Hi Danny, I think the 60 MHz spacing is not related to delays at all, although I may be wrong… I never heard that argument within SKA.
That requirement was derived from the following argument (from a “calibration requirement” document by Stephan Wijnholds): ——————————————————— " This requirement is currently formulated as “The stability of the average station band shape post RFI-mitigation shall be within +/- TBD %” [1]. Combined with the requirement on station beam stability, this indicates, that in the envisaged mode of operation of the LFAA element, the station calibration should ensure that the station beam behaves spectrally and spatially according to a specified full-polarization beam model thus allowing sufficiently accurate prediction of the station response during processing of the station signals. To set a meaningful quantitative requirement on the spectral and spatial stability of the station beam, we thus need to see what accuracy is required for array level calibration. We expect to be able to exploit our knowledge of station configuration and antenna response to predict the station beam after station calibration. In practice, station calibration will be done with finite accuracy and we will have imperfect knowledge of the antenna response, for example due to manufacturing tolerances. This may result in systematic deviations from the predicted station response. Fortunately, we can correct such errors by direction dependent calibration [2][3] at a cadence of typically 10 minutes. Below, we derive a requirement on the required station beam accuracy for sources inside the FoV. For the impact of sources outside the FoV, we rely on suppression of these sources by the station sidelobes. Combined with the assumed 10-minute update rate, the station beam accuracy requirement naturally leads to requirements on the spectral and spatial beam stability. In [4], two distinct approaches are presented that relate the impact of station beam errors to the thermal noise. Although the mathematical bounds used in these two approaches can lead to slightly different proportionality constants (the factor 1/√2 in the equation below), both lead to a similar result stating that the relative errors on the station beam (relative to the main beam peak) should be smaller than where ∆S0/√(B·t) is the noise level of a single station after integration over bandwidth B and time t and Srms is the total RMS flux in the image. The instantaneous thermal noise level ∆S0 = 2 kB·Tsys / Aeff follows directly from the sensitivity requirement and Srms can be calculated based on the source statistics from [5] and the size of the FoV of a 35-m station. We will assume that the sensitivity of the full LFAA system will be 100, 760, 1025 and 975 m2/K at 50, 100, 160 and 220 MHz respectively and that the data are split in slices of about 1 MHz for EoR tomography [6]. Since direction dependent array calibration can be exploited to correct systematic errors in the beam model at time scales of order 10 minute, we will use t = 600 s. This leads to the following reformulation of requirement SKA1-SYS_REQ-2621: Spectral stability. The spectral stability of the station beam bandpass post station calibration and RFI mitigation shall be within 1.3%, 0.4%, 0.6% and 1.1% at 50, 100, 160 and 220 MHz respectively compared to then full polarization parameterized beam model. " ——————————————————— Cheers, Eloy. > On 8 Oct 2015, at 00:48, danny jacobs <[email protected]> wrote: > > Maybe there is? Looking at the requirements in the "SKA phase 1 (level 1) > requirements" I see the following > > "The spectral stability, on a time scale of 600 sec.,of the station beam > bandpass, post station calibration and RFI- mitigation, shall be within 1.3 > %, 0.4 %, 0.6 % and 1.1 % at 50 MHz, 100 MHz, 160MHz, and 220 MHz > respectively compared to the full polarization, parameterized beam model. > > Translating into the HERA framework: > I read this as a suppression of all variation to the -22dB level at 100MHz. > Since these numbers are given in ~60MHz bins we could read this as requiring > -22dB at 16ns or longer. > > How does this relate to the HERA spec? The HERA specification is -60dB > suppression at reflection time scales of 60ns and longer. (This spec is rough > and will change slightly as we refine it but this is in the ballpark.) > > We can translate the (current) HERA spec to SKA spec language: Spectral > stability shall be better than 1e-4 % on spectral scales of 17MHz or shorter. > > So looked at this way, the HERA spec and the SKA spec are about 4 orders of > magnitude apart. Recently we've discussed the possibility that the HERA spec > is a little more stringent than we absolutely need, so we'll see where we > land. > > > Digging further into the SKA spec: > > Looking back even further into the level 0 (science) requirements that are > cited as the origin of the 0.6% spectral stability requirement I find this > "SKA1 shall possess relative calibration accuracy of adjacent frequency > intervals of better than 40 dB for Δν/ν=10^-2 to Δν/ν=10^-5" > > At 100 MHz this corresponds to a ripple constraint of -40 at 1000ns or > longer. This one is hard to understand as flowing from a 21cm science case. > Its also hard to see how that flows into the ~1% error allowable in the level > 1 spec. > > What am I missing here? > > > > > > > > On Wed, Oct 7, 2015 at 4:15 PM, Eloy de Lera Acedo <[email protected] > <mailto:[email protected]>> wrote: > Hi Miguel, > > Yes, understood. I have to say also that SKA does not have any requirement > for spectral ripple in the sense HERA does. I never heard about anyone > thinking about doing avoidance with SKA for example, or at least that never > got translated into requirements. The only concern I have appreciated is > about calibratabilty and absolute A/T across the field of view. > > Eloy. > >> On 7 Oct 2015, at 23:28, Miguel Morales <[email protected] >> <mailto:[email protected]>> wrote: >> >> Hi Eloy, >> >> I’d like to mention that the spectral features we are interested in are at >> the per element not the per station. While per element spectral features do >> average out in frequency, they don’t go away, they’re just moved to the >> station beam (spatial). As we need exquisite control of both, this doesn’t >> really help us. So the golden metrics for me is per antenna response and how >> repeatable it is antenna-to-antenna. >> >> Best, >> >> Miguel >> >> >> >> >> >>> On Oct 7, 2015, at 8:40 AM, Eloy de Lera Acedo <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> Hi John, >>> >>> I am checking with our australian colleagues, it should not be there. I >>> can’t remember now if we ever discussed this. This is also a very small >>> array of course (16 antennas) so it has some features that won’t be present >>> for larger stations. >>> >>> Eloy. >>> >>>> On 7 Oct 2015, at 16:32, Jonathan Pober <[email protected] >>>> <mailto:[email protected]>> wrote: >>>> >>>> Thanks, Eloy. The feature at 100 MHz in the Y polarization is definitely >>>> the most prominent. Maybe it's related to FM? The X polarization also >>>> has smaller features around the gap at ~130 MHz, possibly also related to >>>> flagging, and a discontinuity at ~180 MHz. I was postulating the that >>>> latter might be due to different 30.72 MHz chunks being observed on >>>> different nights. The explanation for the overall larger values at higher >>>> frequencies seems totally plausible. >>>> >>>> On Wed, Oct 7, 2015 at 7:50 AM, Eloy de Lera Acedo <[email protected] >>>> <mailto:[email protected]>> wrote: >>>> Hi John, >>>> >>>> Do you mean the feature at 100 MHz? That one is not predicted by the >>>> modeling and indeed it is very strange because it does not show up in the >>>> other polarisation. We will check with our Australian colleagues, see what >>>> they think. That should not be there. >>>> >>>> The reason why the A/T measurements give larger values than the model can >>>> be related to this: >>>> "For Hydra A, our model predicts the flux density at 300 MHz to be ∼1/3 >>>> that at 74 MHz. However, detailed measurements specifically targeting >>>> Hydra A at 74 and 330 MHz [35] show that the flux density of the compact >>>> central region reduces less steeply with frequency, and would be only ∼1/2 >>>> that at 74 MHz. Unlike the surrounding diffuse emission, the compact >>>> central region is not spatially filtered at the higher frequencies, thus >>>> our modelled "known" flux density causes an underestimate of the actual >>>> flux density, resulting in a higher than actual A/T . In future processing >>>> of measurement, we expect significant convergence as the models of >>>> calibrator sources are improved for the MWA and other wide-band >>>> low-frequency telescopes." >>>> >>>> Regarding A/T, in this paper (Fig. 15) you have our best estimates for A/T >>>> calculation for SKA before re-baselining (before halving the number of >>>> elements). >>>> >>>> http://rd.springer.com/article/10.1007/s10686-015-9439-0 >>>> <http://rd.springer.com/article/10.1007/s10686-015-9439-0> >>>> >>>> Cheers, >>>> Eloy. >>>> >>>>> On 7 Oct 2015, at 15:31, Jonathan Pober <[email protected] >>>>> <mailto:[email protected]>> wrote: >>>>> >>>>> I'm not used to thinking about A/T this early in the morning, but are >>>>> Figures 14 and 15 what we've always wanted to see from the SKA? Measured >>>>> (and simulated) frequency responses? >>>>> >>>>> http://arxiv.org/abs/1510.01515 <http://arxiv.org/abs/1510.01515> >>>>> >>>>> (There seems to be a prevalance of 15's here, which numerology.com >>>>> <http://numerology.com/> tells me corresponds to "Loving, forgiving, >>>>> tolerant" -- for those of you perhaps looking for guidance in your >>>>> relation to the SKA.) >>>>> >>>>> In Figure 14 there are a few sharp features beyond what the model >>>>> predicts. I need to read the paper in more detail to figure out exactly >>>>> what the measurement is. Those could be due to sidelobes from other >>>>> sources affecting their spatial filter, although they are using the full >>>>> 128 tiles of the MWA for cross correlation, so the PSF should be good. >>>>> They're also stitching together the band from several 30.72 MHz chunks, >>>>> so those could be artifacts at band edges. >>>>> >>>>> Maybe Eloy and/or Nima have some thoughts on these results? Very nice to >>>>> see this work taking place and moving ahead. >>>>> >>>>> Cheers, >>>>> >>>>> Jonnie >>>> >>>> -- >>>> Dr. Eloy de Lera Acedo >>>> >>>> Senior Research Associate >>>> Astrophysics Group >>>> Cavendish Laboratory >>>> University of Cambridge >>>> JJ Thomson Avenue >>>> Cambridge CB3 0HE >>>> >>>> Teaching Associate and Bye-Fellow >>>> Downing College >>>> Regent Street >>>> Cambridge CB2 1DQ >>>> >>>> Telephone: (+44) (0)1223 (3)37365 >>>> Fax: (+44) (0)1223 337563 <tel:%28%2B44%29%20%280%291223%20337563> >>>> Email: [email protected] <mailto:[email protected]> >>>> Webpage: http://eloydeleraacedo.weebly.com >>>> <http://eloydeleraacedo.weebly.com/> >>>> >>> >>> -- >>> Dr. Eloy de Lera Acedo >>> >>> Senior Research Associate >>> Astrophysics Group >>> Cavendish Laboratory >>> University of Cambridge >>> JJ Thomson Avenue >>> Cambridge CB3 0HE >>> >>> Teaching Associate and Bye-Fellow >>> Downing College >>> Regent Street >>> Cambridge CB2 1DQ >>> >>> Telephone: (+44) (0)1223 (3)37365 >>> Fax: (+44) (0)1223 337563 <tel:%28%2B44%29%20%280%291223%20337563> >>> Email: [email protected] <mailto:[email protected]> >>> Webpage: http://eloydeleraacedo.weebly.com >>> <http://eloydeleraacedo.weebly.com/> >> > > -- > Dr. Eloy de Lera Acedo > > Senior Research Associate > Astrophysics Group > Cavendish Laboratory > University of Cambridge > JJ Thomson Avenue > Cambridge CB3 0HE > > Teaching Associate and Bye-Fellow > Downing College > Regent Street > Cambridge CB2 1DQ > > Telephone: (+44) (0)1223 (3)37365 > Fax: (+44) (0)1223 337563 <tel:%28%2B44%29%20%280%291223%20337563> > Email: [email protected] <mailto:[email protected]> > Webpage: http://eloydeleraacedo.weebly.com > <http://eloydeleraacedo.weebly.com/> > > > > -- > > National Science Foundation Fellow > Arizona State University > School of Earth and Space Exploration > Low Frequency Cosmology > Phone: (505) 500 4521 > Homepage: http://loco.lab.asu.edu/danny_jacobs/ > <http://loco.lab.asu.edu/danny_jacobs/> -- Dr. Eloy de Lera Acedo Senior Research Associate Astrophysics Group Cavendish Laboratory University of Cambridge JJ Thomson Avenue Cambridge CB3 0HE Teaching Associate and Bye-Fellow Downing College Regent Street Cambridge CB2 1DQ Telephone: (+44) (0)1223 (3)37365 Fax: (+44) (0)1223 337563 Email: [email protected] Webpage: http://eloydeleraacedo.weebly.com <http://eloydeleraacedo.weebly.com/>
