[alma-config] Histograms, max, min, mean, rms, and fidelityplots for the C arrays

[Stephane Guilloteau]

-----Original Message-----
From: Mark Holdaway <mholdawa at cv3.cv.nrao.edu>
To: Steven <heddle at totalise.co.uk>
Cc: alma-config at zia.aoc.NRAO.EDU <alma-config at zia.aoc.NRAO.EDU>
Date: Tuesday, December 19, 2000 5:55 PM
Subject: Re: [alma-config] Histograms, max, min, mean, rms, and
fidelityplots for the C arrays


>
>
>A few notes on the fidelity calculations and Dec 18 simulations:
>
>
>
>General:
>
>All of the pages (ie, all model sources) say the mean fidelity was
>calculated over 66049 pixels.  I would have to say that the mean
>fidelities cited are incorrect (ie, they represent the fidelity calculated
>with the wrong mask or something).  For example, look at the Spiral
>configuration results for a long track observations on Mars, -23 d case:
>the distribution is fairly flat, out to 50;  you'd think the fidelity
>would be 25, but its quoted as 11.
>
    Beware of the log scale...
>
>
>M51 C array:
>
>The histogram of error values for the Donut array (mostly negative)
>indicates that it is lacking short spacings, as compared to the Spiral
>array.  As you go to longer tracks, the baselines are geometrically
>foreshortened, you get shorter spacings, and the histogram shifts more
>towards zero mean.
>
>I would argue that much of the difference in the fidelity histograms
>for the Donut and Spiral is due to the less complete short baseline
>coverage, and may not be intrinsically related to the general superiority
>of one configuration over another.
>
>A simple modification to the Kogan algorithm would be to simultaneously
>minimize the sidelobes on a variety of scale sizes (ie, even if you
>have 0.03 peak sidelobes at full resolution, you can have large regions
>of small negative sidelobes that, when smoothed to lower resolution,
>become a wopping monster sidelobe).  Optimizing the sidelobes
>simultaneously on several different scales would mandate superior short
>baseline coverage.  As there is not as much real estate in the short
    Yes indeed, however minimizing sidelobes at ALL scales will produce
better
results . This is what a Gaussian distribution of weights does to first
order, and the
Spiral pattern approaches the Gaussian quite nicely...

> portion of the (u,v) plane, improving that short spacing coverage is
>relatively inexpensive, and should not drastically affect the full
>resolution sidelobe level.  I believe I recommended such a modification
>to the Kogan algorithm several years ago.
>
>
>
>Cyg A, C array:
>
>The mean fidelity, etc:
>These numbers are dominated by the very faint emission that isn't showing
>up on your contour plots or grey scale images.  You might want to also
>put in a fidelity weighted by the pixel brightness, or have a higher
>flux cutoff to examine how well the bright stuff is imaged.
>

    One thing we found out usefull in understanding the fidelity is a
correlation (scatter)
plot of residuals vs intensity. The slope of that gives you the mean
fidelity... A similar
plot of fidelity vs intensity is quite interesting too

>We see the "Conway effect" pretty clearly in these snapshot/long track
>sims:  Since the Donut array is optimized for snapshots, it has larger
>near-in sidelobes, which are lower than the far out sidelobes for
>snapshots, but dominate for long tracks.  The Spiral configuration has
>lower inner sidelobes for both snapshot and long track observations.  So,
>the Donut array does better for snapshots on this particular image, but is
>surpassed by the Spiral configuration for long tracks.
>
>A key perspective for weighting the flip flop in snapshot/long track
>superiority is that achieving good image quality is more important
>for long observations where the thermal SNR will be higher, and hence
>the potential dynamic range will also be higher.
>
    That isn't completely true, because the SNR only goes as the square
root of the time, unfortunately. If an image is dynamic range / fidelity
dominated
it is unlikely to require extremely long integrations, thus. Snapshots may
be a bit
extreme, but short integrations ought to be considered.

>
>
>SDC:
>
>I don't understand how you are getting negative fidelities, unless the
>model brightness distribution has negatives in it, in which case we should
>probably take the absoulte value of the model image while doing the
>division.
>
    Yeah, take the absolute value. It doesn't matter anyhow.

>
>
>MPD:
>
>Very striking display of the "Conway effect";  the larger near-in
>sidelobes are especially damaging at imaging very smooth extended
>emission, which describes this image well.
>
>
>
>Mars:
>
>The Donut configuration is lacking short spacings and is falling down
>there (already commented on this).
>
>The error pattern on an image is often dominated by "invisible
>distributions", for which we don't have any or very much Fourier
>information.  When we are lacking short spacings, the invisible
>distributions include very large scale things, and when the source
>has a lot of flux on such large scales, the errors will be dominated
>by these large scale distributions.   IF we get the short spacings
>right, the errors will be dominated by smaller scale invisible
>distributions, which generally end up looking like the size scales of
>the worst sidelobes (as above, think of sidelobes at a variety of
>resolutions).  So, we've got things like sine waves of approximate
>period like the nasty sidelobe spacing floating around the image.
>As the sine waves go up and down, every now and then they will just happen
>to be very close to zero; when we divide by this number to get the
>fidelity, we just happen to get a very large fidelity for that pixel
>(I actually don't understand why the peak fidelities are not higher
>than the 50 numbers).  Anyway, the sand ripple pattern seen in the Spiral
>array fidelity image is explained by this story.
>
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> -mark
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