[mmaimcal] draft results of holography sensitivity calculations
Mark Holdaway
mholdawa at tuc.nrao.edu
Thu Dec 2 11:48:32 EST 2004
> In the current drafts of the AIV&C plans, Rick Murowinski assumes that
> there will be single baseline operations at the OSF. I need to talk to
> Rick and Robert Laing about this assumption because it implies
> significant support at the OSF for interferometry as you indicate
> below. I'll be talking to Robert Laing today at ESO (we are trying to
> determine computing requirements to support AIV and commissioning).
>
> If single baseline ops will be at the OSF, then you will have a
> correlator. I'm still not sure it is worth doing holography both at the
> OSF and at the AOS. I guess it depends on what the surface accuracy is
> when the antennas are delivered. If I were doing this, I would want to
> do 2-element holography at the OSF for the first few antennas to make
> sure there is nothing major wrong with the surface accuracy. I would
> probably also check the inner pannels - and set them if needed to
> minimize AOS activity. If the pannels generally look good, then I would
> either move holography to the high site only or just do the surface
> accuracy check at the OSF. But this is not the current plan so the issue
> is open.
Yeah, it is unclear how we would make good use of holography at the low
site. We would do OSF holography, and find out "Oh NO! The surface is
BAD!", and then drag the antenna up to the high site, do full-array
holography and find out "Ah, this is how we need to adjust the panels",
and then drag the antenna back down to the OSF again and adjust the
panels, and then do OSF one-baseline holography and confirm "OK, the
surface is FINE!" and then drag the antenna back up to the high site
and do more holography and say "OK, the surface is indeed FINE".
If we have a one-baseline interferometer at the OSF, yes, we'll use it,
but if we don't have it, we might actually save a bit of time.
Maybe the one valid use of holography at the OSF is to confirm that
the panel resetting has indeed made life better for us.
-M
> Cheers,
>
> Debra
>
> On Wed, 1 Dec 2004, Mark Holdaway wrote:
>
> >
> >
> > DRAFT!
> >
> > The basic question: is it worthwhile to set up a correlator at the
> > OSF site to do two element holography on astronomical sources?
> >
> >
> > I am scaling from a base sensitivity for a two element interferometer
> > operating at 90~GHz with 8~GHz bandwidth. I had calculated the
> > 1-sigma noise for a 30~s integration, averaging two polarizations,
> > would be 3.5~mJy. If this is in error, we need to scale the results I
> > present here. Furthermore, I use my canonical ``quiescent'' 3C273
> > spectrum, which pegs the non-flaring 90~GHz flux of 3C273 at 15 Jy.
> > Planets cannot be used for interferometric holography, and 3C273 will
> > be among the brightest of compact sources that could be used at 90
> > GHz.
> >
> > I further assume that we need to perform a complete holography scan in
> > 1 hour so we can track surface changes with elevation. This could be
> > somewhat relaxed, ie, we could spend two hours doing holography, and
> > the sensitivity should be scaled by sqrt(2).
> >
> >
> > OK, heres Table 1:
> >
> > t_int sigma Peak NxN
> > [s] [mJy] SNR in 1 hour
> >
> > 30.0 3.5 >4000 11 x 11 (useless?)
> > 3.0 11.1 1300 34 x 34
> > 0.3 35.0 >400 110 x 110 (could set
> > panels?)
> >
> >
> > This table is simple to create. The problem is now: what does the
> > peak SNR mean? Darrel Emerson made a hand-waving argument that
> > translates the peak SNR in the image plane to the sensitivity to
> > surface errors in the aperture plane, and it is probably correct to within
> > a factor of 2-4, depending on how we slice it.
> >
> > I've made a simple holography simulation package in AIPS++/glish
> > (this software package is really great for things like this, I must
> > say; it is such a pity that AIPS++/glish is so underappreciated
> > and underutilized). The package performs the following steps:
> >
> > * We select an aperture-plane cell-size (ie, 0.20~m), a holography
> > observation size (ie, 128x128), and a taper level at the edge
> > of the dish (ie, 0.25 in voltage). A 128x128 pattern with 0.20~m
> > aperture-plane cells will lead to a factor of 1.7 oversampled in the
> > sky plane. From these input parameters, we generate the
> > amplitude of the aperture-plane voltage pattern.
> >
> > * We can optionally simulate surface errors, but this doesn't quite
> > work yet, so we assume zero surface errors and evaluate the
> > success at reconstructing the surface errors by the rms deviation
> > from zero in the reconstructed surface pattern later. Surface
> > errors, measured as a fraction of a wavelength, would contribute
> > twice (ie, once pre-reflction, once post-reflection) toward the
> > phase of the aperture-plane voltage pattern.
> >
> >
> > * We Fourier transform the complex aperture-plane voltage pattern to
> > obtain the complex sky-plane voltage pattern. This is a simulation of
> > what we would obtain if one antenna tracked 3C273 and the other antenna
> > performed an NxN raster scan about 3C273. In the sky-plane, we
> > can verify the oversampling.
> >
> > * The complex sky-plane voltage pattern is normalized wrong for our
> > purposes, so we scale the peak to the brightness of 3C273 (15 Jy).
> > We also add independent complex thermal noise at each
> > pixel. For a 128x128 raster, we added 0.05 Jy (this obviously
> > doesn't account for any move time between observations).
> > For a 64x64 raster, we can spend 4 times as much time integrating
> > at each point, so we added 0.025 Jy to each pixel.
> >
> > * We then perform another complex-to-complex Fourier transform back
> > into the aperture-plane to obtain an estimate of the phase errors
> > across the aperture. We convert these phase distribution into
> > a surface error estimate by scaling by wave_length /(4 pi) (the
> > extra factor of 2 being again due to the coming-and-going nature
> > of phase errors due to surface errors.
> >
> > * Basically, we just transformed thermal noise distributed over the
> > sky-plane holography observation into errors in our surface
> > determination. As we started with zero surface errors, any
> > ``surface errors'' we think we see are actually due to thermal noise.
> > We evaluate our ability to measure surface errors by taking the
> > RMS in 1~m wide aunnuli on the dish.
> >
> >
> > Here are the results:
> >
> > For a 128x128 holography observation, oversampled, with 0.20 m pixels
> > in the aperture plane, and 0.05~Jy noise per sky-plane pixel:
> >
> > Radius Range RMS Error in Surface
> > [m] [micron]
> > 0-1 7.9
> > 1-2 8.9
> > 2-3 9.8
> > 3-4 12.7
> > 4-5 16.3
> > 5-6 22.0
> >
> > We get essentially the same results from a ``just about'' Nyquist-sampled
> > 64x64 holography observation with 0.2m pixels and 0.025 Jy noise.
> > I posit that the noise limitation to surface error detection in the
> > aperture plane for a given amount of total integration time is
> > a function only of the aperture-plane cell-size, and not of the number of
> > points observed in the holography raster.
> >
> > A cell-size of 0.2 m is sort of the largest cell-size which would
> > permit us to make panel adjustments, but we don't have the sensitivity
> > at the outer edge of the dish to detect the expected 25 micron surface
> > errors. If sensitivity were not an issue, we would probably prefer
> > 0.1 m cell sizes so we could get the slope and curvature
> > of the panel settings right and do a really nice job of it.
> >
> > For a 64x64 holography observation, oversampled, with 0.40 m pixels
> > in the aperture plane, and 0.025~Jy noise per sky-plane pixel:
> >
> > Radius Range RMS Error in Surface
> > [m] [micron]
> > 0-1 2.4
> > 1-2 2.3
> > 2-3 2.2
> > 3-4 3.1
> > 4-5 4.1
> > 5-6 5.8
> >
> > Now, this is the sort of accuracy we WANT to set the panels, but
> > we don't have the resolution we need to set the pannels.
> >
> >
> > Basically, our accuracy in the surface measurement will be
> > proportional to 1/cell**2, where cell is the aperture plane
> > cell size. Making the cell a bit smaller will make the
> > error in the surface determination a lot larger. So, it is
> > anticipated that with a two element interferometer doing
> > holography on 3C273, we will hit a hard wall at around 0.3
> > m cell sizes, and it will be very hard to get the desired
> > accuracy the with smaller cell-sizes that are required for
> > accurate panel settings. On the other hand, if we relax to 0.4 m
> > cell sizes, which are too large to set the panels, we will
> > be able to do a basic verification of the surface accuracy
> > of a dish using two element interferometric holography.
> >
> >
> >
> >
> > Summary:
> >
> > Using two-element interferometric holography and the brightest compact
> > celestial radio sources available, we will have enough sensitivity
> > to accurately set the pannels near the center of the dish, and
> > not at the edge of the dish. Alternatively, using a larger cell
> > size (0.4 m) which won't permit panel setting, we can very accurately
> > confirm the surface accuracy of the dishes.
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > _______________________________________________
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> > mmaimcal at listmgr.cv.nrao.edu
> > http://listmgr.cv.nrao.edu/mailman/listinfo/mmaimcal
> >
>
> ----
> -------
> -----------
> Debra Shepherd e-mail: dshepher at aoc.nrao.edu
> National Radio Astronomy Observatory phone: (505) 835-7398
> P.O. Box O FAX: (505) 835-7027
> Socorro, NM 87801 http://www.nrao.edu/~dshepher
>
>
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