian noise. The scatter in amplitude over these channels is likely to be very large, because you've only got 1 MHz of bandwidth, and 10 seconds worth of data. But if you average the data over these 2048 channels, the noise will drop by a factor of about 45. So assuming that each visibility is representing the same amplitude, the scatter between visibilities will be about 45 times smaller than the scatter in an individual visibility.

A further complication is that whatever amplitude you are measuring will have a frequency dependence. That is, the true amplitude of each channel in the visibility will be different. But when uvplt or uvstat is measuring the rms, it doesn't know that, and that true amplitude variation will be transferred over to the rms, making it larger again.

Does this make sense?
cheers
Jamie Stevens
ATCA Senior System Scientist
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Re: rms values from uvplt uvstat

Postby mikepracy » Tue Jul 16, 2013 3:42 pm

Thanks Jamie,

that makes perfect sense. In fact Emil suggested that might be the answer based on the order of magnitude of the rms values.

Cheers
Mike
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Re: rms values from uvplt uvstat

Postby len067 » Tue Jul 16, 2013 3:58 pm

Actually Shane O'Sullivan and I both came to this conclusion after you left our office :-)

I guess my question, based on what I believe Mike was doing, is why does the quoted RMS refer to individual frequency channels (if not using the nofqav option) when they appear to be averaged together when quoting the visibility amplitudes? It seems a little bit inconsistent in behaviour (though admittedly I haven't tried to do this myself on any data to reproduce the behaviour).

Cheers,

Emil.
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Re: rms values from uvplt uvstat

Postby ste616 » Wed Jul 17, 2013 10:08 am

Hi Emil,

I think it is doing what it is supposed to be doing. The 'rms' quantity is the visibility noise, not the noise between the visibilities. That is, it is a quantity that is defined for each visibility, not a quantity that requires multiple visibilities. In fact, I don't think using 'options=nofqav' will make a difference to the output of uvplt when plotting rms, as the visibility noise should be the same for each channel in the visibility.

As an aside, according to the uvplt doc, rms is actually the 'theoretical visibility noise rms', whereas uvstat has a separate 'rms' and 'trms' for measured and theoretical noise respectively.
cheers
Jamie Stevens
ATCA Senior System Scientist
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Re: rms values from uvplt uvstat

Postby len067 » Wed Jul 17, 2013 2:50 pm

Hi Jamie,

I agree with everything you stated ... though the case I'm considering is when you start grouping visibilities. When averaging in time and/of frequency (which is what I believe Mike was doing since all his channels were effectively averaged together to look like one visibility) you end up with less visibilities and each of those should have a proportionally lower rms. It is the equivalent of setting the correlator to dump say 40 s samples (if averaging in time by a factor of 4) or 4 MHz channels (instead of 1 MHz channels) in which case your individual visibilities would have half the RMS as you'll have one-quarter the number of visibilities.

If 'nofqav' and no time averaging were used then the visibility noise would indeed be the same as the noise in the actual correlator visibilities i.e. you have N visibilities each with an rms of x. However, if the band is averaged or the visibilities are averaged in time then I would expect the rms to be adjusted to take this into consideration i.e. something like x_new = x / sqrt(N/N_new). Where N_new is the new number of visibilities after averaging in whichever domain (assuming all visibilities are averaged in the same way). So if each visibility had x=400 mJy/beam and you had 4000 correlator visibilities in a single baseline (spread in time and/or frequency), if you happened to average by a factor of 4 in time and a factor of 4 in frequency you would end up with 250 visibilities each with a rms of x_new=400 / sqrt(4000/250) = 100 mJy/beam. The overall visibility noise would be x_new/sqrt(250) = ~6.3 mJy/beam for that baseline (which is the "noise between the visibilities" that you referred to - this will remain the same regardless of how you average the visibilties).

Is this the situation you were considering also?

Cheers,

Emil.
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