Triple Product using Calred

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Triple Product using Calred

Postby PaulHancock » Thu Aug 15, 2013 12:03 am

For a while now I have been trying to decipher the Calred task as I would like to be able to use the triple product to measure the flux for some of my observations.

My understanding is that the triple product has an amplitude that is
A_TP = (Aij * Ajk * Aki)^1/3
Φ_cl = Φij + Φjk - Φki
where Aab is the amplitude of the visibility on baseline a-b, and Φab is the phase of the visibility on this baseline.
These quantities are related to the visibilities via Vab = Aab*exp(iΦab).

I also understand that calred (options=triple) calculates this quantity for each 3-baseline triangle in the array and then returns the mean (or some sort of average).

My problem is that calred (options=triple) will report negative fluxes for sources in the low SNR regeime. I take this to mean that there is no source detected however the negative flux is very troubling to me.

If the Aab are all amplitudes of the visibility they should all be positive definite numbers and there fore A_TP should also be positive definite.
Clearly there is something wrong with the above, yet I cannot figure it out.

A confounding factor is that when I use the task closure to calculate the triple product (closure options=amp) I always get positive numbers. Am I mis-interpreting something or is there something wrong with calred.

As a side note:
What do the columns Con/The/Act represent? There is nothing in the help file or in the calred.for code that explains these columns.
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Re: Triple Product using Calred

Postby ste616 » Thu Aug 15, 2013 1:04 am

Hi Paul,

The calred task does have a number of problems, but since the closure and uvflux tasks basically do the same thing I don't think anyone has really tried to fix it.

You must be careful with these tasks for flux density measurement though. We do use these tasks (closure specifically) for C007 measurements, but we will be moving away from this to uvfmeas in the very near future. This is because it is very difficult to know exactly what frequency the flux density you get corresponds to, with such a wide bandwidth. The uvfmeas task, while only using normal vector averaging which still requires gain calibration, will perform a spectral fit to your data and therefore you can get the flux density at whichever frequency you need it for. With the other tasks, asymmetric flagging may produce a flux density that is not actually centred at the band's central frequency; with a large enough spectral index, this may change your flux density substantially.
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Re: Triple Product using Calred

Postby Mark.Wieringa » Thu Aug 15, 2013 4:24 pm

Hi Paul,

I had a look at calred to decipher the code - I've added some extra comments in the help with my best interpretation of what it calculates and added a few extra digits in the output.
The basic answer is that the triple product is calculated on the complex visibility and then the real part is taken to give a flux estimate. Since the triple product removes the phase errors the imaginary part should be noise for a source at the phase center. If you want more details on the maths and reasoning behind this you'll have to talk to Bob Sault who wrote this task.

Hope this helps,

Code: Select all
c       CALRED produces a table with the following columns:
c       Sca (mJy) - the scalar average fluxdensity estimate, calculated
c          as the rms of the visibility amplitudes
c       Vec (mJy) - the vector average fluxdensity estimate,
c           not listed with options=triple
c       Tri (mJy) - the triple product fluxdensity estimate, this
c          is the cube root of the real part of the average of
c          V12*V23*conj(V13) (note that this can be negative).
c          Only listed with options=triple.
c       Con - the confusion percentage, calculated from the ratio of the
c          rms in the imaginary and real component of the triple ampl.
c       The - the theoretical noise in mJy
c       Act - the actual noise in mJy
c       NCorr - the number of correlations contributing
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Re: Triple Product using Calred

Postby PaulHancock » Mon Aug 19, 2013 10:30 am

Jamie, Mark,

Thanks for the replies, I have a much better idea of what these tasks are doing now.

I am surprised to see that only the real part of the triple product is reported, and that the imaginary part is assumed to be zero. I understand that for enough S/N and a source that the phase center, this is an ok assumption. However for lower S/N or for sources that are not at the phase center, it would be good to see both the real and imaginary components. (For a source at the phase center you could calculate S/N as re/im, and when a source is not at the phase center the mod/arg of the complex number tell you something about the flux and ~location).

Do you think I would be correct to assume that using closure to calculate the real component, and the closure phase, I could reconstruct the re+im components of the complex triple product?

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Re: Triple Product using Calred

Postby Mark.Wieringa » Mon Aug 19, 2013 1:40 pm

Hi Paul,

I must admit I don't have much insight in what triple product values tell you about the source - if antenna based errors are removed, presumably this means phase slopes across the array are not visible either - ie no position information. What is left must be source structure.

I think closure uses the same triple amplitude calculation as calred (except calred can deal with planets as well), so you can work out the real component and the phase, but I don't think you can get at the imaginary component. I could try to add this to one or both of these tasks if you're keen to have this.


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