[mmaimcal] draft results of holography sensitivity calculations
Jeff Mangum
jmangum at nrao.edu
Mon Dec 6 11:08:17 EST 2004
Hi Peter,
"Peter" == Peter Napier <pnapier at aoc.nrao.edu> writes:
Peter> I have always expected that the final tweak of the surface would have to
Peter> be made based on holography measurements made at the AOS. Remember that
Peter> there is a significant difference between the average temperature, water
Peter> vapor and barometric pressure at the OSF and AOS. We must check to see
Peter> if these differences cause any change (hopefully small) in the surface
Peter> and be prepared to readjust.
Peter> Peter
Good point. I see this as an operations issue, in the same category
as using the FEM to set the surface to the rigging angle based on a
holography measurement at a fixed elevation.
--- Jeff
Peter> Jeff Mangum wrote:
>> Let me try to clear-up a number of misconceptions and
>> misunderstandings in this discussion. First, some facts:
>>
>> (1) Transmitter holography will be used to verify the 25 micron spec
>> at the OSF. The main drawback of this technique is that we cannot
>> check the elevation dependence of the surface.
>>
>> (2) Some technique is needed to check the dependence upon elevation of
>> the surface. This can be done in several ways with a
>> low-frequency (1mm or 3mm) system:
>>
>> (a) Interferometric holography (3mm).
>> (b) OOF beam maps (1mm).
>>
>> Pick your poison as to which technique you want to use. Both are
>> difficult to implement. Note, though, that high resolution on the
>> surface is not necessary for this measurement. You need to look
>> for large-scale deformations with elevation as the basic elevation
>> check.
>>
>> (3) For safety reasons, we should not plan on doing surface setting at
>> the AOS. This means that all antenna surface settings will need
>> to be done at the OSF.
>>
>> (4) The surface as a function of elevation check is really an antenna
>> acceptance issue. Likely something one would do on the first N
>> antennas (where N is greater than 2 but less than 6).
>>
>>
>> More comments below...
>>
>> "Mark" == Mark Holdaway <mholdawa at tuc.nrao.edu> writes:
>>
>>
>>>> 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.
>>
>>
>> There is absolutely no reason to check just a subset of panels. In
>> fact, the only reason ever to do a limited surface measurement/setting
>> would be to correct an incorrect setting of the surface (i.e. to
>> re-adjust the focal point of the paraboloid or to raise/lower the
>> surface, both of which I have had to do).
>>
Mark> Yeah, it is unclear how we would make good use of holography at the low
Mark> site. We would do OSF holography, and find out "Oh NO! The surface is
Mark> BAD!", and then drag the antenna up to the high site, do full-array
Mark> holography and find out "Ah, this is how we need to adjust the panels",
Mark> and then drag the antenna back down to the OSF again and adjust the
Mark> panels, and then do OSF one-baseline holography and confirm "OK, the
Mark> surface is FINE!" and then drag the antenna back up to the high site
Mark> and do more holography and say "OK, the surface is indeed FINE".
>>
>> If you discovered a mis-set surface, there would be no reason to move
>> it to the AOS.
>>
Mark> If we have a one-baseline interferometer at the OSF, yes, we'll use it,
Mark> but if we don't have it, we might actually save a bit of time.
Mark> Maybe the one valid use of holography at the OSF is to confirm that
Mark> the panel resetting has indeed made life better for us.
>>
>> As I said above, interferometric holography serves only one purpose,
>> to check the elevation dependence of the surface. I believe that this
>> can be done with low-spatial resolution measurements.
>>
>> --- Jeff
>>
>>
>>
>>
>>>> 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.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> mmaimcal mailing list
>>>>> 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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