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

[Mark Holdaway]

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.



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
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.

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.



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.



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.




	-mark